Planck stars (exploding black holes): A possibly observable quantum gravitational phenomenon

Transcription

1 Planck stars (exploding black holes): A possibly observable quantum gravitational phenomenon Carlo Rovelli

2 Planck stars (exploding black holes): A possibly observable quantum gravitational phenomenon Carlo Rovelli i. Why black holes can explode Because quantum tunnelling allow them to explode ii. How long does it take a black hole to explode? Perhaps T~m 2. T can be computed in Loop Quantum Gravity. iii. Can we observe a black hole explosion? Yes. We might even have already observed explosions of primordial holes. We can soon find out.

3 The Universe appears to be full of gravitationally collapsed objects ( Black holes ) What is their lifetime T? Classical GR: T = (Event horizon) QFT on a classical dynamical geometry: T ~ m 3 (Hawking radiation) Full Quantum Gravity: T ~ m 2 (Black to white hole tunnelling) For m ~10 24 (Venus), m 2 ~10 50 Hubble times, while m 3 ~Hubble time

4 In (the approximation given by) classical general relativity, a black hole is stable. In quantum field theory on a classical gravitational field, a black hole decays via Hawking radiation, in an extremely long time. (10 50 Hubble times, for a stellar bh.) A brief (very incomplete) In quantum gravity, a black hole can decay via a non perturbative quantum tunnelling. I I

5 What happens here?

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7 We expect quantum effects when some physical quantity becomes ~ 1 in Planck units. - R ~ 1 around singularities - RT ~ 1 RT ~ m/r 3 T = T/m 2 ~ 1 T ~ m 2

8 What happens here?

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10 Exploding holes At MG2 and in a paper 79-8 rd in 06 Frolov, Vilkovinski 79 Stephen, t Hooft, Whithing 93 Ashtekar, Bojowald 05 Modesto 06 Hayward region 3 Haggard, Rovelli 15

11 A technical result in classical GR: I The following metric is an exact vacuum solution, of the Einstein equations outside a finite spacetime region (grey), plus an ingoing and outgoing null shell, III II ds 2 = F (u, v)dudv + r 2 (u, v)(d 2 + sin 2 d 2 ) I Region I Region II Matching: Region III F (u I,v I )=1, r I (u I,v I )= v I u I. 2 v I < 0. F (u, v) = 32m3 r r I (u I,v I )=r(u, v) e r 2m F (u q,v q )= 32m3 r q 1 r e r 2m 2m = uv. u(u I )= 1 1+ u I e u I 4m. v o 4m e rq 2m, rq = v q u q. The metric is determined by two constants:

12 Minkowski region I Outgoing (null) shell Quantum region III II Past trapped horizon White hole Schwarzschild region I Conventional black hole Future trapped horizon Incoming (null) shell Minkowski region

13 I I The Fingers Crossed

14 The external metric is determined by two constants: - m is the mass of the collapsing shell. - is the external bounce time:

15 Time dilation R =2R m ln( /m) T: bounce time (very large) internal m 1ms external m years A black hole is a short cut to the future

16 What determines T? Quantum gravity

17 Covariant loop quantum gravity. Full definition. n 0 Kinematics Boundary State space Operators: H = L 2 [SU(2) L /SU(2) N ] where 3 (h l ) H = lim!1 H h l l n spin network (nodes, links) Dynamics Bulk Transition amplitudes Vertex amplitude W C (h l )=N C Z A(h vf )= Z Y dh vf SU(2) f Y X dge 0 SL(2,C) f j (h f ) Y v A(h vf ) (2j + 1) D j mn(h vf )D (j+1) j jmjn (g e g 1 e 0 ) h f = Y v h vf v e C f spinfoam (vertices, edges, faces) W = lim C!1 W C 8 ~G =1

