BLACK HOLE MECHANICS AND THERMODYNAMICS

Transcription

1 PHYS 253:THERMAL PHYSICS BLACK HOLE MECHANICS AND THERMODYNAMICS (NASA)

2 THE TAKE-AWAY In General Relativity, the laws of black hole mechanics describe black holes near equilibrium. There is a deep analogy between the laws of black hole mechanics and thermodynamics. Confusion: BH mechanics are exact, thermodynamics is average, statistical. This analogy has driven research in relativity, quantum field theory, and quantum gravity for ~40 yrs. Output: Hawking radiation, black hole evaporation, Beckenstein entropy,. general confusion about BHs.

3 OUTLINE OF THE TALK What are black holes? The laws of black hole mechanics Black hole mechanics vs. thermodynamics Black hole mechanics + quantum physics

4 BLACK HOLES (Interstellar)

5 BHS ARE REAL ASTROPHYSICAL OBJECTS BHs are gravitational objects which contain a region of strong gravity from which nothing can escape ( dark stars ). STELLAR: ~ 10 M sol, radius ~ 30km (strong candidates, end-of-life of some star types) SUPERMASSIVE: ~10 7 M sol, radius ~ AU (ubiquitous, appear in center of galaxies) PRIMORDIAL: ~ M pl - (no observational evidence, remnants of big bang/early universe?)

6 WHERE TO FIND BLACK HOLES? This is not Sagittarius A* You are not here! (NASA)

7 HOW DO YOU SEE A BH AT THE CENTER OF THE GALAXY? Keck Observatory (Keck/UCLA Galatic Center Group)

8 HOW DO YOU SEE A BH AT THE CENTER OF THE GALAXY? (UCLA Galactic Center Group, PI: A. Ghez)

9 HOW DO YOU SEE A BH AT THE CENTER OF THE GALAXY? (UCLA Galactic Center Group, PI: A. Ghez)

10 HOW DO YOU SEE A BH AT THE CENTER OF THE GALAXY? (UCLA Galactic Center Group, PI: A. Ghez)

11 BLACK HOLES IN MORE DETAIL Escape velocity in Newtonian gravity: v e = q 2GM r In special relativity, energy/mass/ momentum are interchangeable: E 2 = m 2 c 4 + p 2 c 2 In general relativity, gravitational force couples to energy/mass/ momentum, rather than mass. Even massless objects (like photons) feel force of gravity. event horizon BH event horizon

12 STATIONARY BLACK HOLES BHs near equilibrium characterized by 3 numbers: mass M, angular momentum J, electric charge Q. horizon area A: A =4 2M(M + µ) Q 2 16 M 2 µ = M 2 Q 2 J 2 /M 2 1/2 M surface gravity : acceleration at infinity needed to hold a unit mass at fixed radius. Also governs the strength of tidal forces felt at horizon. F 1 = applem apple =4 µ/a 1 4M (G = ~ = c = k B =1)

13 BLACK HOLE MECHANICS (Dr. Who)

14 0TH LAW The surface gravity apple of a stationary BH is constant everywhere on the horizon. No hot/cool spots from which we could extract more/less work.

15 1ST LAW Penrose process Consider dropping small amount of matter into BH, then compare initial and final states. Matter can have M,J,Q. dm = apple 8 da + dj + dq Use GR to compute change to M,J,Q,A of BH. = angular vel. of horizon = elect. potential on horizon ( (r = 1) =0)

16 2ND LAW The area A of a BH horizon never decreases with time. da Quite reasonable since A ~ M 2, and nothing can escape from within horizon of a BH. Follows from GR + mild assumptions on types of matter (no anti-matter ). Reminiscent of 2nd law of thermodynamics. Law is not time symmetric, has a preferred time direction. dt 0

17 THE LAWS OF BH MECHANICS Laws describe BHs near equilibrium. 0th law: apple =const. 1st law: dm = apple 8 da + dj + dq 2nd law: da dt 0 Laws are exact, follow from Einstein s field equations of GR (analogue of Maxwell s equations of E&M).

18 BH MECHANICS VS. THERMODYNAMICS (Star Trek)

19 BH MECHANICS VS. THERMODYNAMICS BH mech. thermo. Laws: apple! T apple =const. A! S M! E dj! PdV dq! µdn dm = apple 8 da + dj + dq da 0 dt (1,2) are deep part of analogy. (3): Mass is energy (just relativity!). (4,5): work terms, expected.

20 BH MECHANICS VS. THERMODYNAMICS Small puzzles: units! BH mech. thermo. apple! T A! S Classical BH T=0 (BH vs. coal in vacuum). In BH mechanics each A non-decreasing, vs. total entropy S. Big puzzle: BH mechanics come from exact field theory. Thermodynamics is statistical, coarse-grained treatment.

21 BH MECHANICS +QUANTUM PHYSICS

22 HAWKING RADIATION In quantum field theory: in vacuum, particle/anti-particle pairs created and destroyed. time Hawking: consider quantum field in vicinity of BH. If a creation process occurs near BH horizon, one particle could go in, the other escape. Result: BHs radiate with a black body spectrum, like a piece of coal in vacuum! T H = ~apple 2 event horizon r=0 T H = K M sol M

23 GENERALIZED 2ND LAW No hbar in TdS term of BH mechanics, so BH entropy S BH ~ 1/hbar. T H = ~apple Beckenstein: S BH is area in Planck units. These convenient factors of hbar explain the puzzles of classical BH mechanics. Due to Hawking radiation, S BH can decrease. This motivates the Generalized 2nd law: d 2, S BH = A 4~G dt (S BH + S matter ) 0

24 BH MECHANICS VS. THERMODYNAMICS REVISITED T H and S BH sharpen analogy between BH mechanics and thermodynamics. Imply that BHs are quantum mechanical objects. T H = ~apple 2, S BH = A 4~G Imply that BHs can fully evaporate, something which does not occur in classical GR. quantum gravity!

25 SUMMARY In General Relativity, the laws of black hole mechanics describe black holes near equilibrium. There is a deep analogy between the laws of black hole mechanics and thermodynamics. Confusion: BH mechanics are exact, thermodynamics is average, statistical. This analogy has driven research in relativity, quantum field theory, and quantum gravity for ~40 yrs. Output: Hawking radiation, black hole evaporation, Beckenstein entropy,. general confusion about BHs.

26 WANT TO KNOW MORE? UCLA Galactic Center Group Black Holes and Time Warps: Einstein s Outrageous Legacy, K. Thorne [amazon.ca] PHYS514: General Relativity (Winter 2016) R. M. Wald, The thermodynamics of black holes, Living Rev. Rel. 4 (2001) [gr-qc/ ]