Dolan, Brian P. (2015) Intrinsic curvature of thermodynamic potentials for black holes with critical points. Physical Review D, 92 (004013). ISSN 1550-7998

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Abstract

The geometry of thermodynamic state space is studied for asymptotically anti–de Sitter black holes in D-dimensional space-times. Convexity of thermodynamic potentials and the analytic structure of the response functions is analyzed. The thermodynamic potentials can be used to define a metric on the space of thermodynamic variables, and two commonly used such metrics are the Weinhold metric, derived from the internal energy, and the Ruppeiner metric, derived from the entropy. The intrinsic curvature of these metrics is calculated for charged and for rotating black holes, and it is shown that the curvature diverges when heat capacities diverge but, contrary to general expectations, the singularities in the Ricci scalars do not reflect the critical behavior. When a cosmological constant is included as a state space variable, it can be interpreted as a pressure and the thermodynamically conjugate variable as a thermodynamic volume. The geometry of the resulting extended thermodynamic state space is also studied, in the context of rotating black holes, and there are curvature singularities when the heat capacity at constant angular velocity diverges and when the black hole is incompressible. Again the critical behavior is not visible in the singularities of the thermodynamic Ricci scalar.

Item Type:	Article
Keywords:	Intrinsic curvature; thermodynamic potentials; black holes; critical points;
Academic Unit:	Faculty of Science and Engineering > Mathematical Physics
Item ID:	10482
Identification Number:	https://doi.org/10.1103/PhysRevD.92.044013
Depositing User:	Dr. Brian Dolan
Date Deposited:	13 Feb 2019 16:44
Journal or Publication Title:	Physical Review D
Publisher:	American Physical Society
Refereed:	Yes
URI:	https://journals.aps.org/prd/
Use Licence:	This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here

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