22. Black Holes

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 • Two properties of nonrotating black holes • Three properties of rotating black 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 reality is always the same • Presumes no acceleration (constant velocity) • Gravitycausesacceleration (gravity is ignored) • Speed of light in vacuum is 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 are changeable • Length contraction • Length approaches zero as c is approached • Time dilation • Time nearly stands still as c is approached • Mass dilation • Mass approaches infinity as c is approached • Things that are constant • 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 • Masswould 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 2010

8. Acceleration Equivalence Principle

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

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 essentially straight lines • Core collapse to a large-diameter neutron star • Gravity begins to increase as diameter decreases • Light escapes the star surface in slightly curving lines • Core collapse to a small-diameter neutron star • Gravity continues to increase as diameter decreases • Light escapes the star surface in strongly curving lines • Core collapse to a black 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. A Black Hole The “well” is open Curved Spacetime Near 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 MSun

16. A Model of the Cygnus X-1 System

17. Supermassive Black Holes in Galaxies • Galactic mass • A typical galaxy contains 1011 MSun • 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 . 109 MSun • 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 • Primordial black holes • Hypothesized by Stephen Hawking • May have formed as part of the Big Bang event • Masses ranging from Mcloud droplet to MEarth • No evidence that they actually exist • Stellar-mass black holes • Produced during supernova events • > 4 MSun • Intermediate-mass black holes • Produced by accretion • > 103 MSun • Supermassive black holes • Produced during galaxy birth • > 106 MSun

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 center Singularity • Neither degenerate electron nor neutron pressure can support it • The mass continues to collapse forever • It becomes infinitely dense yet ever increasing density • A surface Event horizon

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 Kerr 1963 • 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 RSch • ~ 1,500 km for a 5.0 . MSun black hole • Allow a probe to fall into the black hole • Accelerates initially when gravitational time slowing small • Decelerates later when 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 1015 kg black hole is effectively ~ 10+9 K 0.5 . MDeimos • A 1031 kg black hole is effectively ~ 10–7 K 5.0 . MSun • Very different results • Primordial black holes evaporate very quickly • Supermassive black 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 .c2 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