KERR BLACK HOLES Generalized BH description includes spin –Later researchers use it to predict new...
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Transcript of KERR BLACK HOLES Generalized BH description includes spin –Later researchers use it to predict new...
![Page 1: KERR BLACK HOLES Generalized BH description includes spin –Later researchers use it to predict new effects!! Two crucial surfaces –inner surface = horizon.](https://reader033.fdocuments.us/reader033/viewer/2022051007/5a4d1b217f8b9ab0599954e4/html5/thumbnails/1.jpg)
KERR BLACK HOLES• Generalized BH description includes spin
– Later researchers use it to predict new effects!!• Two crucial surfaces
– inner surface = horizon: smaller than nonrot. hole of same mass
– outer surface = “static limit”• Angular momentum of a black hole
– “Kerr parameter”Ma
Ma /
1/0/
MaMa
(Roy Kerr 1963)
No spin: Schwarzschild holemaximal (or extreme) Kerr hole
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STRUCTURE OF A KERR BH• Horizon smaller in max. Kerr limit• Static limit at equator, touches horizon at poles
2/SrSr
Gas can orbit closer to horizon without plunging in
Higher energy efficiency:
Schwarzschild:
Extreme Kerr:
206.0 Mc242.0 Mc
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THE ERGOSPHERE• Region between horizon and static limit• Nothing can remain stationary in the ergosphere
Must rotate in direction of BH spinbecause
BH spin “drags space” along with it
aka: “dragging of inertial frames”
“Lense-Thirring effect”
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Why “ERGOSPHERE”?• “ERGO” = ENERGY• All the spin energy of a black hole resides outside the
horizon!! it can all be extracted (… in theory)• For maximal Kerr hole with mass M:
Two famous energy extraction schemes:Penrose Process: particle splitting inside the ergosphere
Blandford-Znajek Process: BH spin twists magnetic field
2McSPIN ENERGY = 29% of
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UNIQUENESS OF KERR’S SOLUTION• Kerr’s solution describes all black holes
without electric charge• More generally,
• No-hair theorem: All traces of the matter that formed a BH disappear except for:
“BLACK HOLES HAVE NO HAIR”
MASSANGULAR MOMENTUM
CHARGE
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HOW DOES ALL THE “HAIR” DISAPPEAR?
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AREA THEOREM (Hawking 1970)
• The area of a black hole’s event horizon can stay the same or increase, but can never decrease– Area increases when:
•mass increases•spin decreases
• You can extract spin energy of a BH but cannot add spin energy without also adding mass
• Deep connection to thermodynamics– horizon area ~ entropy
Theorem is true for classical GR, can be violated at quantum level
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WHAT IS ENTROPY?• Entropy = measure of disorder• Example: entropy of a gas
– you see the overall properties (density, pressure, etc.), but don’t know the exact location , energy, etc., of each atom
– ENTROPY = logarithm of the number of diffferent ways you can relocate the atoms and redistribute their energies WITHOUT changing the overall properties of the gas
• 2nd law of thermodynamics: The entropy of a self-contained system never decreases
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BLACK-HOLE THERMODYNAMICS
• Area theorem “looks like” 2nd law of thermo.– could BH horizon area really represent entropy? (Beckenstein
1972)
• Law for addition of mass, ang.mom., etc. to BH “looks like” 1st law of thermodynamics if:
• This turns out to be more than “just an analogy”
HORIZON AREA ~ ENTROPY
GRAV. ACCEL. AT HORIZON ~ TEMPERATURE
(Bardeen, Carter, Hawking 1972)
(Hawking 1974)
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BLACK HOLES EVAPORATE• If black holes really have a finite temperature, they must radiate
• Hawking calculates by working out quantum effects in a curved (non-quantum) space
• Finds that black holes must radiate according to “black body” law – same form of radiation as any warm opaque body
• Where does BH entropy come from?– No. of different ways of throwing stuff together to make
the same BH
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HOW DOES THE HAWKING EFFECT WORK?
“VACUUM FLUCTUATIONS”Creation of “virtual pairs”
of particles
Tidal forces pull them apart
Makes some of them real
One falls in, one flies away
Black hole evaporates
In the very short timethat virtual pairs can exist...
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HOW FAST DO BHs EVAPORATE?
• BH temperature inversely proportional to mass– For 1 solar mass BH: 60 billionths of a degree Kelvin– For BH temp. to exceed cosmic background radiation (3°
K): < 20 billionths of a solar mass (<0.007 Earths)• Evaporation time proportional to (mass)3
– For 1 solar mass BH:– To evaporate in age of Universe (~ 15 billion yr):
need BH mass < 100 million tons (< cu. km of dirt) (size ~ atomic nucleus, temp. ~ 200 billion degrees)
• At final stage (trillions of °K) BH explodes
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