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A Lifshitz black hole in four dimensional R2 gravity

Rong-Gen Cai, Yan Liu and Ya-Wen Sun

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We consider a higher derivative gravity theory in four dimensions with a negative cosmological constant and show that vacuum solutions of both Lifshitz type and Schrödinger type with arbitrary dynamical exponent z exist in this system. Then we find an analytic black hole solution which asymptotes to the vacuum Lifshitz solution with z = 3/2 at a specific value of the coupling constant. We analyze the thermodynamic behavior of this black hole and find that the black hole has zero entropy while non-zero temperature, which is very similar to the case of BTZ black holes in new massive gravity at a specific coupling. In addition, we find that the three dimensional Lifshitz black hole recently found by E. Ayon-Beato et al. has a negative entropy and mass when the Newton constant is taken to be positive.

Keywords

Black Holes

Gauge-gravity correspondence

 

E-print Number: 0909.2807

Cited: by |

Refers: to

PACS

04.70.Dy Quantum aspects of black holes, evaporation, thermodynamics

05.70.Ce Thermodynamic functions and equations of state

98.80.Cq Particle-theory and field-theory models of the early Universe (including cosmic pancakes, cosmic strings, chaotic phenomena, inflationary universe, etc.)

04.60.-m Quantum gravity

Subjects

Gravitation and cosmology

Statistical physics and nonlinear systems

Astrophysics and astroparticles

Dates

Issue 10 (October 2009)

Received 18 September 2009, accepted for publication 14 October 2009

Published 27 October 2009



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