Thermodynamics of tidal charged black holes
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We study the thermodynamics of tidal charged black holes in four dimensions. Such black holes are spherically symmetric vacuum solutions of the effective Einstein equations on the brane and are characterized by the mass m and (generalizing their general relativistic counterparts) by a second parameter, the tidal charge q. The latter is an imprint of the Weyl curvature of the 5-dimensional space-time, in which the brane is embedded. The heat capacity of the tidal charged black hole diverges on a set of measure zero of the parameter space. However, there is no phase transition at those points, similarly to the Reissner-Nordstr\"om black hole. We investigate the thermodynamic geometry of such black holes by deriving the Weinhold and the Ruppeiner metrics. Whereas the Weinhold metric is flat, the Ruppeiner metric has a positive Ricci curvature, which is in sharp contrast with the Reissner-Nordstr\"om black hole, the general relativistic analogue of the tidal charged metric. The state space is conformal to the right half of the interior of the future light cone in a Minkowski plane. We find two constraints on the possible 5-dimensional extensions of the tidal-charged black hole: First, we conjecture that the 5-dimensional black object should have the same entropy as its 4-dimensional section studied here, modulo corrections which are small for large black holes. Second, for constant m any quasi-stationary evolution of the tidal charged black hole leads to a decrease of q, contributing towards the localization of gravity on the brane. This represents an important constraint on the evolution of the 5-dimensional space-time.
black holes, thermodynamics, tidal charged, braneworld
Other Physics Topics
Research subject Theoretical Physics
IdentifiersURN: urn:nbn:se:su:diva-29361OAI: oai:DiVA.org:su-29361DiVA: diva2:232733