The universe is vast. And even though

Transcription

1 Probing Einstein s universe and its physics Michael Kramer examines the enduring power of pulsars, 50 years after their discovery, in the 2016 George Darwin Lecture. The universe is vast. And even though we live on a tiny planet among billions of stars in a galaxy that is one of very many, we are curious enough to seek to understand its beginning and the fundamental laws that govern it. This is curiosity-driven research in its purest form and it is of fundamental importance. Einstein himself said that he had no special talent but that he was only passionately curious. This slight understatement mocks the fact that his theory of general relativity represents our best understanding of gravity by far. But whether it is also our last word, at least on macroscopic scales, remains to be seen. As a theory, general relativity (GR) is conceptually different from the description of the other fundamental forces, describing gravity by means of geometry of spacetime. The theory has passed all the tests that we (or Nature) put forward, with flying colours. But we should not be surprised if GR were to fail eventually, especially given that it is incompatible with quantum theory and that it predicts spacetime singularities under generic conditions, which signal its breakdown. But the real question is whether it will fail in regions of the parameter space that are accessible to our experiments or our observations. And, maybe, dark matter and dark energy are indeed indications that gravity is in fact something beyond GR. It is clear that we need to remain open and curious and that we should push our experiments into regions that we have not probed well so far: very strong 1 Author s illustration of a pulsar and black hole a binary system we have yet to find, although one may exist at the heart of the Milky Way. A pulsar emits a beam of radiation as it spins, which we can detect as a regular pulse if it is directed towards Earth. A pulsar black hole system would provide us with another test for whether general relativity holds up in extreme environments. (M Kramer) A&G June 2017 Vol. 58 aandg.org 3.31

2 gravitational fields and the highly relativistic dynamic regime of gravity. In other words, we need to probe the properties of gravitational waves and the properties of neutron stars and black holes. We are very fortunate to live in a time when we are able to do this right now! The direct detection of gravitational waves in 2015 is a flashing signpost that an era of unprecedented gravity tests has truly begun. And it will only get better! Among the recent exciting developments, there are still experiments with radio pulsars, those rotating lighthouses in space that provided the first evidence for the existence of gravitational waves. Testing gravity with pulsars This year we celebrate the 50th anniversary of the discovery of pulsars. Since that summer in Cambridge in 1967, pulsars have been used as tools in many different applications, from the study of super-dense matter to the magnetic fields structure of the Milky Way, or from the first detection of exoplanets to tests of gravity. Many, but not all, applications of pulsars rely on their clock-like stability in their rotation. Sending out a broadband, coherent and highly polarized beam of radio emission, we can count their rotations by measuring the arrival times of their pulses on Earth. This method of pulsar timing allows us to track pulsars in their orbit about possible companions as the pulse arrival times vary as a result of a reflex motion around the common centre of mass. In the best cases we can track the position of the pulsars in their orbit with positional accuracies of 30 metres or so (Lorimer & Kramer 2005). A pulsar s movement and the propagation of its radio pulses in the curved spacetime of binary systems can be compared to the predictions of different theories of gravity when the measured pulse arrival times reveal a number of relativistic effects. These effects can usually be described in a theoryindependent way, allowing us to determine the describing parameters, with which to confront the theoretical predictions. For eccentric orbits, the relativistic precession of the orbit of a binary pulsar is the first to be measurable. This precession is akin to the perihelion advance in Mercury s orbit, which Einstein was able to use in November 1915 as the first test of his new theory. Clocks suffer a decrease in their clock rate the deeper they are in a gravitational potential well. This effect is taken into account in satellite positioning systems such as GPS, GLONASS or GALILEO, where the uncorrected clock on the satellite runs faster than a clock in a GPS receiver on the Earth s surface. A clock on the top of the Eiffel Tower would run, in the course of one year, one microsecond faster than a clock at its bottom. Pulsar clocks are no different. 