Rotating black holes in Randall-Sundrum II braneworlds

TL;DR

This paper numerically constructs rotating black hole solutions in the Randall-Sundrum II braneworld model, revealing how their properties transition from four-dimensional Kerr-like behavior to five-dimensional Myers-Perry characteristics depending on their size relative to the AdS length scale.

Contribution

The study provides the first numerical solutions for rotating black holes in RSII, demonstrating the transition between four- and five-dimensional behaviors based on black hole size.

Findings

Large black holes behave like Kerr black holes in 4D

Small black holes resemble 5D Myers-Perry black holes

Departure from pure 4D gravity affects phenomenological predictions

Abstract

We find rotating black hole solutions in the Randall-Sundrum II (RSII) model, by numerically solving a three-dimensional PDE problem using pseudospectral collocation methods. We compute the area and equatorial inner-most stable orbits of these solutions. For large black holes compared with the AdS length scale, $\ell$, the black hole exhibits four-dimensional behaviour, approaching the Kerr metric on the brane, whilst for small black holes, the solution tends instead towards a five-dimensional Myers-Perry black hole with a single non-zero rotation parameter aligned with the brane. This departure from exact four-dimensional gravity may lead to different phenomenological predictions for rotating black holes in the RSII model to those in standard four-dimensional general relativity. This letter provides a stepping stone for studying such modifications.