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The Hessian of the entropy function can be thought of as a metric tensor on the state space. In the context of thermodynamical fluctuation theory Ruppeiner has argued that the Riemannian geometry of this metric gives insight into the underlying statistical mechanical system; the claim is supported by numerous examples. We study this geometry for some… (More)

We investigate thermodynamic curvatures of the Kerr and Reissner-Nordström (RN) black holes in spacetime dimensions higher than four. These black holes possess thermodynamic geometries similar to those in four dimensional spacetime. The thermodynamic geometries are the Ruppeiner geometry and the conformally related Weinhold geometry. The Ruppeiner geometry… (More)

The Hessian of either the entropy or the energy function can be regarded as a metric on a Gibbs surface. For two parameter families of asymptotically flat black holes in arbitrary dimension one or the other of these metrics are flat, and the state space is a flat wedge. The mathematical reason for this is traced back to the scale invariance of the… (More)

In this talk we present the latest results from our ongoing project on geometrothermodynamics (also known as information geometry of thermodynamics or Ruppeiner geometry) of dilaton BHs in 4D in both Einstein and string frames and a dyonic dilaton BH and at the end we report very briefly results from this approach to the 2D dilaton BHs. The thermodynamic… (More)

Abstract The Hessian of the entropy function can be thought of as a metric tensor on state space. In the context of thermodynamical fluctuation theory Ruppeiner has argued that the Riemannian geometry of this metric gives insight into the underlying statistical mechanical system; the claim is supported by numerous examples. We study these geometries for… (More)

The Ruppeiner metric as determined by the Hessian of the Gibbs surface provides a geometric description of thermodynamic systems in equilibrium. An interesting example is a black hole in equilibrium with its own Hawking radiation. In this article, we present results from the Ruppeiner study of various black hole families from different gravity theories e.g.… (More)

We investigate thermodynamic geometries of two families of asymptotically Anti-de Sitter black holes, i.e. the Reissner-Nordström Anti-de Sitter in four dimensions and the BTZ black hole. It is found that the Anti-de Sitter space renders the geometry nontrivial (cf. the ReissnerNordström black hole in asymptotically flat background). The BTZ black hole’s… (More)

- Jan E. Åman, Stefan Åminneborg, Ingemar Bengtsson, Narit Pidokrajt
- 2008

In 3+1 dimensions there are anti-de Sitter quotients which are black holes with toroidal event horizons. By analytic continuation of the Schwarzschildanti-de Sitter solution (and appropriate identifications) one finds two one parameter families of spacetimes that contain these quotient black holes. One of these families consists of B-metrics (“bubbles of… (More)

- Jan E. Åman, Ingemar Bengtsson, Narit Pidokrajt
- Entropy
- 2015

We give a brief survey of thermodynamic metrics, in particular the Hessian of the entropy function, and how they apply to black hole thermodynamics. We then provide a detailed discussion of the Gibbs surface of Kerr black holes. In particular, we analyze its global properties and extend it to take the entropy of the inner horizon into account. A brief… (More)

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