2 Parameter space of observations and tests of gravity. On the x-axis, v denotes the typical velocity of the system s components while Φ denotes the gravitational potential being probed by photons propagating in the corresponding spacetime. On the y-axis we have the maximum spacetime curvature (taken at the horizon for black holes) in the system as a measure of how much the system deviates from flat spacetime. Filled areas indicate gravitational wave tests, while hollow areas stand for quasi-stationary tests, including accretion onto compact objects. The rightmost hollow blue circle stands for the Shapiro delay test in the double pulsar. (Wex, priv. comm.) If a pulsar is in an eccentric binary orbit, the distance to its companion and hence the depth of the experienced gravitational potentials varies. As a result, the pulsar clock rate also changes over the course of the orbit, in addition to a relativistic change arising from the varying orbital speed. If the pulsar signal has to propagate through the curved spacetime of a massive companion, it will take slightly longer to travel to the observer than it would if spacetime were flat and the companion not present. The resulting Shapiro time delay provides access to both the mass of the companion as well as the inclination angle of the orbit relative to the observer on Earth. Depending on the configuration of the binary system, all of these effects can be measured routinely in binary pulsars today. They not only provide access to precision measurements of neutron star masses, as all of these effects depend on the mass of the pulsar and its companion, but they also enable strong-field tests of gravity. There is often confusion over whether pulsars really test the strong-field regime, because the two masses in a binary pulsar system are still separated by a few 10 5 Schwarzschild radii. It is indeed correct that the orbital speed of pulsars is still much less than the speed of light, and it is also correct that the orbital dynamics are not dominated by the emission of gravitational waves. However, with pulsars we test the gravitational inter action of strongly self-gravitating bodies, especially because gravitational strong self-field effects, predicted in many alternatives to GR, can also modify the orbital and rotational dynamics of pulsars in ways that can be tested with Since the Hulse Taylor pulsar, we have had indisputable evidence that GWs exist our observations. Hence, binary pulsars permit precise measurements of gravitational phenomena in a strong-field context (Will 2014). Also, after pulsar observations provided the first evidence for the existence of gravitational waves (GWs) 30 years ago, GW damping of the orbit is nowadays routinely measured for an increasing variety of systems. There is no question that pulsars test GW damping and the quasi-stationary strong-field regime of gravity theories. Furthermore, in case of the Shapiro delay, the pulsar signal passes the companion very close to its surface. In the best showcase, in the double pulsar PSR J A/B (figure 3), the signal passes the surface of the young neutron star B at only km distance, propagating through the strong gravitational field of the companion (Kramer & Wex 2009). Figure 2 illustrates the gravity regime probed by pulsar experiments and puts these experiments into context with other gravity tests. Pulsars and gravitational waves Since the discovery and timing of the Hulse Taylor pulsar PSR , we have had indisputable evidence that GWs exist. The first detection of them on Earth with Advanced LIGO, albeit from a pair of stellar black holes, appears almost as a logical consequence, but the road to this great achievement was long and deserves admiration and applause, in particular because it opens a completely new window onto the universe. It would be very appropriate if the Earth-bound GW detectors detect a neutron star neutron star merger in the year when we celebrate the 50th anniversary of detecting signals from neutron 3.32 A&G June 2017 Vol. 58 aandg.org

3 3 Artistic impression of the double pulsar system PSR J A/B. In this system two active radio pulsars orbit each other in just 147 min, providing a plethora of interesting astrophysical and relativistic effects. The fast-spinning 22 ms pulsar A was born first and later spun-up to its present period by mass transfer from the progenitor star to B. B formed in a low-kick supernova explosion that kept the system bound. B has a period of 2.8 s. The orbit shrinks every day by 7 mm due to the emission of gravitational waves. The geometry of the system is changing continuously due to periastron precession (17 per year) and relativistic spin precession of pulsar B. Due to the latter effect, since 2008 pulsar B s beam is temporarily missing Earth, but its rotation can still be further observed indirectly by eclipses. As the system is seen nearly completely edge-on (orbital inclination angle of 89 ), the extended magnetosphere of B blocks the light of A at superior conjunction. These 30 s long eclipses are not complete but are modulated by the spin of B as the magnetosphere is dipole-dominated and hence has a torus-like shape rather than being spherical. Additionally observed effects include a Shapiro delay of light propagating in the curved spacetime and gravitational redshift affecting the clock rate of both pulsars. stars for the first time. In 1967, it was found via radio waves, and in 2017 it could be via gravitational waves. The Hulse Taylor system was the first, but not the only binary pulsar where we can detect GWs; it is also no longer the best