Gravitational Thermodynamics Research Articles

The generalized second law in phantom dominated universes in the presence of black holes

This Letter considers the generalized second law of gravitational thermodynamics in two scenarios featuring a phantom dominated expansion plus a black hole. The law is violated in both scenarios.

Dark energy and the generalized second law

We explore the thermodynamics of dark energy taking into account the existence of the observer's event horizon in accelerated universes. Except for the initial stage of Chaplygin gas dominated expansion, the generalized second law of gravitational thermodynamics is fulfilled and the temperature of the phantom fluid results positive. This substantially extends the work of Pollock and Singh [M.D. Pollock, T.P. Singh, Class. Quantum Grav. 6 (1989) 901] on the thermodynamics of super-inflationary expansion.

The library of Babel: on the origin of gravitational thermodynamics

We show that heavy pure states of gravity can appear to be mixed states to almost all probes. For AdS_5 Schwarzschild black holes, our arguments are made using the field theory dual to string theory in such spacetimes. Our results follow from applying information theoretic notions to field theory operators capable of describing very heavy states in gravity. For half-BPS states of the theory which are incipient black holes, our account is exact: typical microstates are described in gravity by a spacetime ``foam'', the precise details of which are almost invisible to almost all probes. We show that universal low-energy effective description of a foam of given global charges is via certain singular spacetime geometries. When one of the specified charges is the number of D-branes, the effective singular geometry is the half-BPS ``superstar''. We propose this as the general mechanism by which the effective thermodynamic character of gravity emerges.

Relic gravitational waves and the generalized second law

The generalized second law of gravitational thermodynamics is applied to the present era of accelerated expansion of the Universe. In spite of the fact that the entropy of matter and relic gravitational waves inside the event horizon diminish, the mentioned law is fulfilled provided that the expression for the entropy density of the gravitational waves satisfies a certain condition.

A REVIEW OF THE N-BOUND AND THE MAXIMAL MASS CONJECTURES USING NUT-CHARGED dS SPACE–TIMES

The proposed dS/CFT correspondence remains an intriguing paradigm in the context of string theory. Recently it has motivated two interesting conjectures: the entropic N-bound and the maximal mass conjecture. The former states that there is an upper bound to the entropy in asymptotically de Sitter space–times, given by the entropy of pure de Sitter space. The latter states that any asymptotically de Sitter space–time cannot have a mass larger than the pure de Sitter case without inducing a cosmological singularity. Here we review the status of these conjectures and demonstrate their limitation. We first describe a generalization of gravitational thermodynamics to asymptotically de Sitter space–times, and show how to compute conserved quantities and gravitational entropy using this formalism. From this we proceed to a discussion of the N-bound and maximal mass conjectures. We then illustrate that these conjectures are not satisfied for certain asymptotically de Sitter space–times with NUT charge. We close with a presentation of explicit examples in various space–time dimensionalities.

Constrained instanton and black hole creation

A gravitational instanton is considered as the seed for the creation of a universe. However, there exist too few instantons. To include many interesting phenomena in the framework of quantum cosmology, the concept of constrained gravitational instanton is inevitable. In this paper we show how a primordial black hole is created from a constrained instanton. The quantum creation of a generic black hole in the closed or open background is completely resolved. The relation of the creation scenario with gravitational thermodynamics and topology is discussed.

THE TOPOLOGICAL ORIGIN OF BLACK HOLE ENTROPY

In gravitational thermodynamics, the origin of a black hole's entropy is the topology of its instanton or constrained instanton. We prove that the entropy of an arbitrary nonrotating black hole is one quarter the sum of the products of the Euler characteristics of its horizons with their respective areas. The Gauss–Bonnet-like form of the action is not only crucial for the evaluation, but also for the existence of the entropy. This result covers all previous results on the entropy of a nonrotating black hole with a regular instanton. The argument can be readily extended into the lower or higher dimensional model. The problem of quantum creation of such a black hole is completely resolved.

