Dolan, Brian P.
(2015)
The intrinsic curvature of thermodynamic
potentials for black holes with critical points.
Working Paper.
ArXiv.
Abstract
The geometry of thermodynamic state space is studied for asymptotically
antide Sitter black holes in Ddimensional space times. Convexity of thermodynamic
potentials and the analytic structure of the response functions is
analysed. The thermodynamic potentials can be used to define a metric on
the space of thermodynamic variables and two commonly used such metrics
are theWeinhold 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
behaviour.
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 behaviour is not visible in the singularities of the thermodynamic
Ricci scalar.
Item Type: 
Monograph
(Working Paper)

Keywords: 
intrinsic curvature; thermodynamic potentials; black holes; critical points; 
Academic Unit: 
Faculty of Science and Engineering > Mathematical Physics 
Item ID: 
6269 
Identification Number: 
arXiv:1504.02951 
Depositing User: 
Dr. Brian Dolan

Date Deposited: 
17 Jul 2015 14:50 
Publisher: 
ArXiv 
URI: 

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