laboratory. What we observe in this and other systems is a shrinkage of the orbit, which is measurable as a cumulative shift in periastron time. With the system losing energy from the emission of GWs, the orbital period decreases and the pulsar reaches periastron, the closest approach to its companion in the case of elliptic orbits, earlier and earlier. In the case of the double pulsar, the orbit shrinks every day by 7 mm. The corresponding change in the orbital period can be measured with a precision of much better than 0.1%. The number measured agrees with GR and, in terms of precision, this is the best test of the GW quadrupole formula existing to date. The double pulsar is a unique system, where two active radio pulsars orbit each other in just 147 minutes. Pulsar A is a fast rotating, old 23 ms pulsar, while pulsar B is young with a period of 2.8 s. The system shows all of the aforementioned effects and is our best laboratory for strong-field tests with binary pulsars, allowing up to five independent gravity tests; GR passes them all comfortably (Kramer & Wex 2009). And even though the double pulsar provides the most precise test of GW damping, we need other systems to probe other aspects of GW emission. Unlike GR, alternative theories, such as those violating the strong equivalence principle, will, in addition to quadrupolar emission and higher multipoles, also emit The helium white dwarf orbits the most massive neutron star known! dipolar GWs because of an effective dipole from additional gravitational charges. In double neutron-star systems, with two (similar) neutron stars in the system, the mass dipole is naturally much smaller than for systems where the compactness of the binary components is sufficiently different. An ideal case to test for the emission of dipolar GWs would be a pulsar black hole system (Damour & Esposito- Farèse 1998). Until we find one, we can make good use of pulsar white dwarf systems. Pulsar white dwarf systems are much more common than double neutron-star systems, where the potential progenitor binary system usually gets disrupted in the supernova explosion forming the second-born neutron star. In a pulsar white dwarf system, the period of mass transfer in which matter is accreted on the first-born neutron star, spinning it up to few milliseconds period, is long and often leads to a wide, nearly circular system. In some cases, however, the orbit is compact and also shows relativistic effects as in the case of PSR J The orbital period of this system is only 15 s longer than that of the double pulsar, but it is also intriguing for another reason: the helium white dwarf of the system is in orbit around the most massive neutron star known! With a mass of about two solar masses, the very existence of this neutron star challenges most equations-of-state of super-dense matter. For tests of alternative theories of gravity, on the other hand, the combination of large mass and compact relativistic orbit delivers valuable constraints, e.g. on the coupling strength of a potential gravitational scalar field to matter, or on the existence of dipolar GW radiation. So far, once again, the observations are consistent with GR but exclude more and more parameter space for theories other than GR (Antoniadis et al. 2013). A galaxy-sized gravitational wave detector Pulsars are not just sources of GWs: there is a global effort to use them also as GW detectors. The basic idea is not very different from the concept of GW laser interferometers such as LIGO. There, a laser signal travelling in two orthogonal tubes is used to measure a small difference in arm lengths caused by a passing GW. In a so-called pulsar timing array (PTA) we can use the arrival time of pulsars observed at various parts of the sky to detect directiondependent variations, which manifest themselves as a correlated red-noise signal in the combined data set of many quasisimultaneously observed pulsars, in case of a stochastic GW background. This background may be a superposition of signals caused by the binary orbit of supermassive black hole binaries (SMBHB), as expected in the centre of two merging galaxies during the hierarchical growth of the galaxies in the cosmological past. The GW frequency range that a PTA is sensitive to depends on the cadence and length of the pulsar timing observations. The highest frequency detectable thereby is typically about 1 μhz, while data sets spanning tens of years extend the sensitivity down to about 1 nhz. There are competing noise processes, such as interstellar weather, that also affect the arrival times as radio signals are delayed due to dispersion in the ionized interstellar medium (ISM). Variations of the ISM along the line-of-sight cause frequencydependent noise that is uncorrelated with A&G June 2017 Vol. 58 aandg.org 3.33

