1. 22. Black Holes Einstein’s Special Theory of Relativity Einstein’s General Theory of Relativity Black holes exist in some binary star systems Supermassive black holes at of galaxy centers Twoproperties ofnonrotatingblack holes Threeproperties ofrotatingblack holes Falling into a black hole is an infinite voyage Black holes evaporate

2. Einstein’s Special Theory of Relativity Published in 1905 –“Special” ⇒ It applies only in special circumstances No acceleration or deceleration –“Relative” in contrast to “absolute” Neither distance nor time are absolute Founded on two basic principles –Description of physical realityis always the same Presumes no acceleration (constant velocity) Gravity causes acceleration (gravity is ignored) –Speed of light in vacuumis always the same Independent of speed & direction of motion The concept of spacetime –By definition,speed = distance per unit time –By implication,spacetime is a fourth dimension

3. Changeability & Constancy Things that arechangeable –Lengthcontraction Lengthapproaches zeroas c is approached –Timedilation Timenearly stands stillas c is approached –Massdilation Massapproaches infinityas c is approached Things that areconstant –The speed of light in vacuum Independent of any two observers All matter must move less than speed of light –Two mutually contradictory phenomena Length would contract to zero Mass would expand to infinity

4. Relativistic Length Contraction

5. Relativistic Time Dilation

6. Einstein’s General Theory of Relativity Einstein’s “geometric theory of gravity” –Gravity affects the shape of space & the flow of time Spacetime becomes distorted Principle of equivalence –All accelerations appear identical Things accelerating relative to a stationary massive object Things accelerating relative to a moving spacecraft

7. Tests of General Relativity Gravitational bending of light –Caused by distortions in spacetime –First tested in the 1919 total solar eclipse Precession of Mercury’s orbit –Explained 531 arc-sec / century due to planets –Unexplained 43 arc-sec / century due to relativity Gravitational redshift & time dilation –Light slowed in gravitational fields –Time slowed in gravitational fields Gravitational waves –Caused by rapidly oscillating massive objects –Not confirmed as of 29 May 2014

8. Acceleration Equivalence Principle

9. Spacetime Gravitational Curvature A Normal Star The “well” is closed

10. Gravitational Deflection of Light

11. Precession of Mercury’s Orbit

12. One Way to Form a Black Hole Life of a high-mass star –Gravity is normal Light escapes the star surface in nearly straight lines Core collapse to alarge-diameter neutron star –Gravity begins to increase as diameter decreases Light escapes the star surface in slightly curving lines Core collapse to asmall-diameter neutron star –Gravity increases as diameter decreases Light escapes the star surface in strongly curving lines Core collapse to ablack hole –Gravity almost infinitely strong as diameter nears 0 Light curves back to the surface, unable to escape –The matter continues to collapse forever No kind of pressure can ever stop it

13. The Formation of a Black Hole

14. Curved Spacetime Near a Black Hole The “well” is open A Black Hole

15. Black Holes in Binary Star Systems The nature of the search –Black holes cannot be seen directly No emitted or reflected light can escape –Black holes can be detected indirectly Binary star systems are very common A small number of binary systems contain a black hole Kepler’s third law tells us the mass of the black hole Some recent successes –Cygnus X-1 X-ray flickering as quickly as 0.01 seconds Necessarily < 3,000 km in diameter Possibly gas concentrations in an accretion disk –V 404 Cygni Doppler shift confirms orbital period of 6.47 days Unseen companion > 6.26 M ☉

16. A Model of the Cygnus X-1 System

17. Supermassive Black Holes in Galaxies Galactic mass –A typical galaxy contains 10 11 M ☉ –A tiny fraction of this = A supermassive black hole One example: M87 –High-resolution HST Doppler shift measurements Stars orbiting galaxy center at 100’s of km / sec Kepler’s third law tells us the mass The galactic center contains ~ 3.0. 10 9 M ☉ The galactic center is the diameter of the Solar System –Dozens of other supermassive black holes identified Analysis of surrounding gas & dust –The Milky Way galaxy Our galaxy apparently also has a supermassive black hole

18. Four Kinds of Black Holes Primordialblack holes –Hypothesized by Stephen Hawking May have formed as part of the Big Bang event Masses ranging from M cloud droplet to M Earth No evidence that they actually exist Stellar-massblack holes –Produced during supernova events > 4 M ☉ Intermediate-massblack holes –Produced by accretion > 10 3 M ☉ Supermassiveblack holes –Produced during galaxy birth > 10 6 M ☉

