Related papers: A Commentary on Ruppeiner Metrics for Black Holes
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…
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…
In some recent studies \cite{aman1, aman2, aman3}, Aman {\it et al.} used the Ruppeiner scalar as a measure of underlying interactions of Reissner-Nordstr\"{o}m black holes, indicating that it is a non-interacting statistical system for…
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…
Thermodynamic Riemannian geometry provides great insights into the microscopic structure of black holes (BHs). One such example is the Ruppeiner geometry which is the metric space comprising the second derivatives of entropy with respect to…
In this paper we show that the vanishing of the scalar curvature of Ruppeiner-like metrics does not characterize the ideal gas. Furthermore, we claim through an example that flatness is not a sufficient condition to establish the absence of…
The thermodynamics of black holes is reformulated within the context of the recently developed formalism of geometrothermodynamics. This reformulation is shown to be invariant with respect to Legendre transformations, and to allow several…
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…
We explore purely metric theories of gravity with second-order equations of motion and a single additional, purely gravitational, propagating, scalar degree of freedom. We identify a subclass of these theories in which this scalar causes a…
Some well-known metrics used as models of static non-rotating black holes are considered. These are the Reissner-Nordstrom-de Sitter, Bardeen-Kiselev and McVittie models. A significant difference between them in how adequately they can…
We study a multiply warped products manifold associated with the Reissner-Nordstrom metric to investigate the physical properties inside the black hole event horizons. It is shown that, different from the uncharged Schwarzschild metric, the…
The metric for a Reissner-Nordstr$\ddot{o}$m black hole in the background of the Friedman-Robertson-Walker universe is obtained. Then we verified it and discussed the influence of the evolution of the universe on the size of the black hole.…
We resolve the controversial issue of the geometric approach to the black hole thermodynamics. The geometric description of the equilibrium thermodynamics comes from Ruppeiner geometry based on a metric on the thermodynamic state space. For…
We study the thermodynamics and the thermodynamic geometries of charged rotating BTZ (CR-BTZ) black holes in (2+1)-gravity. We investigate the thermodynamics of these systems within the context of the Weinhold and Ruppeiner thermodynamic…
In recent years there have appeared in the literature a large number of static, spherically symmetric metrics, which are regular at the origin, asymptotically flat, and have both an event and a Cauchy horizon for certain range of the…
Some thermodynamic properties of the Ba\~nados-Teitelboim-Zanelli (BTZ) black hole are studied to get the effective dimension of its corresponding statistical model. For this purpose, we make use of the geometrical approach to the…
In this paper we try to clarify that a regular metric can generate a singular spacetime. Our work focuses on a static and spherically symmetric spacetime in which regularity exists when all components of the Riemann tensor are finite. There…
An important phase transition in black hole thermodynamics is associated with the divergence of the specific heat with fixed charge and angular momenta, yet one can demonstrate that neither Ruppeiner's entropy metric nor Weinhold's energy…
The connection between the shadow radius and the Ruppeiner geometry of a charged static spherically symmetric black hole is investigated. The normalized curvature scalar is adopted, and its close relation to the Van der Waals-like and…
Under the framework of thermodynamics, the phase transition of the black hole is a general issue in general relativity. In this work, the phase transition of charged black holes is discussed carefully. The metric tensor of thermodynamics is…