Black Holes Mysteries

Transcription

1 Black Holes Mysteries Classical description Schwartzchild radius No entropy, temperature, stable! Quantum mechanics The smallest we can measure: Planck length Hawking radiation Entropy of a black hole Holographic principle Maximum amount Are our 3 dimensions an illusion? cf J.D. Bekenstein Scientific American Reports 2007 p 67 Leonard SusskindThe Black Hole War Quantum gravity and the Big Bang 1

2 Classical Black Holes Horizon separates inner part of black hole from which you cannot escape from outer part Schwartzchild radius For non rotating black hole. If mass concentrated in less than r s => black hole Escape velocity =velocity of light No hair theorem Classically a black hole has just mass, charge and spin No structure No temperature, entropy, does not decay! 2

3 Quantum Mechanics and Gravity No unified theory yet Best candidate: string theory but plagued with large number of ground states ( Landscape ) Meanwhile: Semiclassical arguments General character Diffraction <=wave character size h = λ(wave length) p Discrete quanta quanta of energy e.g. photon ε=hv = hc λ 3 1st Quantification Wave like 2nd Quantification Discrete particles Massive Particles Discrete states Obvious Photons Obvious Planck # photons / mode particle of mass m ε mc 2 + p2 (non relativistic) 2m Minimum measurable length= Planck length minimum wave length that a photon can have without collision leading to a black hole Planck length L p = Energy after collision ε = hc λ m Schartzchild radius r s 2Gmc2 Gh 2πc 3 c 4 = 2G c 4 hc λ m λ m λ m = 2Gh c 3

4 Hawking Radiation Quantum mechanics and horizon Vacuum is full of pairs of particles and anti particles Sometimes one of the members of the pair is gobbled up => one particle left: radiation As you cannot extract energy from vacuum, black hole looses mass (if energy E is emitted, energy -E is absorbed) Fluctuations on the horizon small hair: extended horizon Entropy Temperature T = t evaporation = 5120i2πG2 M 3 Entropy S = k B log( W ) W=number of accessible quantum states S = k B 4πr s 2 4L p 2 hc 4 hc 3 16π 2 GMk B 4

5 Entropy of a black hole Log(W) =surface area of horizon divided by 4 L p 2 5

6 Bound on number of states Holographic Bound Entropy<Area/(4L p 2) Squeeze object within surface area A to make it a black hole Entropy has to increase => initial entropy <entropy of black hole with has surface area smaller => bound cf Hologram Universal entropy bound Entropy of an object with mass m and diameter d Merge it with a black hole of the same diameter Entropy has to increase => bound on initial entropy 6

7 Consequences Holographic bond much higher than practical devices However seems to indicate mapping 3 dimensional world on 2 dimensional surface Can be made formal in some string theory models Are 3 dimensions an illusion? Holographic_principle Can we test experimentally? Hogan s idea about holographic noise 7

8 Epilogue 8

9 Quantum Gravity and the Big Bang Quantum Gravity is not yet a full theory but conjectures likely to be true Hawking s guess Singularity smoothed by quantum effect Absence of boundary: no initial conditions Metaphysical consequences In his view solves the problem of the origin of time the problem of God. Much too simplistic! 9