Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum Amplitudes in Black-Hole Evaporation I. Complex Approach   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.

8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an
17
The categories of this paper are: q-fin
36
The categories of this paper are: cmp-lg
34
The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn
33
The categories of this paper are: plasm-ph
1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
19
The categories of this paper are: eess