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 innermost stable orbits of these solutions. For large black holes compared with the AdS length scale ℓ the black hole exhibits four-dimensional behavior, approaching the Kerr metric on the brane, while for small black holes, the solution tends instead towards a five-dimensional Myers-Perry black hole with a single nonzero 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.
Highlights
In this Letter we present the first fully backreacted, rotating black hole solution in the Randall-Sundrum II (RSII) model, by utilising the method pioneered in Ref. [24]
We found that for large rotating RSII black holes, the induced metric on the brane closely resembles the fourdimensional Kerr black hole, while small rotating RSII black holes exhibit five-dimensional behavior, approaching the five-dimensional Myers-Perry black holes [25] with a single nonzero rotation aligned with the brane
This transition from four-dimensional to five-dimensional behavior means that finite-sized RSII black holes have slightly different induced geometry on the brane to the usual four-dimensional Kerr black hole, and will lead to different phenomenological predictions for fourdimensional observers
Summary
Introduction.—For some time there has been great interest in the idea that our Universe is a brane embedded in a higher dimensional space. [11], where static, stable black hole solutions on the brane were found for both small and large radii. In order for the RSII model to be phenomenologically viable it must admit static black hole solutions, and rotating ones.
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