19. Properties of Nonrotating Black Holes These are theoretical objects –Virtually all celestial objects rotate –They rotate faster as they become smaller Properties of nonrotating black holes –A centerSingularity Degenerate electron & neutron pressure cannot support it The mass continues to collapse forever It becomes infinitely dense yet ever increasing density –A surfaceEvent horizon Maximum distance at which even light cannot escape

20. The Schwarzchild Radius Property of nonrotating black holes –Distance from the singularity to the event horizon Considered to be the “surface” of a black hole –Directly proportional to the mass of the black hole

21. Geometry of Non-Rotating Black Holes

22. 3 Numbers Describe Black Holes Mass –This exerts force that acts over long distances –Kepler’s third law tells us the mass of the black hole Observe stars orbiting very close to the black hole Electric charge –This exerts force that acts over long distances Appropriate instruments on a hypothetical spacecraft –Expected to be very nearly zero Number of p + & e – in any vicinity is normally about equal Angular momentum –This distorts spacetime over long distances Observe gas spiraling into a black hole –Virtually all black holes are expected to rotate Everything we observe has some angular momentum

23. Rotating (Kerr) Black Holes Predicted by Roy Kerr1963 –Known angular momentum of high-mass stars Most rotating black holes spin thousands of times per sec. Much faster than the fastest neutron stars Effects of rotating black holes –The singularity becomes an infinitely thin ring It is centered on the geometric center of the black hole –Spacetime is dragged along Ellipsoidal ergoregion surrounds spherical event horizon An unusual property of rotating black holes –The Penrose process Objects skipping off the ergoregion can steal momentum

24. Geometry of a Rotating Black Hole

25. One Concept of a Black Hole

26. Wormholes & Time Machines Einstein & Rosen discover passageways –Einstein-Rosen bridges Connect two parallel universes –Wormholes Connect two parts of our Universe Problems –Powerful gravity causes the passageway to collapse Travel faster than light required to traverse the bridge –Pressure may generate antigravity This may support the bridge long enough for travel Time machines –Move one end of the wormhole very quickly Generate a time differential between the two ends –The problem of violating causality

27. Einstein-Rosen Bridge (Another Universe)

28. A Wormhole (Within Our Universe)

29. Fall Infinitely Into a Black Hole Playing with black holes –Seems like a normal star at ~ 1,000 R Sch ~ 1,500 km for a 5.0. M ☉ black hole –Allow a probe to fall into the black hole Acceleratesinitiallywhen gravitational time slowing small Decelerateslaterwhen gravitational time slowing large Seems to take infinitely long to enter the event horizon –Tidal forces become overwhelming Probe is stretched out by differential gravity –The probe & its atoms are torn apart Probe is squeezed in by force directed to the singularity Strange phenomenon –Blurred distinction between space & time Limited ability to move backward in time Limited ability to move backward in space

30. Distortion Falling Into a Black Hole

31. Black Holes Evaporate Basic physical processes –Heisenberg uncertainty principle Both location & velocity cannot be known with certainty If one is well known, the other is poorly known –Virtual pairs form just outside the event horizon One particle escapes & the other is captured Mass is lost by the black hole Basic properties –Black holes have a “temperature” Measure of the amount of mass lost per unit time This temperature is inversely proportional to mass –A 10 15 kg black hole is effectively ~ 10 +9 K0.5. M Deimos –A 10 31 kg black hole is effectively ~ 10 –7 K5.0. M ☉ –Very different results Primordialblack holes evaporate very quickly Supermassiveblack holes evaporate very slowly

32. Mass Evaporation from a Black Hole

33. Special theory of relativity –Attempt to understand EMR Acceleration must be zero –Foundational principles Description of reality constant Speed of light in vacuum constant –Famous predictions E = m. c 2 Length contraction Time & mass dilation Concept of spacetime General theory of relativity –Attempt to understand gravity Acceleration may be non-zero –Famous predictions Equivalence of all acceleration types Bending of light by massive objects Gravitational redshift Existence of gravity waves Existence of black holes Black holes – Primordial, stellar mass, supermassive – Non-rotating black holes Point singularity & event horizon – Rotating black holes Ring singularity & event horizon Also an ellipsoidal ergoregion – Passageways Wormholes to our Universe Einstein-Rosen bridges to other univ. – Falling into black holes Tidal stretching toward singularity Squeezing perpendicular to singularity – Evaporation of black holes Equivalent of black hole temperature Inversely proportional to mass Primordial bl. holes evaporate quickly Important Concepts