The Chern-Simons Caps for Rotating Black Holes

TL;DR

This paper explores how dynamical Chern-Simons gravity modifies rotating black holes, revealing novel cap-like structures with unusual properties that challenge traditional singularity theorems.

Contribution

It demonstrates that within a valid parameter range, rotating black holes develop unique geometric caps due to Chern-Simons effects, a novel feature not previously described.

Findings

Black holes acquire cap-like domains at poles

Caps extend a few percent of the black hole's size

Geodesic focusing conditions are violated in caps

Abstract

We study the dynamical Chern-Simons gravity as an effective quantum field theory, and discuss a broad range of its parameter space where the theory is valid. Within that validity range, we show that slowly rotating black holes acquire novel geometric structures due to the gravitational dynamical Chern-Simons term. In particular, the rotating black hole solutions get endowed with two, cap-like domains, emanating from the north and south poles in the standard Boyer-Lindquist coordinates. The domains extend out to a distance that is approximately a few percent of the black hole's size. The cap-like domains have an unusual equation of state, pointing to non-standard dynamics within the caps. In particular, the focusing condition for geodesics is violated in those domains. This in turn implies that the Hawking-Penrose singularity theorem cannot be straightforwardly applied to hypothetical probe matter placed within the Chern-Simons caps.