A no-go theorem for regular black holes

TL;DR

This paper proves a no-go theorem showing that regular black holes cannot be generated from a Lagrangian theory without Schwarzschild-like terms, establishing fundamental limitations on such models.

Contribution

It demonstrates that solutions must include a Schwarzschild-like term and that certain conditions are equivalent, revealing intrinsic constraints on regular black hole models.

Findings

Any Lagrangian-based regular black hole solution includes a $c/r$ term.

Under specific conditions, the metric components satisfy $g_{00}g_{11} = -1$.

The $c/r$ term is the only non-Lagrangian singularity in these solutions.

Abstract

In this article we discuss a no-go theorem for generating regular black holes from a Lagrangian theory. We prove that the general solution has always a Schwarzschild-like term $c/r$, as long as the matter Lagrangian depends neither on the metric, nor on its derivatives; we also prove that, under suitable additional conditions, these two conditions are also equivalent to $g_{00}g_{11} = -1$. Finally, we prove that $c/r$ is the only non-Lagrangian singularity eventually present into the solution.