Quasi-homogeneous thermodynamics and black holes (original) (raw)

General symmetries: From homogeneous thermodynamics to black holes

The European Physical Journal Plus, 2011

We consider the topic of symmetries as classifying tools for thermodynamic systems. We adopt the contact geometry approach, in a general framework including standard homogeneous thermodynamics but not limited to it, and we focus our attention on the problem of the existence of a general symmetry, to be defined as a symmetry which is the same for a class of thermodynamic systems. Homogeneity symmetry of standard equilibrium thermodynamics is the paradigmatic example of general symmetry, and we point out its being associated with a multi-class thermodynamics, whose mathematical characterization is taken into account. Furthermore, quasi-homogeneity symmetry, which describes some non-extensive systems, is shown to give rise to a general symmetry, in the above sense, in the case of non-relativistic self-gravitating fermions. In the latter case, it is also conjectured to give rise to a multi-class structure. An analysis of the behavior of transversal symmetries under the partial Legendre involutions enhances a special role of quasi-homogeneity symmetry, as well as the role of special thermodynamic limit is pointed out as a tool for investigating the topic of general symmetries.

The zeroth law in quasi-homogeneous thermodynamics and black holes

Physics Letters B

Motivated by black holes thermodynamics, we consider the zeroth law of thermodynamics for systems whose entropy is a quasihomogeneous function of the extensive variables. We show that the generalized Gibbs-Duhem identity and the Maxwell construction for phase coexistence based on the standard zeroth law are incompatible in this case. We argue that the generalized Gibbs-Duhem identity suggests a revision of the zeroth law which in turns permits to reconsider Maxwell's construction in analogy with the standard case. The physical feasibility of our proposal is considered in the particular case of black holes.

Fundamental thermodynamical equation of a self-gravitating system

Physical Review D, 1996

The features of the fundamental thermodynamical relation (expressing entropy as function of state variables) that arise from the self-gravitating character of a system are analyzed. The models studied include not only a spherically symmetric hot matter shell with constant particle number but also a black hole characterized by a general thermal equation of state. These examples illustrate the formal structure of thermodynamics developed by Callen as applied to a gravitational configuration as well as the phenomenological manner in which Einstein equations largely determine the thermodynamical equations of state. We consider in detail the thermodynamics and quasi-static collapse of a self-gravitating shell. This includes a discussion of intrinsic stability for a one-parameter family of thermal equations of state and the interpretation of the Bekenstein bound. The entropy growth associated with a collapsing sequence of equilibrium states of a shell is computed under different boundary conditions in the quasi-static approximation and compared with black hole entropy. Although explicit expressions involve empirical coefficients, these are constrained by physical conditions of thermodynamical origin. The absence of a Gibbs-Duhem relation and the associated scaling laws for self-gravitating matter systems are presented.

Black hole thermodynamics and massive gravity

Journal of High Energy Physics, 2011

We consider the generalized laws of thermodynamics in massive gravity. Making use of explicit black hole solutions, we devise black hole merger processes in which i) total entropy of the system decreases ii) the zero-temperature extremal black hole is created. Thus, both second and third laws of thermodynamics are violated. In both cases, the violation can be traced back to the presence of negative-mass black holes, which, in turn, is related to the violation of the null energy condition. The violation of the third law of thermodynamics implies, in particular, that a naked singularity may be created as a result of the evolution of a singularity-free state. This may signal a problem in the model, unless the creation of the negative-mass black holes from positive-mass states can be forbidden dynamically or the naked singularity may somehow be resolved in a full quantum theory.

Extended phase-space thermodynamics of black holes in massive gravity

Modern Physics Letters A

We study the extended phase-space thermodynamics of black holes in massive gravity. Particularly, we examine the critical behavior of this black hole using the extended phase-space formalism. Extended phase-space can be defined as one in which the cosmological constant should be treated as a thermodynamic pressure and its conjugate variable as a thermodynamic volume. In this phase-space, we derive the black hole equation of state, the critical pressure, the critical volume and the critical temperature at the critical point. We also derive the critical ratio of this black hole. Moreover, we derive the black hole reduced equation of state in terms of the reduced pressure, the reduced volume and the reduced temperature. Furthermore, we examine the Ehrenfest equations of black holes in massive gravity in the extended phase-space at the critical point. We show that the Ehrenfest equations are satisfied on this black hole and the black hole encounters a second-order phase transition at th...

Thermodynamic Metrics and Black Hole Physics

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 discussion of Kerr-Newman black holes is included.

Black hole thermodynamics without a black hole?

Nuclear Physics B, 2003

In the present paper we consider, using our earlier results, the process of quantum gravitational collapse and argue that there exists the final quantum state when the collapse stops. This state, which can be called the "no-memory state", reminds the final "no-hair state" of the classical gravitational collapse. Translating the "no-memory state" into classical language we construct the classical analogue of quantum black hole and show that such a model has a topological temperature which equals exactly the Hawking's temperature. Assuming for the entropy the Bekenstein-Hawking value we develop the local thermodynamics for our model and show that the entropy is naturally quantized with the equidistant spectrum S + γ 0 N. Our model allows, in principle, to calculate the value of γ 0. In the simplest case, considered here, we obtain γ 0 = ln 2.

Black holes and gravitational thermodynamics

Classical and Quantum Gravity, 1990

The 0-loop approximation for black-hole thermodynamics is applicable only when there are globally stable classical solutions to the corresponding boundary value problem. By including contributions from a specific class of non-classical geometries and by giving a measure for the path integral compatible with the classical limit, it has been possible to evaluate corrections to the partition function of the , y = 2 topological sector, even when no classical solution exists. A density of states with very reasonable physical properties is also determined for this black-hole topology, consistent with earlier work.

Black hole thermodynamics in Carathéodory's approach

Physics Letters A, 2003

We show that, in the framework of Carathéodory's approach to thermodynamics, one can implement black hole thermodynamics by realizing that there exixts a quasihomogeneity symmetry of the Pfaffian form δQ rev representing the infinitesimal heat exchanged reversibly by a Kerr-Newman black hole; this allow us to calculate readily an integrating factor, and, as a consequence, a foliation of the thermodynamic manifold can be recovered.

A new approach toward geometrical concept of black hole thermodynamics

Motivated by the energy representation of Riemannian metric, in this paper we will study different approaches toward the geometrical concept of black hole thermodynamics. We investigate thermodynamical Ricci scalar of Weinhold, Ruppeiner and Quevedo metrics and show that their number and location of divergences do not coincide with phase transition points arisen from heat capacity. Next, we introduce a new metric to solving these problems. The denominator of the this thermodynamical metric whose Ricci scalar only contains terms that match to the phase transition of heat capacity.