18 A process and its amplitude h l Boundary state Boundary state Amplitude = in out A = W ( ) Spacetime region Boundary Quantum system = Spacetime region Hamilton function: S(q,t,q,t ) In GR, distance and time measurements are field measurements like any other one: they are part of the boundary data of the problem Boundary values of the gravitational field = geometry of box surface = distance and time separation of measurements Particle detectors = field measurements Spacetime region Distance and time measurements = gravitational field measurements

19 Covariant loop quantum gravity. Calculation of T(m). j, -k j, k Boundary: B3 U B3 (Joined on a S2) Each B3 can be triangulated by 4 isosceles tetrahedra. The bulk cal be approximated to first order by two 4-simplices joined by a tetrahedron

20 Choose a Boundary surface around the quantum region.

21 Full expression for T(m):

22 2 T m

23 Primordial Black Holes What? Primordial matter density fluctuations When? Early universe (typically reheating) Why? Density contrast δ 0.45 How? Large possible spectrum of PBH M M H t. t 0.3g 1 2 T 2,

24 Primordial black holes!

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26 Primordial Black Hole Explosion exploding now: r th m m(t) = t=th 4k kg R = 2Gm c 2.02 cm { LOW ENERGY: size of the source wavelength predicted &.02 cm HIGH ENERGY: energy of the particle liberated Tev fast process ( few milliseconds? ) the source disappears with the burst very compact object: big flux E = mc erg

