# Rotating 5D Black Holes: Interactions and deformations near extremality

### Submission summary

 As Contributors: Alejandra Castro · Juan Pedraza · Chiara Toldo Arxiv Link: https://arxiv.org/abs/2106.00649v3 (pdf) Date accepted: 2021-10-22 Date submitted: 2021-10-15 11:27 Submitted by: Toldo, Chiara Submitted to: SciPost Physics Academic field: Physics Specialties: High-Energy Physics - Theory Approach: Theoretical

### Abstract

We study a two-dimensional theory of gravity coupled to matter that is relevant to describe holographic properties of black holes with a single rotational parameter in five dimensions (with or without cosmological constant). We focus on the near-horizon geometry of the near-extremal black hole, where the effective theory reduces to Jackiw-Teitelboim (JT) gravity coupled to a massive scalar field. We compute the corrections to correlation functions due to cubic interactions present in this theory. A novel feature is that these corrections do not have a definite sign: for AdS$_5$ black holes the sign depends on the mass of the extremal solution. We discuss possible interpretations of these corrections from a gravitational and holographic perspective. We also quantify the imprint of the JT sector on the UV region, i.e. how these degrees of freedom, characteristic for the near-horizon region, influence the asymptotically far region of the black hole. This gives an interesting insight on how to interpret the IR modes in the context of their UV completion, which depends on the environment that contains the black hole.

###### Current status:
Publication decision taken: accept

Editorial decision: For Journal SciPost Physics: Publish
(status: Editorial decision fixed and (if required) accepted by authors)

First of all, we would like to thank the referees for their useful comments and remarks on our manuscript, especially those regarding possible further directions. Following their suggestions, we have elucidated some points in the text, and made minor revisions to the manuscript.

### List of changes

We have done the following modifications:

1) We have replaced the descriptor with a single rotational parameter'' with with equal angular momenta,'' as requested.

2) We have added the example of the Myers Perry solution in section 2.2, where we begin describing the procedure of dimensional reduction, as requested.

3) We thank the referee for mentioning KK BHs. The KK black hole in hep-th/9809063 is exactly the 5D Myers-Perry solution we are studying, and we have added a remark in section 2.2 to make this explicit. The solutions in hep-th/0701150 (which is based on solutions constructed in hep-th/0002166) are much more complicated to study and, while interesting per se, are outside our scope. We suggested instead to consider the solutions in 1009.5039 as a possible extension, which is now mentioned on page 27.

4) We added a remark at the end of section 3.5 (after eqn (3.48)) to stress that the background that has $\tilde{D}=0$ requires further attention. We are indeed very puzzled about it, and explored various possibilities in section 5, but it remains an open problem to understand why the value of $q = 2.85$ is special.

5) We added a paragraph in section 5, page 27, to highlight other black holes for which our methods and setup can easily be extended. This includes other rotating black holes that would be as tractable as ours, and solutions in de Sitter. Some of these points are currently under investigation and we hope to report on them, in separate papers, soon. We also remark that adding rotation in 4D or considering a black ring configuration can be very cumbersome due to the intricate way that the rotational parameters enter in the geometry. This makes it more difficult to capture dynamical aspects of near-AdS$_2$, and we remark how one could perhaps overcome them.