Interacting black holes

We revisit the geometry representing l collinear Schwarzschild black holes. It is seen that the black holes' horizons are deformed by their mutual gravitational attraction. The geometry has a string like conical singularity that connects the holes but has nevertheless a well defined action. Using standard gravitational thermodynamics techniques we determine the Free energy for two black holes at fixed temperature and distance, their entropy and mutual force. When the black holes are far apart the results agree with Newtonian gravity expectations. This analyses is generalized to the case of charged black holes. Then we consider black holes embedded in String/M-theory as bound states of branes. Using the effective string description of these bound states and for large separation we reproduce exactly the semi-classical result for the entropy, including the correction associated with the interaction between the holes.

Entropy of a Black Hole with Distinct Surface Gravities

In gravitational thermodynamics, the entropy of a black hole with distinct surface gravities can be evaluated in a microcanonical ensemble. At the WKB level, the entropy becomes the negative of the Euclidean action of the constrained instanton, which is the seed for the black hole creation in the no-boundary universe. Using the Gauss-Bonnet theorem, we prove the quite universal formula in Euclidean quantum gravity that the entropy of a nonrotating black hole is one quarter the sum of the products of the Euler characteristics and the areas of the horizons. For Lovelock gravity, the entropy and quantum creation of a black hole are also studied.

Negative specific heat in astronomy, physics and chemistry

Starting from Antonov's discovery that there is no maximum to the entropy of a gravitating system of point particles at fixed energy in a spherical box if the density contrast between centre and edge exceeds 709, we review progress in the understanding of gravitational thermodynamics. We pinpoint the error in the proof that all systems have positive specific heat and say when it can occur. We discuss the development of the thermal runaway in both the gravothermal catastrophe and its inverse. The energy range over which microcanonical ensembles have negative heat capacity is replaced by a first order phase transition in the corresponding canonical ensembles. We conjecture that all first order phase transitions may be viewed as caused by negative heat capacities of units within them. We find such units in the theory of ionization, chemical dissociation and in the Van der Waals gas so these concepts are applicable outside the realm of stars, star clusters and black holes.

The postulates of gravitational thermodynamics.

The general principles and logical structure of a thermodynamic formalism that incorporates strongly self-gravitating systems are presented. This framework generalizes and simplifies the formulation of thermodynamics developed by Callen. The definition of extensive variables, the homogeneity properties of intensive parameters, and the fundamental problem of gravitational thermodynamics are discussed in detail. In particular, extensive parameters include quasilocal quantities and are naturally incorporated into a set of basic general postulates for thermodynamics. These include additivity of entropies (Massieu functions) and the generalized second law. Fundamental equations are no longer homogeneous first-order functions of their extensive variables. It is shown that the postulates lead to a formal resolution of the fundamental problem despite non-additivity of extensive parameters and thermodynamic potentials. Therefore, all the results of (gravitational) thermodynamics are an outgrowth of these postulates. The origin and nature of the differences with ordinary thermodynamics are analyzed. Consequences of the formalism include the (spatially) inhomogeneous character of thermodynamic equilibrium states, a reformulation of the Euler equation, and the absence of a Gibbs-Duhem relation.

On the canonical reduction of spherically symmetric gravity

In a thorough paper Kuchar has examined the canonical reduction of the most general action functional describing the geometrodynamics of the maximally extended Schwarzschild geometry. This reduction yields the true degrees of freedom for (vacuum) spherically symmetric general relativity (SSGR). The essential technical ingredient in Kuchar's analysis is a canonical transformation to a certain chart on the gravitational phase space which features the Schwarzschild mass parameter , expressed in terms of what are essentially Arnowitt - Deser - Misner variables, as a canonical coordinate. (Kuchar's paper complements earlier work by Kastrup and Thiemann, based mostly on Ashtekar variables, which has also explicitly isolated the true degrees of freedom for vacuum SSGR.) In this paper we discuss the geometric interpretation of Kuchar's canonical transformation in terms of the theory of quasilocal energy - momentum in general relativity given by Brown and York. We find Kuchar's transformation to be a `sphere-dependent boost to the rest frame', where the `rest frame' is defined by vanishing quasilocal momentum. Furthermore, our formalism is general enough to cover the case of (vacuum) two-dimensional dilaton gravity. Therefore, besides reviewing Kuchar's original work for Schwarzschild black holes from the framework of hyperbolic geometry, we present new results concerning the canonical reduction of Witten black-hole geometrodynamics. Finally, addressing a recent work of Louko and Whiting, we discuss some delicate points concerning the canonical reduction of the `thermodynamical action', which is of central importance in the path-integral formulation of gravitational thermodynamics.