27 Signature: distance/energy relation v " u 1/2 1 u 2Gm H0 1 t (1 + z) sinh (z + 1) obs 2 1/2 c M 6 k 3/2 # l A real-time FRB 5 Figure 2. The full-stokes parameters of FRB recorded in the centre beam of the multibeam receiver with BPSR. Total intensity, and Stokes Q, U, and V are represented in black, red, green, and blue, respectively. FRB has 21 ± 7% (3- ) circular polarisation averaged over the pulse, and a 1- upper limit on linear polarisation of L < 10%. On the leading edge of the pulse the circular polarisation is 42 ± 9% (5- ) of the total intensity. The data have been smoothed from an initial sampling of 64 µs using a Gaussian filter of full-width half-maximum 90 µs. source given the temporal proximity of the GMRT observation and the FRB detection. The other two sources, GMRT2 and GMRT3, correlated well with positions for known radio sources in the NVSS catalog with consistent flux densities. Subsequent observations were taken through the GMRT ToO queue on 20 May, 3 June, and 8 June in the 325 MHz, 1390 MHz, and 610 MHz bands, respectively. The second epoch was largely unusable due to technical difficulties. The search for variablility focused on monitoring each source for flux variations across observing epochs. All sources from the first epoch appeared in the third and fourth epochs with no measureable change in flux densities Gamma-Ray Burst Optical/Near-Infrared Detector After 13 hours, a trigger was sent to the Gamma-Ray Burst Optical/Near-Infrared Detector (GROND) operating on the 2.2-m MPI/ESO telescope on La Silla in Chile (Greiner et al. 2008). GROND is able to observe simultaneously in J, H, and K near-infrared (NIR) bands with a field of view (FOV) and the optical g 0, r0, i0, and z 0 bands with a FOV. A 2 2 tiling observation was done, providing 61% (JHK) and 22% (g 0 r0 i0 z 0 ) coverage of the inner part of the FRB error circle. The first epoch began 16 hours after FRB with 460 second exposures, and a second epoch was taken 2.5 days after the FRB with an identical observing setup and 690 s (g 0 r0 i0 z 0 ) and 720 s (JHK) exposures, respectively. Limiting magnitudes for J, H, and K bands were 21.1, 20.4, and 18.4 in the first epoch and 21.1, 20.5, and 18.6 in the second epoch, respectively (all in the AB system). Of all the objects in the field, analysis identified three variable objects, all very close to the limiting magnitude and varying on scales of mag in the NIR bands identified with di erence imaging. Of the three objects one is a galaxy, another is likely to be an AGN, and the last is a main sequence star. Both XRT1 and GMRT1 sources were also detected in the GROND infrared imaging but were not observed to vary in the infrared bands on the timescales probed. Swift X-Ray Telescope The first observation of the FRB field was taken using Swift XRT (Gehrels et al. 2004) only 8.5 hours after the FRB was discovered at Parkes. This was the fastest Swift follow-up ever undertaken for an FRB. 4 ks of XRT data were taken in the first epoch, and a further 2 ks of data were taken in a second epoch later that day, 23 hours after FRB , to search for short term variability. A final epoch, 18 days later, was taken to search for long term variability. Two X-ray sources were identified in the first epoch of data within the 150 diameter of the Parkes beam. Both sources were consistent with sources in the USNO catalog (Monet et al. 2003). The first source (XRT1) is located at RA = 22:34:41.49, Dec = -12:21:39.8 with RUSNO = 17.5 and the second (XRT2) is located at RA = 22:34:02.33 Dec = -12:08:48.2 with RUSNO = Both XRT1 and XRT2 appeared in all subsequent epochs with no observable variability on the level of 10% and 20% for XRT1 and XRT2, respectively, both calculated from photon counts from the XRT. Both sources were later found to be active galactic nuclei (AGN). 4.6 Swope Telescope An optical image of the FRB field was taken 16h51m after the burst event with the 1-m Swope Telescope at Las Campanas. The field was re-imaged with the Swope Telescope on 17 May, 2 days after the FRB. No variable optical sources c 0000 RAS, MNRAS 000, A real-time FRB 5 2 Figure 2. The full-stokes parameters of FRB recorded in the centre beam of the multibeam receiver with BPSR. Total intensity, and Stokes Q, U, and V are represented in black, red, green, and blue, respectively. FRB has 21 ± 7% (3- ) circular polarisation averaged over the pulse, and a 1- upper limit on linear polarisation of L < 10%. On the leading edge of the pulse the circular polarisation is 42 ± 9% (5- ) of the total intensity. The data have been smoothed from an initial sampling of 64 µs using a Gaussian filter of full-width half-maximum 90 µs. source given the temporal proximity of the GMRT observation and the FRB detection. The other two sources, GMRT2 and GMRT3, correlated well with positions for known radio sources in the NVSS catalog with consistent flux densities. Subsequent observations were taken through the GMRT ToO queue on 20 May, 3 June, and 8 June in the 325 MHz, 1390 MHz, and 610 MHz bands, respectively. The second epoch was largely unusable due to technical difficulties. The search for variablility focused on monitoring each source for flux variations across observing epochs. All sources from the first epoch appeared in the third and fourth epochs with no measureable change in flux densities. 4.4 Swift X-Ray Telescope The first observation of the FRB field was taken using Swift XRT (Gehrels et al. 2004) only 8.5 hours after the FRB was discovered at Parkes. This was the fastest Swift follow-up ever undertaken for an FRB. 4 ks of XRT data were taken in the first epoch, and a further 2 ks of data were taken in a second epoch later that day, 23 hours af- 4.5 Gamma-Ray Burst Optical/Near-Infrared Detector After 13 hours, a trigger was sent to the Gamma-Ray Burst Optical/Near-Infrared Detector (GROND) operating on the 2.2-m MPI/ESO telescope on La Silla in Chile (Greiner et al. 2008). GROND is able to observe simultaneously in J, H, and K near-infrared (NIR) bands with a field of view (FOV) and the optical g 0, r0, i0, and z 0 bands with a FOV. A 2 2 tiling observation was done, providing 61% (JHK) and 22% (g 0 r0 i0 z 0 ) coverage of the inner part of the FRB error circle. The first epoch began 16 hours after FRB with 460 second exposures, and a second epoch was taken 2.5 days after the FRB with an identical observing setup and 690 s (g 0 r0 i0 z 0 ) and 720 s (JHK) exposures, respectively. Limiting magnitudes for J, H, and K bands were 21.1, 20.4, and 18.4 in the first epoch and 21.1, 20.5, and 18.6 in the second epoch, respectively (all in the AB system). Of all the objects in the field, analysis identified three variable objects, all very close to the limiting magnitude and varying on scales of mag in the NIR bands identified with di erence imaging. Of the three ob z

