On the partner particles for black-hole evaporation

Transcription

1 On the partner particles for black-hole evaporation Ralf Schützhold Fakultät für Physik Universität Duisburg-Essen On the partner particles for black-hole evaporation p.1/12

2 Quantum Radiation Relativistic quantum fields (,c) in vacuum state 0 in Hawking radiation gravitational field Sauter-Schwinger effect electric field Unruh radiation acceleration Dynamical Casimir effect mirror motion Cosmological particle creation expansion Particles are created in pairs On the partner particles for black-hole evaporation p.2/12

3 Squeezing Bogoliubov transformation (linear) â out k = dk αkk â in k + dk β kk Time evolution [ for { bi-linear Hamiltonian }] Û = T exp i dt Ĥ(t) (âin ) Generalized squeezing operation { } 0 in = exp dkdk (âout ) (âout ) ξ kk k k h.c. Creation of particles 0 ˆn out k 0 in 0 in pairs 0 in = 0 out + dkdk ξ kk k,k out +... k 0 out Note: asymptotics... On the partner particles for black-hole evaporation p.3/12

4 Hawking Radiation T Hawking S. W. Hawking, Nature 248, 30 (1974); Comm. Math. Phys. 43, 199 (1975). 0> t r T Hawking = 1 c 3 8πM G N k B But: trans-plankian problem, information puzzle etc. On the partner particles for black-hole evaporation p.4/12

5 Definition of Partner Particle A) reduced density matrix for Hawking mode plus partner ˆ HP = Tr rest { 0 in 0 in } is a pure state only correlations between Hawking mode and its partner but not with any other modes Note: ˆ H = Tr P {ˆ HP } is a mixed (thermal) state B) state after annihilating one Hawking particle is the same (up to normalization) as after creating one partner particleâ H 0 in â P 0 in particles come in pairs Note: in most simple cases symmetric, i.e., equivalent to â P 0 in â H 0 in 0> t r T Hawking On the partner particles for black-hole evaporation p.5/12

6 Partner Particle Hawking mode in terms of in-operatorsâ in k 0 in = 0 â H = dkα kâin k + (âin ) dkβ k k Assume orthogonality (most simple case) dkα kβ k = 0 Unique partner mode from conditions A and B â P = cothξ dkβkâ in (âin ) k +tanhξ dkα k k with squeezing parameter sinh 2 ξ = dk β 2 k 0 in = e ξâ Hâ P h.c. 0 HP whereâ H 0 HP = â P 0 HP = 0 On the partner particles for black-hole evaporation p.6/12

7 Moving Mirror in 1+1 D Toy model for black hole evaporation: accelerated mirror with v = e κu κ v = t+x u = t x emits thermal radiation with T = κ 2π Partner mode in local vacuum! D P Detector mode Detector Partner But: â H 0 in â P 0 in On the partner particles for black-hole evaporation p.7/12

8 Black Hole Evaporation T Hawking Infalling partners are locally nearly indistinguishable from vacuum fluctuations! 0> t r On the partner particles for black-hole evaporation p.8/12

9 Black Hole Information Puzzle Is black hole formation evaporation unitary? regularity near horizon ( firewall etc.) correlations between Hawking particles and vacuum fluctuations falling towards singularity a) information is lost non-unitarity? b) singularity stores information black-hole entropy? simple picture: one qubit per l 3 Planck? 0> c) singularity re-emits information causal structure? information energy t r T Hawking On the partner particles for black-hole evaporation p.9/12

10 Summary M. Hotta, R.S., W.G. Unruh,arXiv: , to appear in Phys. Rev. D (2015) quantum radiation: particles in pairs determination of partner particle 20 Detector mode moving mirror and black hole 10 0 D P partners vacuum fluctuations information energy black hole information puzzle Partner Detector > T Hawking t r On the partner particles for black-hole evaporation p.10/12

11 Ion Trap Analogue Squeezing creation of phonons ˆn ξ ξ ( ) 3 ξ exp π 8 xmin 3 Creation of entanglement if e ξ > 1+2n thermal x crit C. Fey, Ms Thesis (2014); C. Fey, T. Schätz, R.S., manuscript in preparation See also R. S. et al., Phys. Rev. Lett. 99, (2007). On the partner particles for black-hole evaporation p.11/12

12 Black Hole Evaporation Formula for Hawking temperature T Hawking = 1 c 3 8πM G N k B Combines four (apparently) different areas of physics quantum theory relativity gravity thermodynamics Is nature trying to give us a hint? ( black hole entropy area etc.) c G N Problems: M BH = 30M sun T Hawking 2nK... + trans-plankian problem On the partner particles for black-hole evaporation p.12/12 k B