Thermodynamic instability of rotating black holes

Journal Article · Wed Jul 15 00:00:00 EDT 2009 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.80.024041· OSTI ID:21316264

Monteiro, R; Perry, M J; Santos, J E ^[1]

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1. DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA (United Kingdom)

We show that the quasi-Euclidean sections of various rotating black holes in different dimensions possess at least one nonconformal negative mode when thermodynamic instabilities are expected. The boundary conditions of the fixed induced metric correspond to the partition function of the grand-canonical ensemble. Indeed, in the asymptotically flat cases, we find that a negative mode persists even if the specific heat at constant angular momenta is positive, since the stability in this ensemble also requires the positivity of the isothermal moment of inertia. We focus, in particular, on Kerr black holes, on Myers-Perry black holes in five and six dimensions, and on the Emparan-Reall black ring solution. We go on further to consider the richer case of the asymptotically AdS Kerr black hole in four dimensions, where thermodynamic stability is expected for a large enough cosmological constant. The results are consistent with previous findings in the nonrotation limit and support the use of quasi-Euclidean instantons to construct gravitational partition functions.

• OSTI ID: 21316264
• Journal Information: Physical Review. D, Particles Fields, Vol. 80, Issue 2; Other Information: DOI: 10.1103/PhysRevD.80.024041; (c) 2009 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

79 ASTROPHYSICS
COSMOLOGY AND ASTRONOMY
99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE
ANGULAR MOMENTUM
ANTI DE SITTER SPACE
BLACK HOLES
BOUNDARY CONDITIONS
COSMOLOGICAL CONSTANT
EUCLIDEAN SPACE
GRAVITATIONAL FIELDS
INSTABILITY
INSTANTONS
KERR FIELD
MANY-DIMENSIONAL CALCULATIONS
MATHEMATICAL SOLUTIONS
METRICS
MOMENT OF INERTIA
PARTITION FUNCTIONS
SPECIFIC HEAT
STABILITY