Regular Spacetimes in the Effective Metric Description

TL;DR

This paper extends the Effective Metric Description to systematically analyze the regularity of static, spherically symmetric spacetimes, deriving conditions for curvature finiteness and geodesic completeness, and classifying spacetime cores.

Contribution

It provides a systematic framework for assessing regularity in the EMD, including conditions for curvature regularity and geodesic completeness, and applies these to known black hole models.

Findings

Derived conditions for curvature scalars to remain finite

Classified spacetime cores based on asymptotic behavior

Applied regularity criteria to known black hole solutions

Abstract

Over the past few decades, significant effort has been directed towards developing various regularized models for compact objects. Recently, a new observable-based parametrization was introduced to account for black hole deformations in a model-independent fashion, referred to as the Effective Metric Description (EMD) \cite{Binetti:2022xdi, DelPiano:2023fiw, DelPiano:2024gvw, DelPiano:2024nrl}. In this paper, we carry out a systematic investigation of the regularity of static and spherically symmetric spacetimes by extending the EMD. We derive the conditions under which curvature scalars remain finite everywhere and the associated spacetime is geodesically complete. Our results are then used to classify the cores of regular spacetimes based on their asymptotic behavior near the origin. To illustrate our findings, we apply our regularity conditions to known black hole examples.