Abstract
We study the prelude to black-hole formation using a suspended shell composed of physical matter that fulfills the dominant energy condition. Here, the collapse of the shell is brought to rest when the formation of the horizon is imminent but has not yet occurred. As the main achievement of this work, we obtain the Feynman propagator which connects the interior and the exterior of the shell within two local coordinate patches. It is derived by drawing an analogy to the propagation of light across interfaces that separate regions with different susceptibilities inside a medium. As a first application, we use this propagator to determine the vacuum persistence amplitude in the presence of external sources. On timescales much shorter than the Page time, we find that the amplitude builds up with time yet remains consistent with perturbative unitarity.
Highlights
In recent years, observations have been able to test our understanding of black holes with increasing accuracy
The gravitational wave signal from a binary blackhole merger provides us with information about their masses and intrinsic vibrational modes [1]; the event horizon telescope [2] probes the classical geometry close to the event horizon
Provided the shell radius R is slightly larger than the Schwarzschild radius rg, explicitly R > 25rg=24, we find that the shell can be brought to a complete stop while still being composed of matter fulfilling the strong and Published by the American Physical Society
Summary
Observations have been able to test our understanding of black holes with increasing accuracy. We study the quantum consistency of a thinshell system close to black-hole formation To this end, we will pursue a very conservative approach where we employ the standard semiclassical toolkit. We will calculate for an inertial observer the persistence amplitude of the Minkowski vacuum inside the shell in the presence of an external source [20] This diagnostic tool is sensitive to effects that build up over time and could be missed in a standard stability perturbative analysis.. Together with the interior Minkowski spacetime, this flat patch provides a local covering of the physical manifold This approximation enables us to derive an analytic result for the Feynman propagator and isolate its reflective and transmissive contributions.
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