4 variations in other pulsars. Clock errors, either in the observatory clock or even in terrestrial time standards, would be visible as noise common to all pulsars. In this way, one can deploy multi-frequency observations of an ensemble of pulsars to separate different red-noise contributions and search for the quadru polar emission features that would signify the detection of low-frequency GWs. There are three major PTA experiments: NANOGrav in North America, the Parkes Pulsar Timing Array in Australia, and the European Pulsar Timing Array (EPTA). The EPTA combines the collective power of all major radio telescopes in Europe, being an important programme for both the UK s Lovell Telescope at Jodrell Bank and the 100 m telescope in Effelsberg, Germany. Combined in the ERC-funded LEAP (Large European Array for Pulsars) mode, the telescopes form the equivalent of a powerful 200 m dish. All PTAs have very similar sensitivities, producing essentially identical limits on the amplitude of a stochastic GW background. This limit is already smaller than predicted from the theoretical understanding of the hierarchical galaxy formation process that was present when the PTA experiments began in earnest. Hence, even though a GW detection via PTAs has not been achieved yet, they already provide constraints on the astrophysics of the merger process. Continuous improvement in timing precision, going hand in hand with access to larger telescopes and ultimately with the Square Kilometre Array (SKA) operational and the combination of all available data in the so-called International Pulsar Timing Array (IPTA) will eventually lead to a direct detection of GWs using pulsars (Manchester 2013). It is entirely possible that a single SMBHB is strong enough to be eventually detected as a single continuous wave signal in the PTA data sets. If the distance of the PTA pulsars is known to within a GW wavelength, which may be possible with SKA astrometry, one can even use the impact of the GW on the pulsars, rather than on the Earth alone (as used so far), to utilize the phase information of the wave to essentially triangulate the direction of the source. This would enable a precise localization and hence electromagnetic follow-up of the source, while the retardation of the GW signal between pulsar and Earth would provide information about the source evolution (Lee et al. 2011). In this way, PTAs provide access to the nhz to μhz frequency range of the GW spectrum, thereby complementing the frequency coverage from μhz to mhz or larger with the future space-based LISA detector, and the high-frequency GWs probed by the Earth-bound detectors. 4 Gravitational wave spectrum and source population. Pulsar timing arrays (PTAs) cover the low-frequency part of the spectrum, complementing terrestrial and spacebased detectors. Relativistic spin effects So far, we have described the use of pulsars as clocks to test theories of gravity. But pulsars are also gyroscopes that, when orbiting in curved spacetime, suffer an effect known as geodetic precession or de Sitter precession, such that the spin vector points in a different direction from its starting point (relative to a distant observer) after a full orbit. Experimental verification of this effect has been achieved by precision tests in the solar system, i.e. by Lunar Laser Ranging (LLR) measurements or the Gravity Probe-B mission (Will 2014). In the case of pulsars, we can probe this effect with strongly self-gravitating objects. Here one loosely refers to this effect often as geodetic precession, but the observed effect is more general and should be better referred to as relativistic spin precession or simply relativistic spin orbit coupling. The consequence of this relativistic spin orbit coupling is a precession of the pulsar spin about the total angular moment vector. But since the orbital angular momentum is much larger than the spin of the pulsar, the orbital angular momentum practically coincides with the total angular momentum and represents a (nearly) fixed direction in space, perpendicular to the orbital plane of the binary system. Therefore, if the spin vector of the pulsar is misaligned with the orbital angular momentum, relativistic spin precession leads to a characteristic change in viewing geometry, as the pulsar spin precesses about the total angular momentum vector. Because many of the observed pulsar properties are determined by the relative orientation of the pulsar magnetic and spin axes towards the distant observer on Earth, i.e. especially by the way our line-of-sight cuts the extended emission beam, we expect a modulation in the measured pulse profile properties. This was predicted immediately after the discovery of the Hulse Taylor pulsar and binary supermassive black holes in galactic nuclei pulsar timing compact objects captured by supermassive black holes compact binaries in our galaxy and beyond years hours sec ms merging NS and BH, rotating NS, supernovae log(hz) We will have to wait some years for B s beam to move back into our line of sight space interferometers terrestrial interferometers indeed later detected (Damour & Ruffini 1974, Kramer 1998). As with the other relativistic effects described above, relativistic spin precession is nowadays routinely observed in suitable binary pulsars. The changing cuts through the extended cone-like emission beam as the pulsar spin axis precesses mean that we observe the pulse shape narrow or widen, depending on the precession phase and beam structure. In the best cases, careful studies of the polarization properties of the coherent radio beam allow us to infer the complete viewing geometry, enabling determination of the precession rate of the pulsar spin axis and hence a further test of gravity. While this is the method used for all suitable pulsars, the double pulsar is also a special case for this test. In the double pulsar, we observe spin precession only for the second-born pulsar B. Here the supernova explosion led to a post-natal spin orientation that is not aligned with the orbital angular momentum vector. Studying the orientation of the spin direction of pulsars in double neutron star systems via spin precession can therefore provide information about the still not very well understood processes that occur when a neutron star is formed in the collapsing core of an exploding star. For instance, the spin of pulsar A, in contrast to B, is aligned with the orbital angular momentum, and hence spin precession is not observed. We can expect that prior to the explosion all spins in the systems (i.e. the pulsar spin, the companion spin and orbital spin vector) were aligned as a result of tidal interaction during the mass accretion process. When the progenitor to B exploded, it led to the misalignment of B s spin vector, while A s spin was not affected and still pointed in the pre-supernova direction. Pulsar A will therefore continue to be visible to us before it eventually merges in 86 million years. In contrast, the 3.34 A&G June 2017 Vol. 58 aandg.org

5 spin axis of B precesses and as a result there are times when B s beam does not shine towards Earth, before the pulsar becomes visible again. Indeed, in 2008 the beam of B started to miss Earth; only A is currently observable. We will have to wait some years for B s beam to move back into our line of sight. How long this takes depends on the geometry, the width and structure of the radio beam. With a precession period of 71 years, it may take a while, in principle, but our current knowledge suggests that B may have disappeared for only years (Kramer & Wex 2009). It happens that the orbit of the double pulsar is seen edge-on, with the orbital inclination angle measured via the Shapiro delay to be very close to 89. The result is an eclipse of the radiation of pulsar A, which lasts for about 30 s, at each superior conjunction. During the eclipse the extended plasma-filled magnetosphere of B blocks the radio light of A as a result of synchrotron self-absorption. But the eclipse is not complete. As B s magnetosphere is not a sphere, but doughnutshaped, the background light from A can pass B at certain spin phases of B. The phases, when this is possible, depend on the orientation of B s spin vector, which in turn precesses in space. The result is a secular evolution of the eclipse pattern, which describes the particular rotation phases of B when A is visible and when not. Consequently, using a straightforward but completely geometric model, the precession rate of B can be measured quantitatively. It is found to agree with GR within the 13% precision of the measurement. The observation of relativistic spin precession is useful not only for testing GR or other theories of gravity, but also it can help as a tool to probe other branches of physics. For example, it is interesting that the changing line-of-sight relative to the spin and magnetic axes also means a changing slice through the emission beam of the pulsar. So, with time, we are building up a tomogram that reveals the two-dimensional structure of the pulsar beam. This is possible for a few examples already, and it allows us to better understand the extreme plasma processes within these highly magnetized magnetospheres. A second example relates again to pulsars being extremely compact objects that probe the physics of superdense matter. Relativistic spin orbit coupling also causes a small shift in the measured value of the periastron precession discussed earlier (Lense Thirring precession of the orbit). The magnitude of the effect depends on the geometry of the vectors involved, but scales also on the moment of inertia of It is possible to measure the black hole spin by its impact on the pulsar orbit the neutron star. In the double pulsar, the experimental precession and the magnitude of the effect is so large that we can expect to measure this eventually for pulsar A. One long-term goal of the continued timing of the double pulsar with the Lovell Telescope, the 100 m Effelsberg telescope and others, is therefore the first measurement of the moment of inertia, which encodes extremely valuable information of the equation of state of ultra-dense matter. Probing black holes Since the discovery of the first binary pulsar, astronomers have been eager to find the first pulsar black hole system. Indeed, in many respects such a system would be the ideal pulsar laboratory to test theories of gravity. One could use the orbiting pulsar as a test mass that probes the black hole spacetime in very much the same way as is done around neutron stars or white dwarfs in other binary systems. Apart from testing GR and alternative theories of gravity in general, for instance by searching for signatures of dipolar GWs in such extreme systems, the ultimate goal would be to use the pulsar for a determination of the spin and quadrupole moment of the black hole. The spin of a black hole is related to its event horizon, which is the boundary in spacetime