Regular black holes without mass-inflation instability and gravastars from modified gravity

Abstract

We derive regular black-hole solutions, including the Hayward metric, from four-dimensional action principles involving vector fields in addition to the metric. These black holes possess additional hair associated with the vector fields, manifesting as free integration constants that regularize the geometry. These constants can be chosen such that regular black holes of all masses are extremal. As a result, they have vanishing surface gravity and are not susceptible to mass-inflation instability. We also discover another regular black-hole metric with these properties, which constitutes a gravastar for an appropriate choice of integration constant.

Figures (2)

• Figure 1: Upper panel: Our solutions depend on two integration constants, $q_a$ and $q_b$, here combined with the BH mass $M$ and the beyond-GR scale $\ell$ into dimensionless quantities. For $q_b = -q_a$, the BHs are regular, and for $q_a = 16M^3/(27\ell^2)$ they are extremal. The green star marks the largest $|q_{a,b}|$ for which horizonless objects have light rings. Lower panel: The Hayward extremality bound $M = (3 \sqrt{3} \ell)/4$ (red line) sets a limit below which no BHs exist described by Eq. \ref{['eq:hayward']}. In contrast, in our theory, choosing $q_a$ as indicated by the contours, yields an extremal, regular BH for any $M$ and $\ell$.
• Figure 2: Upper panel: The metric function in Eq. \ref{['eq:newregular']} describes a regular object that reduces to a gravastar in the limit $Q = \lambda$, and smoothly departs from this regime as $Q > \lambda$ increases. Lower panel: space of solutions in the $\lambda-Q$ plane.