Black holes and gravitational thermodynamics

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 chi =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.

The role of gravitation in thermal physics (and thermo field theory)

With his introduction of quantum mechanical considerations in the treatment of gravitating systems, Hawking indicated a way for the inclusion of general relativity into quantum (and, in particular, thermal) physics. However, probably the single most difficult phenomenon to deal with, subsequent to his work, has been the gravitational attraction of the very feature which his work leads to, viz, the thermal bath surrounding a black hole in equilibrium. It was not until York introduced a finite containing box for the system that certain problematical infinities could be removed and the treatment became well defined, with a sensible, describable, thermodynamic limit, and the possibility of finally realizing a satisfactory canonical ensemble for a black hole in a box. Gravitating systems could then be described thermodynamically, and the problem naturally admitted a path integral formulation which has been used to determine the contribution of non-classical geometries to the partition function for the black hole topological sector of the gravitational field. The application of this method to more familiar problems with a fixed space-time suggests an explicit interpretation of the theory of thermo field dynamics when thermal disturbances of the gravitational field can be ignored. This particular understanding may be extended to include small perturbative fluctuations of the geometry (loosely called gravitons) but it seems inappropriate for dealing with the actual structure of the space-time manifold, whereas gravitational thermodynamics, as referred to above, would remain perfectly adequate.

Gravitational thermodynamics and the generalized second law

We survey the statistical thermodynamics of systems, occurring in astrophysics, whose properties are dominated by gravitational forces. In the non-relativistic case, the lack of extensivity of these systems leads to a non-standard thermodynamics, with a two-phase region in which the microcanonical specific heat is negative. In the relativistic case, there arises the phenomenon of gravitational collapse, in which stars become black holes. We argue that, since these systems have no microstructure that can be observed from outside, the statistical mechanical concepts of microstates and entropy are inapplicable to them. Accordingly, we formulate the thermodynamics of processes, in which a black hole participates, in terms of observable quantities that govern changes in the Gibbs potential of the open system constituting the exterior region. By a simple argument, based only on general demands of quantum theory, relativity and statistical thermodynamics, we infer that the sum of the entropy of the exterior region and a universal constant times the area of the black hole does not decrease in any process. This is precisely the generalized second law, first proposed by Bekenstein on the basis of the hypothesis that a black hole has an entropy proportional to its surface area. By contrast, our derivation of this law does not involve any concept of black hole entropy, since it is based on the statistical thermodynamics of observable open systems.

Thermodynamics and galaxy clustering - Relaxation of N-body experiments

view Abstract Citations (25) References (8) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Thermodynamics and galaxy clustering - Relaxation of N-body experiments Saslaw, W. C. Abstract An examination of computer N-body experiments for galaxy clustering is reported. The examination shows that initial conditions over a fairly wide range relax toward the distribution predicted by gravitational thermodynamics. Insofar as the observed galaxy distribution also has this form, it will not readily yield information about its initial distribution or about omega-sub-zero. Publication: The Astrophysical Journal Pub Date: October 1985 DOI: 10.1086/163502 Bibcode: 1985ApJ...297...49S Keywords: Galactic Clusters; Gravitational Effects; Many Body Problem; Relaxation Method (Mathematics); Thermodynamics; Computational Astrophysics; Mass Distribution; Astrophysics full text sources ADS |