Spherically symmetric black holes in minimally modified self-dual gravity

TL;DR

This paper explores spherically symmetric black holes in a modified self-dual gravity theory, revealing unique singularity structures and charge screening effects that differ from classical general relativity.

Contribution

It extends the modified self-dual gravity to include electromagnetic fields and analyzes black hole solutions, highlighting the nature of singularities and charge screening phenomena.

Findings

Existence of true and non-metric singularities in the theory.

Charge screening or anti-screening effects modify black hole charge limits.

Singularities are generally hidden behind horizons or within non-metric regions.

Abstract

We discuss spherically symmetric black holes in the modified self-dual theory of gravity recently studied by Krasnov, obtained adding a Weyl-curvature dependent `cosmological term' to the Plebanski lagrangian for general relativity. This type of modified gravity admits two different types of singularities: one is a true singularity for the theory where the fundamental fields of the theory, as well as the (auxiliary) spacetime metric, become singular, and the other one is a milder "non-metric singularity" where the metric description of the spacetime breaks down but the fundamental fields themselves are regular. We first generalise this modified self-dual gravity to include Maxwell's field and then study basic features of spherically symmetric, charged black holes, with particular focus on whether these two types of singularities are hidden or naked. We restrict our attention to minimal forms of the modification, and find that the theory exhibits `screening' effects of the electric charge (or `anti-screening', depending upon the sign of the modification term), in the sense that it leads to the possibility of charging the black hole more (or less) than it would be possible in general relativity without exposing a naked singularity. We also find that for any (even arbitrarily large) value of charge, true singularities of the theory appear to be either achronal (non-timelike) covered by the hypersurface of a harmless non-metric singularity, or simply hidden inside at least one Killing horizon.