caa a22 4500 467887241 CHVBK 20180406152738.0 cr unu---uuuuu 170328e20060301xx s 000 0 eng 10.1007/s10714-006-0231-3 doi (NATIONALLICENCE)springer-10.1007/s10714-006-0231-3 Vaidya Space-Time in Black-Hole Evaporation [Elektronische Daten] [A. Farley, P. D'Eath] We take a boundary-value approach to quantum amplitudes arising in gravitational collapse to a black hole. Pose boundary data on initial and final space-like hypersurfaces Σ F,I , separated at spatial infinity by a Lorentzian proper-time interval T. Quantum amplitudes are calculated following Feynman's approach; rotate: T→|T|exp (−iθ) into the complex, where 0< θ≤π/2, and solve the corresponding well-posed complex classical boundary-value problem. We compute the classical Lorentzian action S class and corresponding semi-classical quantum amplitude, proportional to exp (iS class). To recover the Lorentzian amplitude, take the limit θ→ 0+ of the semi-classical amplitude. For the classical boundary-value problem with given perturbative boundary data, we compute an effective spherically-symmetric energy-momentum tensor 〉 T μν〈 EFF , averaged over several wavelengths of the radiation, describing the averaged extra energy-momentum contribution in the Einstein field equations, due to the perturbations. This takes the form of a null fluid, describing the radiation (of quantum origin) streaming radially outwards. The classical space-time metric, in this region of the space time, is of Vaidya form, justifying the adiabatic radial mode equations, for spins s = 0 and s = 2. Springer-Verlag, 2006 Black Holes nationallicence Quantum evaporation nationallicence Boundary-value formulation nationallicence Vaidya geometry nationallicence Farley A. Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, CB3 0WA, Cambridge, UK aut D'Eath P. Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, CB3 0WA, Cambridge, UK aut General Relativity and Gravitation Springer US; http://www.springer-ny.com 38/3(2006-03-01), 425-443 0001-7701 38:3<425 2006 38 10714 https://doi.org/10.1007/s10714-006-0231-3 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10714-006-0231-3 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Farley A. Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, CB3 0WA, Cambridge, UK aut NATIONALLICENCE 700 1- D'Eath P. Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, CB3 0WA, Cambridge, UK aut NATIONALLICENCE 773 0- General Relativity and Gravitation Springer US; http://www.springer-ny.com 38/3(2006-03-01), 425-443 0001-7701 38:3<425 2006 38 10714 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer