Regular spacetimes in the effective metric description

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) (Binetti et al. in Phys Rev D 106(4):046006, 2022. https://doi.org/10.1103/PhysRevD.106.046006 ; Del Piano et al. in Phys Rev D 109(2):024045, 2024. https://doi.org/10.1103/PhysRevD.109.024045 ; Del Piano et al. in Eur Phys J. C 84(12):1273, 2024. https://doi.org/10.1140/epjc/s10052-024-13609-5 ; Del Piano et al. in Black hole shadow and other observables away from the horizon: extending the effective metric descriptions, 2024). 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.