Year: 2025
Type: article
Abstract: We provide a general algorithm to construct a Hamiltonian, such that its dynamical flow covariantly defines any given spherically symmetric and static metric. This Hamiltonian is defined as a linear combination of the standard (general relativistic) radial diffeomorphism constraint plus a Hamiltonian constraint that is appropriately deformed as compared to its corresponding form in general relativity though it does not include higher-derivative terms. Therefore, given a static model of spherical gravity, it is possible to obtain its Hamiltonian, and, thus, its canonical (second-order) equations of motion. A particularly relevant application of this construction is the study of regular black holes, where proposed geometries often lack an underlying dynamical theory. The present method provides such a theory. In particular, for a wide class of deformations of the Schwarzschild geometry, we explicitly obtain their corresponding Hamiltonian. This construction can be further used to covariantly couple matter. In this way, one can analyze the backreaction of matter fields on the geometry of interest, and, specifically, whether a particular black-hole model may emerge as the end state of a dynamical collapse.
DOI: 10.1103/ttfy-yjdh
Authors: Asier Alonso-Bardaji, David Brizuela
Institution: University of the Basque Country
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Awards: G1578893264, G4269502044
OpenAlex ID: W4416224140