Perturbative black-hole and horizon solutions in gravity with explicit spacetime-symmetry breaking

TL;DR

This paper derives and classifies static, spherically symmetric black hole solutions in a gravity theory with explicit spacetime-symmetry breaking, analyzing their horizons, thermodynamics, and observational implications.

Contribution

It provides the first systematic classification of black hole solutions with explicit symmetry-breaking coefficients in a modified gravity framework.

Findings

Some solutions have horizons similar to Reissner-Nordström black holes.

Certain solutions exhibit physical singularities at the horizon radius.

Multiple non-zero symmetry-breaking coefficients can produce black holes with three horizons.

Abstract

In this paper, we present static and spherically symmetric vacuum solutions to the mass-dimension $d\leq 4$ action of an effective-field theory, choosing the diffeomorphism symmetry to be broken explicitly. By using the reduced-action method with a Schwarzschild seed-solution, we find static and spherically symmetric black hole solutions to the field equations to linear order in the symmetry-breaking coefficients, which are consistent solutions to the modified Einstein equations at the same order. Using several ans\"atze for the symmetry-breaking coefficient we classify the allowed solutions, and we compute standard consequences and observables, including horizons, thermodynamics, photon geodesics, and perihelion precession. We find that the horizon structure of some of our solutions are similar to the Reissner-Nordstr\"om case, and that several of them exhibit physical singularities at $r=2M$. We note in particular that introducing more than one non-zero coefficient for spacetime-symmetry breaking coefficient leads to a solution with three horizons; the aim is to obtain observables that can be confronted to black holes observational data.