Extremal black holes and holographic c-theorem

Yongjoon Kwon; Soonkeon Nam; Jong Dae Park; Sang Heon Yi

doi:10.1016/j.nuclphysb.2012.12.016

Extremal black holes and holographic c-theorem

Yongjoon Kwon
, Soonkeon Nam
, Jong Dae Park
, Sang Heon Yi

Research output: Contribution to journal › Article › peer-review

6 Citations (Scopus)

Abstract

We found Bogomol'nyi type of the first order differential equations in three-dimensional Einstein gravity and the effective second order ones in new massive gravity when an interacting scalar field is minimally coupled. Using these equations in Einstein gravity, we obtain analytic solutions corresponding to extremally rotating hairy black holes. We also obtain perturbatively extremal black hole solutions in new massive gravity using these lower order differential equations. All these solutions have the anti-de Sitter spaces as their asymptotic geometries and as the near horizon ones. This feature of solutions interpolating two anti-de Sitter spaces leads to the construction of holographic c-theorem in these cases. Since our lower order equations reduce naturally to the well-known equations for domain walls, our results can be regarded as the natural extension of domain walls to more generic cases.

Original language	English
Pages (from-to)	189-215
Number of pages	27
Journal	Nuclear Physics B
Volume	869
Issue number	2
DOIs	https://doi.org/10.1016/j.nuclphysb.2012.12.016
Publication status	Published - 11 Apr 2013

Bibliographical note

Funding Information:
S.N. and S.H.Y. were supported by the National Research Foundation (NRF) of Korea grant funded by the Korea government (MEST) through the Center for Quantum Spacetime (CQUeST) of Sogang University with grant number 2005-0049409 . S.H.Y. was supported by Basic Science Research Program through the NRF of Korea funded by the MEST ( 2012R1A1A2004410 ). S.H.Y. would like to thank Prof. Won Tae Kim for some useful discussions. J.D.P. was supported by a grant from the Kyung Hee University in 2009 ( KHU-20110060 ) and Basic Science Research Program through the NRF of Korea funded by the MEST ( 2012R1A1A2008020 ). S.N. was supported by Basic Science Research Program through the NRF of Korea funded by the MEST (No. 2012-0001955 ). Y.K. was supported by the NRF of Korea grant funded by the Korean government (MEST) ( NRF-2011-355-C00027 ). Y.K. would like to thank Dr. Hyojoong Kim for some helpful discussions.

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title = "Extremal black holes and holographic c-theorem",

abstract = "We found Bogomol'nyi type of the first order differential equations in three-dimensional Einstein gravity and the effective second order ones in new massive gravity when an interacting scalar field is minimally coupled. Using these equations in Einstein gravity, we obtain analytic solutions corresponding to extremally rotating hairy black holes. We also obtain perturbatively extremal black hole solutions in new massive gravity using these lower order differential equations. All these solutions have the anti-de Sitter spaces as their asymptotic geometries and as the near horizon ones. This feature of solutions interpolating two anti-de Sitter spaces leads to the construction of holographic c-theorem in these cases. Since our lower order equations reduce naturally to the well-known equations for domain walls, our results can be regarded as the natural extension of domain walls to more generic cases.",

author = "Yongjoon Kwon and Soonkeon Nam and Park, \{Jong Dae\} and Yi, \{Sang Heon\}",

note = "Funding Information: S.N. and S.H.Y. were supported by the National Research Foundation (NRF) of Korea grant funded by the Korea government (MEST) through the Center for Quantum Spacetime (CQUeST) of Sogang University with grant number 2005-0049409 . S.H.Y. was supported by Basic Science Research Program through the NRF of Korea funded by the MEST ( 2012R1A1A2004410 ). S.H.Y. would like to thank Prof. Won Tae Kim for some useful discussions. J.D.P. was supported by a grant from the Kyung Hee University in 2009 ( KHU-20110060 ) and Basic Science Research Program through the NRF of Korea funded by the MEST ( 2012R1A1A2008020 ). S.N. was supported by Basic Science Research Program through the NRF of Korea funded by the MEST (No. 2012-0001955 ). Y.K. was supported by the NRF of Korea grant funded by the Korean government (MEST) ( NRF-2011-355-C00027 ). Y.K. would like to thank Dr. Hyojoong Kim for some helpful discussions. ",

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doi = "10.1016/j.nuclphysb.2012.12.016",

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AU - Nam, Soonkeon

AU - Park, Jong Dae

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PY - 2013/4/11

Y1 - 2013/4/11

N2 - We found Bogomol'nyi type of the first order differential equations in three-dimensional Einstein gravity and the effective second order ones in new massive gravity when an interacting scalar field is minimally coupled. Using these equations in Einstein gravity, we obtain analytic solutions corresponding to extremally rotating hairy black holes. We also obtain perturbatively extremal black hole solutions in new massive gravity using these lower order differential equations. All these solutions have the anti-de Sitter spaces as their asymptotic geometries and as the near horizon ones. This feature of solutions interpolating two anti-de Sitter spaces leads to the construction of holographic c-theorem in these cases. Since our lower order equations reduce naturally to the well-known equations for domain walls, our results can be regarded as the natural extension of domain walls to more generic cases.

AB - We found Bogomol'nyi type of the first order differential equations in three-dimensional Einstein gravity and the effective second order ones in new massive gravity when an interacting scalar field is minimally coupled. Using these equations in Einstein gravity, we obtain analytic solutions corresponding to extremally rotating hairy black holes. We also obtain perturbatively extremal black hole solutions in new massive gravity using these lower order differential equations. All these solutions have the anti-de Sitter spaces as their asymptotic geometries and as the near horizon ones. This feature of solutions interpolating two anti-de Sitter spaces leads to the construction of holographic c-theorem in these cases. Since our lower order equations reduce naturally to the well-known equations for domain walls, our results can be regarded as the natural extension of domain walls to more generic cases.

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DO - 10.1016/j.nuclphysb.2012.12.016

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VL - 869

SP - 189

EP - 215

JO - Nuclear Physics B

JF - Nuclear Physics B

IS - 2

ER -

Extremal black holes and holographic c-theorem

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