A Note on Thermodynamics of Black Holes in Lovelock Gravity

By R. Cai. 2003

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Abstract The Lovelock gravity consists of the dimensionally extended Euler densities. The geometry and horizon structure of black hole solutions could be quite complicated in this gravity, however, we find that some thermodynamic quantities of the black holes like the mass, Hawking temperature and entropy, have simple forms expressed in terms of horizon radius. The case with black hole horizon being a Ricci flat hypersurface is particularly simple. In that case the black holes are always thermodynamically stable with a positive heat capacity and their entropy still obeys the area formula, which is no longer valid for black holes with positive or negative constant curvature horizon hypersurface. In addition, for black holes in the gravity theory of Ricci scalar plus a 2n-dimensional Euler density with a positive coefficient, thermodynamically stable small black holes always exist in D=2n+1 dimensions, which are absent in the case without the Euler density term, while the thermodynamic properties of the black hole solutions with the Euler density term are qualitatively similar to those of black holes without the Euler density term as D>2n+1.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/2cba81dbf529d73374bb5952749a7621cfd7bed8

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Citations in the corpus

Causality in AdS/CFT and Lovelock theory (2009, background): “This is general for any Lovelock black hole of the type considered here, since the only term that contributes to the temperature is the Einstein-Hilbert one and the area law for the entropy has also been found to be valid in general for Lovelock black holes with flat horizons [36].”
Multiple reentrant phase transitions and triple points in Lovelock thermodynamics (2014, background): “The black hole mass M , the temperature T , the entropy S, and the gauge potential Φ are given by [62]”
Holographic calculations of Rényi entropy (2011, methodology): “Relevant for the present analysis, asymptotically AdS black hole solutions with hyperbolic horizons were found for GB gravity in [29].”
The Lovelock Black Holes (2008, background): “References [100, 101, 102] also analyze topological black holes and their thermodynamics; see also [77, 103].”
Smarr formula and an extended first law for Lovelock gravity (2010, methodology): “7 See also [14, 61, 62] for further discussions of the thermodynamic and stability properties of Lovelock black holes.”
On Gauss-Bonnet black hole entropy (2004, background): “(2)The entropy for the more general Lovelock Lagrangian was studied in [42, 43].”
Isolated critical point from Lovelock gravity (2014, background): “The odd-order Lovelock theories (in any dimension in which they exist) all have massless topological black holes [15, 16, 19] as solutions, and so will exhibit this phenomenon for an appropriate choice of coupling constants.”