Vaidya Space-Time in Black-Hole Evaporation

Abstract

Recently we have studied, using a boundary-value approach, quantum amplitudes resulting from gravitational collapse to a black hole. Suitable boundary data for all fields present are posed on initial and final space-like asymptotically flat hypersurfaces ${\Sigma }_{I,F}$. The Lorentzian proper-time separation between the surfaces, as measured at spatial infinity, is denoted by $T$. Following Feynman's $+i\epsilon$ approach, we rotate $T$ into the complex: $T\to \mid T\mid \exp (-i\theta )$, where $0<\theta \le \pi /2$. The corresponding {\it classical} complex boundary-value problem is expected to be well-posed for $\theta >0$. The Lorentzian amplitude is found by taking the limit $\theta \to 0_{+}$ of the quantum amplitude, itself closely approximated by the semi-classical expression $\exp (i{S}_{\mathrm{class}})$, where $S_{\mathrm{class}}$ is the classical action. For given weak anisotropic spin-0 and spin-2 boundary data on ${\Sigma }_F$, one can compute an effective classical energy-momentum tensor in the interior, which has been averaged over several wave-lengths of the radiation. This averaged extra contribution will be spherically symmetric, equivalent to a null fluid, and describing the radial outward streaming of the radiation (of quantum origin). The corresponding space-time metric, in this region containing radially-outgoing radiation, is of the Vaidya form. This, in turn, justifies the treatment of the adiabatic radial mode equations, for spins $s=0$ and $s=2$, which is used throughout this larger project.

References in corpus (8)

• Bogoliubov transformations for amplitudes in black-hole evaporation
• Scalar--Field Amplitudes in Black--Hole Evaporation
• Quantum Amplitudes in Black-Hole Evaporation II. Spin-0 Amplitude
• Quantum Amplitudes in Black-Hole Evaporation I. Complex Approach
• Spin-$\frac{1}{2}$ amplitudes in black-hole evaporation
• Spin-1 Amplitudes in Black-Hole Evaporation
• Bogoliubov transformations in black-hole evaporation
• Spin-2 Amplitudes in Black-Hole Evaporation

Cited by in corpus (21)

• Hawking radiation as tunneling from a Vaidya black hole in noncommutative gravity
• Black hole evaporation in a spherically symmetric non-commutative space-time
• Surrounded Vaidya Solution by Cosmological Fields
• Gravitational amplitudes in black-hole evaporation: the effect of non-commutative geometry
• Bogoliubov transformations for amplitudes in black-hole evaporation
• Semiclassical Methods for Hawking Radiation from a Vaidya Black Hole
• Vaidya Spacetime in the Diagonal Coordinates
• Hawking Radiation from a Vaidya Black Hole: A Semi-Classical Approach and Beyond
• Quantum Amplitudes in Black-Hole Evaporation II. Spin-0 Amplitude
• Black Hole Evaporation in a Noncommutative Charged Vaidya Model
• Planck-scale nonthermal correlations in a noncommutative geometry inspired Vaidya black hole
• On maximal analytical extension of the Vaidya metric
• Quantum amplitudes in black-hole evaporation: Spins 1 and 2
• Spin-2 Amplitudes in Black-Hole Evaporation
• Constructing Maximal Extensions of the Vaidya Metric in Israel Coordinates: I. Integration of the Field Equations
• Quantum amplitudes in black-hole evaporation: coherent and squeezed states
• Relic Radiation from an Evaporating Black Hole
• Wave equations on the linear mass Vaidya metric
• Quantum Amplitudes in Black-Hole Evaporation: Complex Approach and Spin-0 Amplitude
• A linear mass Vaidya metric at the end of black hole evaporation
• From a collapsing radiating star to an evaporating black hole: A smooth transition from classical to quantum entropy