Relativity and Black Holes
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1 Relativity and Black Holes Post-MS Evolution of Very High Mass (>15 M Θ ) Stars similar to high mass except more rapid lives end in Type II supernova explosions main difference: mass of iron core at end of fusion > 3 M Θ core is too massive to form a neutron star! must collapse into something even denser a black hole! Escape Velocity, v e Measure of gravitational strength Minimum speed to escape the gravity of an object e.g. Earth, v e = 11.2 km/s v e mass v e size v e highest for objects which are small and massive i.e. dense! Neutron Stars, v e = 0.5c A neutron star only has to become 25% smaller in order to make v e = c Such an object is so dense that not even light can escape! Such an object is called a black hole! Problem: if light has no mass, how can it be affected by gravity? Newton s Theory of gravity has no explanation for this! To understand the properties of black holes we need a new theory of gravity! Einstein s Relativity! 1
2 Relative Motion Since everything in the Universe is in motion, measurements can only be made relatively and not absolutely! The Principles of Relativity 1. The Laws of Physics are the same for everyone and are independent of our location or motion in the Universe 2. The speed of light, c is constant and is the same for everyone and independent of our location or motion in the Universe Everything else is relative! Person Running Towards a Ball Person Traveling Towards Photon A photon always travels towards an observer at the speed of light, c regardless of their motion! Special Theory of Relativity (1905) Only deals with motion in straight lines and at constant speeds Is not a theory of gravity! 2
3 Lorentz Contraction Relativistic Effects Strange things effects are observed when objects are seen traveling close to the speed of light: Mass increases! Length decreases along the direction of motion! (Lorentz Contraction) The rate of passage of time slows down! (Time Dilation) Why can t we travel at or faster than the speed of light? A object observed to be traveling at the speed of light would be seen to have An infinite mass! A zero length! A rate of passage of time of zero = time stops! It is impossible to observe these things so it must be impossible to travel at or faster than c! The Equivalence Principle General Theory of Relativity (1915) Includes effects of accelerated motion which is the type of motion produced by gravity Is a theory of gravity! The effects of gravity and acceleration are identical 3
4 Newtonian Gravity: 3 dimension of space + 1 dimension of time Conclusion: strong gravitational fields produce the same relativistic effects seen for rapid motion e.g. time dilation! Einstein s Gravity: 4 dimensions of space-time Space-time is a 4-dimensional surface or hyperspace which is impossible to comprehend directly but can be thought of as representing the fabric of the Universe A 2D Analogy of 4D Spacetime Explains: The action of gravity across distance The shapes of planetary orbits they follow the curvature of spacetime around the Sun! Prediction: masses curve the fabric of spacetime around them e.g. a person on a trampoline Gravitational Bending of Light Experimental Confirmation of General Relativity Light follows the curvature of spacetime around a massive object! 4
5 Precession of the Orbit of Mercury Gravitational Time Dilation weaker gravity stronger gravity time slows Mercury s orbit is not stationary in space due to curvature of spacetime around the Sun Gravitational Redshift Gravitational Waves Ripples in spacetime caused by the acceleration of masses e.g. core collapse of massive a star light loses energy as it escapes from a source of gravity result: longer wavelengths Only prediction of General Relativity not measured Laser Interferometer Gravitational-Wave Observatory (LIGO) How it works! 5
6 The Formation of a Black Hole Each interferometer arm is 4 km long! Two observatories separated by 2000 miles! Able to confirm detections! A Black Hole is Highly Curved Spacetime The Structure of a Black Hole Schwartzschild Radius, R sh R sh = 3M km where: M = mass of black hole is solar masses Example: a 4 M Θ black hole has a radius of 3 x 4 = 12 km Common Misconception: Black holes gobble up all matter for 1000 s of light years around them! Not so! Spacetime highly curved close to hole but not far from it! Example: replace Sun with solar mass black hole planetary orbits would not change! 6
7 You can only be pulled into a black hole if you are very close to it! Properties of Singularities definition: non zero mass occupies zero volume a point of infinite density and gravity fabric of spacetime breaks a passage to parallel Universe? problem: laws of physics (even relativity) break down! have no way of predicting properties! Minimum stable orbit = 3R sh Problem: If singularities are places where the laws of physics do not apply, do black holes contradict the principle of relativity that the laws of physics are the same everywhere? Law of Cosmic Censorship Singularities are always surrounded by event horizons Blocks us from observing the unpredictable properties of singularities Black holes do not contradict relativity! Are any properties of black holes measurable? Yes! But only those properties that can be measured without electromagnetic radiation! 7
8 No Hair Theorem Only 3 properties can be measured for a black hole: mass charge rotation Mass Place a test probe of mass, M p in orbit around a black hole at a (safe!) chosen distance, a Measuring the orbital period, P of the probe will allow the mass of the black hole, M bh to be determined: P 2 = a 3 /(M bh + M p ) Charge A charged particle will be attracted or repelled by a black hole if it is charged! e - What is the charge of the hole? Negative! Rotation Frame dragging: close to a rotating black hole spacetime is dragged around Impossible to be still! Place probe in ergoregion to determine rotation! 8
9 Isolated black holes will distort the light from background objects Detecting Black Holes Isolated black holes very difficult to detect! Easier to detect black holes by the effect they have on neighboring matter e.g. a star Gravitational Microlensing Cygnus X-1 A very strong X-ray source in Cygnus the Swan General Relativity predicts that a black hole should magnify the light from a background star as it passes in front on it due to the distortion of space-time around it At the location of the X-ray source is a B0 I star Is this the source of the X-rays? A B0 star has T = 25,000 K Wien s Law T = 25,000 K λ max = UV The star is not hot enough to produce the X-rays! 9
10 Does the star have a companion? Spectrum? Single set of lines from B0 I star Lines are Doppler shifted back and forth with P = 5.6 days! A single-lined spectroscopic binary Conclusion: the companion must be dark and close Analyze orbit to obtain masses Mass B0 I star = 30 M Θ Mass companion = 3-7 M Θ Properties of Companion Emits little visible radiation Massive What could it be? A black hole! Cygnus X-1 is a Mass Transfer Binary Where do the X-rays come from? The X-rays come from the accretion disk of gas spiralling into the hole 10
11 Still some doubt due to uncertain mass of companion! If mass companion = 3 M Θ then could be a neutron star! Better examples of black hole candidates that cannot be neutron stars: V404 Cygni Mass companion > 6.26 M Θ A in Monoceros Mass companion > 3.2 M Θ IC 10 X-1 in the nearby galaxy IC 10 Mass companion M Θ Most massive known stellar mass black hole as of Fall 2007 Thought Experiment Release a probe and let it fall into a black hole from a safe distance! Equipment: a blue flashing light so you can follow its path a video camera to transmit back images Video Camera Images Results? 11
12 Gravitational Time Dilation Initially the probe will accelerate towards the hole However, as it approaches the event horizon it will appear to slow down due to the strong gravity! It will only reach the event horizon after an infinite amount of time where it will appear to be frozen in space! Gravitational Redshift As the probe approaches the event horizon the light from the probe is gravitationally redshifted from blue to green to yellow to red and will eventually become invisible as it shifts into non-visible wavelengths! It would disappear from view long before it reaches the event horizon! Tidal Forces Eventually the probe will break into pieces! As the probe approaches the hole, tidal forces will distort the shape of the probe! Wormholes A shortcut (tunnel) through hyperspace between two distant parts of the Universe allowing very rapid travel! Interstellar Travel Through Wormholes Big problem: we don t yet know how to create wormholes, and even if we did they would require enormous amounts of energy to form and keep open! 12
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