Master field equations for spherically symmetric gravitational fields beyond general relativity

TL;DR

This paper develops the most general spherically symmetric gravitational field equations beyond general relativity, enabling the study of black hole dynamics and interiors free from Einstein's theory limitations.

Contribution

It introduces a comprehensive framework for spherically symmetric field equations beyond general relativity, including proofs and models for regular black holes.

Findings

Proof of Birkhoff--Jebsen theorem for vacuum solutions

Construction of equations for regular black hole geometrodynamics

Tools for exploring black hole interiors beyond Einstein's theory

Abstract

According to general relativity, black holes are incomplete, which prevents developing a complete physical description of their dynamical formation and evolution once quantum effects are taken into account. Theories beyond general relativity may provide a more complete description of black hole interiors. In this work, the most general form of the field equations for spherically symmetric gravitational fields, in which the Einstein tensor is deformed into a conserved tensor constructed from up to second-order derivatives of the metric, is described. These equations set up the stage for the study of the dynamics of spherically symmetric spacetimes beyond general relativity, providing tools for the theoretical exploration of a paradigm of black hole physics free of the incompleteness characteristic of Einstein's theory. A general proof of the Birkhoff--Jebsen theorem for vacuum solutions, and the construction of field equations describing the effective geometrodynamics of regular black holes interacting with matter, are discussed.