Quantum Amplitudes in Black-Hole Evaporation I. Complex Approach
| dc.creator | Farley, A. N. St. J. | |
| dc.creator | D'Eath, P. D. | |
| dc.date | 2005-10-07 | |
| dc.date.accessioned | 2026-07-07T06:46:21Z | |
| dc.date.available | 2026-07-07T06:46:21Z | |
| dc.description | Here we examine the quantum-mechanical decay of a Schwarzschild-like black hole, formed by gravitational collapse, into almost-flat space-time and weak radiation at a very late time, in order to evaluate quantum amplitudes (not just probabilities) for final states. No information is lost in collapse to a black hole. Boundary data are specified on initial and final hypersurfaces $Σ_{I, F}$, separated by a Lorentzian proper-time interval $T$, as measured at spatial infinity. For simplicity, consider Einstein gravity coupled minimally to a massless scalar field $ϕ$. In Lorentzian signature, the classical Dirichlet boundary-value problem, corresponding to specification of the intrinsic spatial metric $h_{ij} (i,j =1,2,3)$ and $ϕ$ on the bounding surfaces, is badly posed, being a boundary-value problem for a wave-like (hyperbolic) set of equations. Following Feynman's $+iε$ prescription, the problem is made well-posed by rotating the asymptotic time interval $T$ into the complex: $T\to{\mid} T{\mid}\exp(-iθ)$, with $0<θ\leqπ/2$. After calculating the amplitude for $θ>0$, one takes the 'Lorentzian limit' $θ\to 0_+$ to obtain the Lorentzian quantum amplitude. | |
| dc.identifier | https://arxiv.org/abs/gr-qc/0510028 | |
| dc.identifier | http://arxiv.org/abs/gr-qc/0510028 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/103306 | |
| dc.subject | General Relativity and Quantum Cosmology | |
| dc.title | Quantum Amplitudes in Black-Hole Evaporation I. Complex Approach | |
| dc.type | text |