JT gravity and near-extremal thermodynamics for Kerr black holes in \(AdS_{4, 5}\) for rotating perturbations

DOI10.1007/JHEP02(2023)132arXiv2212.12332OpenAlexW4320881649MaRDI QIDQ6041729

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Publication date: 12 May 2023

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Abstract: We study the near horizon 2d gravity theory which captures the near extremal thermodynamics of Kerr black holes where a linear combination of excess angular momentum

d e l t a J

and excess mass

d e l t a M

is held fixed. These correspond to processes where both the mass and the angular momenta of extremal Kerr black holes are perturbed leaving them near extremal. For the Kerr

A d S_{4}

we hold

d e l t a J - m a t h c a l L, d e l t a M = 0

while for Myers-Perry(MP) type Kerr black hole in

A d S_{5}

we hold

d e l t a J_{v a r p h i_{1, 2}} h s p a c e - 0.2 c m - m a t h c a l L_{v a r p h i_{1, 2}}, d e l t a M = 0

. We show that in near horizon, the 2d Jackiw-Teitelboim theory is able to capture the thermodynamics of the higher dimensional black holes at small near extremal temperatures

T_{H}

. We show this by generalizing the near horizon limits found in literature by parameters

m a t h c a l L

and

m a t h c a l L_{v a r p h i_{1, 2}}

for the two geometries. The resulting JT theory captures the near extremal thermodynamics of such geometries provided we identify the temperature

T_{H}^{(2)}

of the near horizon

A d S_{2}

geometry to be

T_{H}^{(2)} = T_{H} / (1 - m u, m a t h c a l L)

for 4d Kerr and

T_{H}^{(2)} = T_{H} / (1 - m u, (m a t h c a l L_{v a r p h i_{1}} + m a t h c a l L_{v a r p h i_{2}}))

for 5d Kerr where

m u

is their chemical potential, with

m u, m a t h c a l L < 1

and

m u, (m a t h c a l L_{v a r p h i_{1}} + m a t h c a l L_{v a r p h i_{2}}) < 1

respectively. We also argue that such a theory embeds itself non-trivially in the higher dimensional theory dual to the Kerr geometries.

Full work available at URL: https://arxiv.org/abs/2212.12332

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