beyond which events cannot affect an outside observer. In GR, the spin must not exceed a maximum value, otherwise the central spacetime singularity would be visible from the outside world. This is the core of the cosmic censorship conjecture, which postulates that astrophysical black holes, which are all believed to spin, must have an event horizon and hence a spin smaller than this value. At the same time, spinning astrophysical black holes are oblate, characterized by a non-zero quadrupole moment. However, black holes are also expected to be the result of gravitational collapse, during which all properties of the progenitor are radiated away by gravitational radiation. The resulting black holes are therefore expected to be simple, characterized solely by their mass and spin (note that in astrophysical situations, black holes are believed to be practically free of any net electrical charge, which would otherwise be a third characterizing parameter). In other words, according to this no-hair theorem, all other black hole properties, including the quadrupole moment, should be functions of the mass and the spin only. Thereby, by measuring all three quantities, using a pulsar orbiting a black hole, both the cosmic censorship conjecture and the no-hair theorem could be tested quantitatively. Indeed, it is in principle possible to measure the black hole spin by its impact on the pulsar orbit via the dragging of inertial frames caused by the rotation of the black hole, leading to a Lense Thirring precession of the orbital plane. This would cause characteristic variations in the observed pulse arrival times, from which the spin parameters could be extracted. Similarly, the oblateness of the black hole, expressed by its quadrupole moment, also causes characteristic variations in the pulse arrival times, in particular when the pulsar is closest to the black hole. Again, in principle, the corresponding parameter can be extracted from timing observations (Psaltis et al. 2016). However, these measurements will be extremely difficult for stellar-mass black holes, even with the SKA. Things become much easier if the black hole is supermassive, because the amplitudes of the spin and quadrupole effect increase with the square and cube of the black hole mass, respectively. Where do we find a pulsar around a supermassive black hole? The answer lies at the centre of the Milky Way. Near-infrared observations of the socalled S-stars in the galactic centre have shown that they orbit an unseen central object with a mass of about 4.3 million solar masses. The location of this central mass is coincident with that of a bright and prominent radio point source, Sgr A*. It is therefore generally accepted that Sgr A* emission comes from a central super massive black hole, where inspiralling matter feeds the accreting black hole gently with matter, producing the observed radio emission from the accretion disc. We have shown that a slow, normal pulsar in an appropriate orbit would, in principle, be sufficient to measure the mass of Sgr A* with a precision of a few solar masses (i.e. with a precision of a few parts in a million). In an ideal situation, the black hole spin would also be measured and allow us to test the cosmic censorship conjecture to a precision of about 0.1%. Observations of the pulsar near periapsis would reveal the quadruple moment and allow tests of the no-hair theorem to a precision of 1%. But even in a less favourable situation with perturbations by an external mass distribution, one can still expect to perform such tests with good precision (Psaltis et al. 2016). Given the huge rewards for finding and timing pulsars in the galactic centre, various surveys have been conducted in the last 30 years. None of these efforts has been successful in finding pulsars in the galactic centre, despite the expectation of finding more than 1000, including fast-spinning milli second pulsars or even highly eccentric stellar-mass black hole millisecond pulsar systems. The lack of detection was at first understood in terms of severe inter stellar A&G June 2017 Vol. 58 aandg.org 3.35

6 5 Simulation of experimental constraints expected from the shape of the black hole shadow to be measured in the EHT observations of Sgr A* (orange), the orbits of two stars (green), and timing of three periapsis passages of a lowprecision pulsar (red). The solid curve (blue) shows the expected relation between the spin and quadrupole moment for the Kerr metric. The filled circle marks an assumed spin and quadrupole moment (χ = 0.6, q = 0.36). Combining these three independent types of measurements, which each suffer from different biases and potential systematic uncertainties, will significantly increase our confidence in the inference of these two black hole properties and in the test of the no-hair theorem (after Psaltis et al. 2016). scattering arising from the highly turbulent interstellar medium in the galactic centre region. Scattering is the result of multipath propagation and leads to pulse broadening that cannot be removed by instrumental means and renders the source undetectable as a pulsar, in particular if the scattering timescale exceeds a pulse period. The scattering time, however, decreases as a strong function of frequency, so that these pulsar searches were conducted at ever increasing frequencies the latest at around 20 GHz. The difficulty in finding pulsars at these frequencies arises mainly from a much-reduced flux density of pulsars thanks to their typically steep spectra. This situation changed in 2013 when, triggered by a detection of a periodic X-ray source by SWIFT and NuStar, we discovered a 3.8 s radio magnetar using the 100 m Effelsberg radio telescope, and found that it was only 2ʺ away from Sgr A* (Eatough et al. 2013). To find a magnetar, now called PSR J , was very surprising. Magnetars are highly magnetized neutron stars, and are usually only seen via their high-energy emission. Prior to the discovery of the galactic centre magnetar, only three of them had been detected at radio wavelengths. The fact that a rare Efforts to find a pulsar around Sgr A* will continue with new methods object like a radio-emitting magnetar may be found in such proximity to Sgr A* suggests that many more ordinary pulsars exist there. However, the magnetar also showed a scattering of emission that was far less than expected for the galactic centre region, begging the question of why we haven t detected many pulsars. Solving this question is at the focus of current research, and subject of ongoing searches and continued studies of the magnetar and the galactic centre. Pulsars and an image of Sgr A* An international effort is underway to perform a mm-vlbi experiment known as the Event Horizon Telescope (EHT) with the aim of imaging the shadow of Sgr A* against the background radiation from the hot accretion disc. With its mass of about 4 million solar masses, the central black hole is not very large compared to those in the centre of other galaxies, but it is the closest, and therefore the largest in terms of angular size. The idea is that the precise measurement of the shadow will also lead to an extraction of the black hole parameters, assuming the shadow is determined purely by gravitational effects and that the modelling does not depend on understanding the accretion flow properties. A partner in the EHT experiment is the BlackHoleCam project, which is funded by an ERC Synergy Grant of the European Research Council to Heino Falcke (Nijmegen), Luciano Rezzolla (Frankfurt) and me. Besides being part of the global EHT efforts, which involve ALMA or the IRAM telescopes in Spain and France, our BlackHoleCam project aims specifically to combine the information that can be extracted from the image with those that can be obtained from successful pulsar searching and timing information. One can indeed show (Psaltis et al. 2016) that the correlated uncertainties in the measurements of the black hole spin and quadrupole moment using pulsars are nearly orthogonal to those obtained from measuring the shape and size of the black hole shadow. Combining the different types of observations allows one, therefore, to assess and quantify systematic biases and uncertainties in each measurement, which will finally lead to a highly accurate, quantitative test of the no-hair theorem (see figure 5). This is possible because the image and the pulsar measurements probe simultaneously the near- and far-field of Sgr A*, promising a unique probe of gravity. The BlackHoleCam team, together with our EHT colleagues, is looking forward to the first imaging observing run later this year. At the same time, our efforts to find a suitable pulsar orbiting Sgr A* will continue with new methods and improved instrumentation. The future is bright and exciting More than a hundred years after Einstein formulated general relativity, we have tools and experiments at our disposal that use methods, objects and instruments unknown to him. Whether it is radio telescopes or gravitational wave detectors, radio pulsars, the image of a supermassive black hole or the gravitational wave signature of merging stellar-mass black holes, all of these experiments test a theory that has so far survived all its challenges. The predictive power of Einstein s theory is irreproachable and only because Einstein was simply curious. We should follow in his steps, standing on the shoulders of giants. Let s continue to be curious! AUTHOR Michael Kramer, Max-Planck-Institute für Radioastronomie, Germany and Jodrell Bank Centre for Astrophysics, University of Manchester, UK. GEORGE DARWIN LECTURE The RAS George Darwin Lecture is given annually by a distinguished and eloquent speaker on a suitable topic in astronomy. Prof. Kramer delivered his lecture at the RAS meeting of 9 December ACKNOWLEDGMENTs This work is supported by the ERC Advanced Grant LEAP: Large European Array for Pulsars (Grant ) and ERC Synergy Grant BlackHoleCam: Imaging the Event Horizon of Black Holes (Grant ). references Antoniadis J et al Science Damour T & Esposito-Farèse G 1998 Phys. Rev. D Damour T & Ruffini R 1974 Acad. Sci. Paris Comptes Rendus A Eatough R et al Nature Kramer M 1998 Astrophys. J Kramer M & Wex N 2009 Class. Quantum Grav Lee K J et al Mon. Not. Roy. Astron. Soc Lorimer D R & Kramer M 2005 Handbook of Pulsar Astronomy (Cambridge University Press) Manchester R N 2013 Class. Quantum Grav Psaltis D et al Astrophys. J Will C M 2014 Living Reviews in Relativity A&G June 2017 Vol. 58 aandg.org