Conserved Energy Flux for the Spherically Symmetric System and the Backreaction Problem in the Black Hole Evaporation

1980 ◽  
Vol 63 (4) ◽  
pp. 1217-1228 ◽  
Author(s):  
H. Kodama
Keyword(s):  
Black Hole ◽  
Energy Flux ◽  
Symmetric System ◽  
Spherically Symmetric ◽  
Black Hole Evaporation

scholarly journals Black hole evaporation in a spherically symmetric non-commutative spacetime

2008 ◽  
Vol 41 (16) ◽  
pp. 164063 ◽  
Author(s):  
Elisabetta Di Grezia ◽  
Giampiero Esposito ◽  
Gennaro Miele
Keyword(s):  
Black Hole ◽  
Spherically Symmetric ◽  
Black Hole Evaporation

scholarly journals BOGOLIUBOV TRANSFORMATIONS IN BLACK-HOLE EVAPORATION

2007 ◽  
Vol 16 (04) ◽  
pp. 569-590 ◽  
Author(s):  
A. N. St. J. FARLEY ◽  
P. D. D'EATH
Keyword(s):  
Black Hole ◽  
Scalar Field ◽  
Probability Distribution ◽  
Boundary Value Problem ◽  
Boundary Data ◽  
Boundary Value ◽  
Spherically Symmetric ◽  
Black Hole Evaporation ◽  
Quantum Amplitude ◽  
Classical Boundary

In previous papers and letters on quantum amplitudes in black-hole evaporation, a boundary-value approach was developed for calculating (for example) the quantum amplitude to have a prescribed slightly non-spherical configuration of a massless scalar field ϕ on a final hypersurface ΣF at a very late time T, given initial almost-stationary spherically symmetric gravitational and scalar data on a space-like hypersurface ΣI at time t = 0. For definiteness, we assumed that the gravitational data are also spherically symmetric on ΣF. Such boundary data can correspond to a classical solution for the Einstein/scalar system, describing gravitational collapse from an early low-density configuration to a nearly Schwarzschild black hole. This approach provides the quantum amplitude (not just the probability) for a transition from an initial to a final state. For a real Lorentzian time-interval T, the classical boundary-value problem refers to a set of hyperbolic equations (modulo gauge), and is badly posed. Instead, the boundary-value approach of the previous letters and papers requires (following Feynman) a rotation into the complex: T → |T| exp (-iθ), for 0 < θ ≤ π/2, of the time-separation-at-infinity T. The classical boundary-value problem, for a complex solution of the coupled nonlinear classical field equations, is expected to be well-posed for 0 < θ ≤ π/2. For a locally supersymmetric Lagrangian, containing supergravity coupled to supermatter, the classical Lorentzian action S class , a functional of the boundary data (which include the complexified T), yields a quantum amplitude proportional to exp (iS class ), apart from possible loop corrections which are negligible for boundary data with frequencies below the Planck scale. Finally (still following Feynman), one computes the Lorentzian quantum amplitude by taking the limit of exp (iS class ) as θ → 0+. In the present paper, a connection is made between the above boundary-value approach and the original approach to quantum evaporation in gravitational collapse to a black hole, via Bogoliubov coefficients. This connection is developed through consideration of the radial equation obeyed by the (adiabatic) non-spherical classical perturbations. When one studies the probability distribution for configurations of the final scalar field, based on our quantum amplitudes above, one finds that this distribution can also be interpreted in terms of the Wigner quasi-probability distribution for a harmonic oscillator.

THE UNREASONABLE EFFECTIVENESS OF EXPONENTIALLY SUPPRESSED CORRECTIONS IN PRESERVING INFORMATION

2013 ◽  
Vol 22 (12) ◽  
pp. 1342030 ◽  
Author(s):  
KYRIAKOS PAPADODIMAS ◽  
SUVRAT RAJU
Keyword(s):  
Hilbert Space ◽  
Black Hole ◽  
Quantum Mechanics ◽  
Nonperturbative Effects ◽  
Von Neumann Entropy ◽  
Von Neumann ◽  
Information Theoretic ◽  
Black Hole Evaporation ◽  
Strong Subadditivity ◽  
Unreasonable Effectiveness

We point out that nonperturbative effects in quantum gravity are sufficient to reconcile the process of black hole evaporation with quantum mechanics. In ordinary processes, these corrections are unimportant because they are suppressed by e-S. However, they gain relevance in information-theoretic considerations because their small size is offset by the corresponding largeness of the Hilbert space. In particular, we show how such corrections can cause the von Neumann entropy of the emitted Hawking quanta to decrease after the Page time, without modifying the thermal nature of each emitted quantum. Second, we show that exponentially suppressed commutators between operators inside and outside the black hole are sufficient to resolve paradoxes associated with the strong subadditivity of entropy without any dramatic modifications of the geometry near the horizon.

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