We investigate the Ruppeiner geometry of the thermodynamic state space of a general class of BTZ black holes. It is shown that the thermodynamic geometry is flat for both the rotating BTZ and the BTZ Chern Simons black holes in the canonical ensemble. We further investigate the inclusion of thermal fluctuations to the canonical entropy of the BTZ Chern Simons black holes and show that the leading logartithmic correction due to Carlip is reproduced. We establish that the inclusion of thermal fluctuations induces a non zero scalar curvature to the thermodynamic geometry.
A microscopic characterization, based on the thermodynamic curvature R, is proposed for first-order liquid-gas phase transitions. Near the critical point, where R is proportional to the correlation volume ξ(3), we propose that R takes the same value in the coexisting phases. This proposal allows a determination of the liquid-gas coexistence curve with no use of the problematic Maxwell equal area construction. Furthermore, |R| ~ ξ(3) allows a direct determination of the Widom line in the supercritical regime. We illustrate with input from the van der Waals model and the National Institute of Standards and Technology Chemistry WebBook.
In this paper, we study various aspects of the equilibrium thermodynamic state space geometry of AdS black holes. We first examine the ReissnerNordstrom-AdS (RN-AdS) and the Kerr-AdS black holes. In this context, the state space scalar curvature of these black holes is analysed in various regions of their thermodynamic parameter space. This provides important new insights into the structure and significance of the scalar curvature. We further investigate critical phenomena, and the behaviour of the scalar curvature near criticality, for KN-AdS black holes in two mixed ensembles, introduced and elucidated in our earlier work arXiv:1002.2538 [hep-th]. The critical exponents are identical to those in the RN-AdS and KerrAdS cases in the canonical ensemble. This suggests an universality in the scaling behaviour near critical points of AdS black holes. Our results further highlight qualitative differences in the thermodynamic state space geometry for electric charge and angular momentum fluctuations of these. *
We consider D-branes wrapped around supersymmetric cycles of Calabi-Yau
manifolds from the viewpoint of N=2 Landau-Ginzburg models with boundary as
well as by consideration of boundary states in the corresponding Gepner models.
The Landau-Ginzburg approach enables us to provide a target space
interpretation for the boundary states. The boundary states are obtained by
applying Cardy's procedure to combinations of characters in the Gepner models
which are invariant under spectral flow. We are able to relate the two
descriptions using the common discrete symmetries of the two descriptions. We
are thus able to provide an extension to the boundary of the bulk
correspondence between Landau-Ginzburg orbifolds and the corresponding Gepner
models.Comment: 28 pages, LaTeX with revtex; (v2) Condition involving superpotential
in the boundary LG model imposed, references included ; (v3) final version to
appear in journa
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