https://doi.org/10.1140/epjc/s10052-024-13609-5
Regular Article
Effective metric descriptions of quantum black holes
1
Scuola Superiore Meridionale, Largo S. Marcellino, 10, 80138, Naples, Italy
2
Department of Physics E. Pancini, Università di Napoli Federico II, Via Cintia, 80126, Naples, Italy
3
INFN sezione di Napoli, Via Cintia, 80126, Naples, Italy
4
Univ Lyon, Univ Claude Bernard Lyon 1, CNRS/IN2P3, IP2I Lyon, UMR 5822, 69622, Villeurbanne, France
5
Quantum Theory Center (ћQTC) and D-IAS, Southern Denmark University, Campusvej 55, 5230, Odense M, Denmark
Received:
2
September
2024
Accepted:
11
November
2024
Published online:
9
December
2024
In a recent work (Del Piano et al. in Phys Rev D 109(2):024045, 2024), we have described spherically symmetric and static quantum black holes as deformations of the classical Schwarzschild metric that depend on the physical distance to the horizon. We have developed a framework that allows us to compute the latter in a self-consistent fashion from the deformed geometry, in the vicinity of the horizon. However, in this formalism, the distance can be replaced by other physical quantities, e.g. curvature invariants such as the Ricci- or Kretschmann scalar. Here, we, therefore, define a more general framework, which we call an effective metric description (EMD), that captures the deformed geometry based on a generic physical quantity. We develop in detail the Ricci- and Kretschmann scalar EMD, in particular demonstrating how to compute the geometry in a self-consistent manner. Moreover, we provide explicit relations that allow us to express one EMD in terms of the others, thus demonstrating their equivalence.
© The Author(s) 2024
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