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A family of regular quantum interiors for non-rotating black holes I: The GRNSS spacetimes

Emilio Elizalde·Sergi R. Hildebrandt
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Abstract

A seemingly natural mechanism is proposed, that could stop the gravitational collapse of a very massive body. Without needing to change the concept of the collapsing process itself, that is, without invoking thin layers nor resorting to asymptoticity (as has been usually done in the literature), it is proven that a model can be built in which the quantum vacuum is able to produce a negative stress that may stop the collapse of the black hole, reaching a final state of the spacetime structure that is a static de Sitter model. The solution is found by looking into a generic family of spacetimes: that of maximal spherically symmetric ones expanded by a geodesic radial null one-form from flat spacetime. They are called here GRNSS spaces, and are proven to constitute a distinguished family of Kerr-Schild metrics. The models considered previously in the literature are easily recovered in this approach, which yields, moreover, an infinite set of possible candidates for the interior of the black hole. First steps towards their semiclassical quantization are undertaken. It is shown that the quantization protocol may be here more easily carried out than within conformal field theory.

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Emilio Elizalde, Sergi R. Hildebrandt. 2001-03-16. A family of regular quantum interiors for non-rotating black holes I: The GRNSS spacetimes. https://arxiv.org/abs/gr-qc/0103063

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