28 Integrated emission m 3 Low energy channel High energy channel k=10 22 direct decayed k=10 22 direct+decayed enlarged dn mes dedtds = Z ind((1+z)e,r) n(r) ) Acc Abs(E,R)dR, characteristic shape: distorted black body depends on how much DM are PBL

29 Short Gamma Ray Burst the white hole should eject particles at the same temperature as the particles that felt in the black hole limited horizon due to absorption 100 million light-years / z=0.01 known GRB have energy Tev telescopes spanning large surfaces needed (CTA?) obs / (1 + z) sinh 1 " M 1 #! (z + 1) 2

30 Fast Radio Burst Unknown source! Short Observed width milliseconds Thornton et al Spitler et al E. Petroff et al No Long GRB associated No Afterglow Punctual No repetition Enormous flux density Energy erg Likely Extragalactic Dispersion Measure: z event/day A pretty common object? Circular polarization Intrinsic

31 Fast Radio Burst Short λ 20 cm Observed width milliseconds size of the source fast process predicted &.02 cm No Long GRB associated No Afterglow Punctual No repetition Enormous flux density Energy erg Likely Extragalactic Dispersion Measure: z event/day A pretty common object? Very short GRB? gravitational waves? the source disappears with the burst very compact object erg peculiar distance/energy relation Are they bouncing Black Holes? Circular polarization Intrinsic

32 4 Detectable? Already detected? For T~m3 primordial black hole give signals in the cosmic ray spectrum For T~m2 primordial black hole give signals in the radio: Fast Radio Bursts? Fast Radio Bursts Duration: ~ milliseconds Frequency: 1.3 GHz Figure 2. Characteristic plots of FRB data were smoothed in time and frequency by a f Observed at: Parkes, Arecibo respectively. The top panel is a dynamic spect Origin: Likely extragalactic ery observation showing the 0.7 s during which F Estimated emitted power: 1038 erg across the frequency band. The signal is seen cantly dimmer towards the lower part of the ba Physical source: unknown. facts due to RFI are also visible. The two white c pected sweep for a ν 2 dispersed signal at a DM The lower left panel shows the dedispersed pul across the bandpass. The lower right panel com spectrum (black) with an off-pulse spectrum (li

33 Summary - Technical results: black holes may tunnel to white holes locally and explode. - The tunnelling time can be computed with LQG. - T~m 2: Fast Radio Bursts and high energy Gamma phenomenology: first quantum gravity signals? l - Wavelength-to-distance relation signature z

34 Main papers Planck Stars Classical metric Planck stars Carlo Rovelli, Francesca Vidotto Int. J. Mod. Phys. D23 (2014) 12, Black hole fireworks: quantum-gravity effects outside the horizon spark black to white hole tunneling Hal Haggard, Carlo Rovelli Phys. Rev. D Improved Black Hole Fireworks: Asymmetric Black-Hole-to-White-Hole Tunneling Scenario Tommaso De Lorenzo, Alejandro Perez arxiv: Phenomenology Planck star phenomenology Aurelien Barrau, Carlo Rovelli. Phys. Lett. B739 (2014) 405 Phenomenology of bouncing black holes in quantum gravity: a closer look Aurélien Barrau, Boris Bolliet, Francesca Vidotto, Celine Weimer JCAP 1602 (2016) no.02, 022 Fast Radio Bursts Fast Radio Bursts and White Hole Signals Aurélien Barrau, Carlo Rovelli, Francesca Vidotto. Phys. Rev. D90 (2014) 12, LQG lifetime calculation Computing a Realistic Observable in Background-Free Quantum Gravity: Planck-Star Tunnelling-Time from Loop Gravity Marios Chistodoulou, Carlo Rovelli, Simone Speziale, Ilya Vilensky. ArXiv: