Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2005-10-07
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
Scientific paper
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 $\Sigma_{I, F}$, 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 $\phi$. 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 $\phi$ on the bounding surfaces, is badly posed, being a boundary-value problem for a wave-like (hyperbolic) set of equations. Following Feynman's $+i\epsilon$ prescription, the problem is made well-posed by rotating the asymptotic time interval $T$ into the complex: $T\to{\mid} T{\mid}\exp(-i\theta)$, with $0<\theta\leq\pi/2$. After calculating the amplitude for $\theta>0$, one takes the 'Lorentzian limit' $\theta\to 0_+$ to obtain the Lorentzian quantum amplitude.
D'Eath Peter D.
Farley Andrew N. S. J.
No associations
LandOfFree
Quantum Amplitudes in Black-Hole Evaporation I. Complex Approach does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Quantum Amplitudes in Black-Hole Evaporation I. Complex Approach, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Quantum Amplitudes in Black-Hole Evaporation I. Complex Approach will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-560995