Gravitational Thermodynamics Research Articles

Erratum: Gravitational thermodynamics and the Wheeler–DeWitt equation

Erratum: Gravitational thermodynamics and the Wheeler–DeWitt equation

Reentrant phase transition in holographic thermodynamicsof Born–Infeld AdS black hole

In this paper, we study the phase tranisions in the extended holographic thermodynamics of Born–Infeld AdS black holes. The extended gravitational thermodynamics of black holes is related to the thermodynamics of the dual field theory by varying both cosmological constant and Newton’s constant. With topological analysis and numerical calculation, we find that the reentrant large-small-large black hole phase transition still exists in D=4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$D=4$$\\end{document}. Interestingly, a similar reentrant phase transition is also observed in the dual field theory, between the high-, low- and high-entropy thermal states. For higher dimension D>4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$D>4$$\\end{document}, only the van der Waals like phase transition is observed, both in the bulk and the dual field theory.

Thermodynamics of spherically symmetric thin-shell spacetimes

We analyze the thermodynamics of spherically symmetric thin-shell solutions to Einstein’s equations, including solutions with negative interior mass. We show the inclusion of such solutions is essential for the thermodynamic consistency of the system: the maximum energy principle applies when we include an entropy term from the singularity of the negative-mass solutions, in addition to the Bekenstein–Hawking term for the entropy of solutions with positive interior mass. Then, the thermodynamic analysis leads to four distinct thermodynamic phases. We also show that all types of solutions can be either thermodynamically stable or dynamically stable, but only solutions with zero interior mass can be both. Since most of our results are analytic, thin shell models emerge as a useful theoretical paradigm for exploring gravitational thermodynamics. Our results provide an additional argument in support of the assignment of entropy to the singularity of negative-mass Schwarzschild spacetimes, and, consequently, to Penrose’s conjecture about the assignment of entropy to singularities.

First principle study of gravitational pressure and thermodynamics of FRW universe

We make a first principle study of gravitational pressure in cosmic thermo- dynamics. The pressure is directly derived from the unified first law, in fact the Einstein field equation in spherically symmetric spacetime. By using this pressure, we obtain the thermodynamics for the FRW universe, especially presenting the gravitational equation of state for the FRW spacetime itself, i.e. P = P (RA, T) for the first time. Furthermore, we study the Joule-Thomson expansion as an application of the thermodynamic equation of state to find the cooling-heating property of the FRW universe. We demonstrate that there is an inversion temperature for a FRW universe if its enthalpy ℋ is negative. These investigations shed insights on the evolution of our universe in view of thermodynamics.

On the thermodynamics of PP-waves

This paper deals with gravitational thermodynamics. The first and second laws of thermodynamics are established in terms of energy density and pressure, which are defined in the scope of Teleparallelism Equivalent to General Relativity (TEGR). Such laws are applied to gravitational waves, in particular the PP-wave. A negative entropy variation for an isothermal process is obtained.

Holographic CFT phase transitions and criticality for charged AdS black holes

We study the holographic dual of the extended thermodynamics of spherically symmetric, charged AdS black holes in the context of the AdS/CFT correspondence. The gravitational thermodynamics of AdS black holes can be extended by allowing for variations of the cosmological constant and Newton’s constant. In the dual CFT this corresponds to including the central charge C and its chemical potential μ as a new pair of conjugate thermodynamic variables, in addition to the standard pairs: temperature vs. entropy (T, S), electric potential vs. charge ( overset{sim }{Phi},overset{sim }{Q} ) and field theory pressure vs. volume (p, mathcal{V} ). For the (grand) canonical ensembles at fixed ( overset{sim }{Q},mathcal{V},C ), ( overset{sim }{Phi},mathcal{V},C ) and ( overset{sim }{Q},mathcal{V},mu ), based on the holographic dictionary, we argue the CFT description of charged AdS black holes contains either critical phenomena or interesting phase behaviour. In the fixed ( overset{sim }{Q},mathcal{V},mu ) we find a new zeroth-order phase transition between a high- and low-entropy phase at some μ-dependent temperature. Finally, we point out there is no critical behaviour in the fixed p ensembles, i.e. there is no p − mathcal{V} criticality, and hence the CFT state dual to a classical charged black hole cannot be a Van der Waals fluid. Whether or not this phase structure is supported by CFT computations remains an interesting open question.

Gravitational and gravitoscalar thermodynamics

Gravitational thermodynamics and gravitoscalar thermodynamics with S2 × ℝ boundary geometry are investigated through the partition function, assuming that all Euclidean saddle point geometries contribute to the path integral and dominant ones are in the B3 × S1 or S2 × Disc topology sector. In the first part, I concentrate on the purely gravitational case with or without a cosmological constant and show there exists a new type of saddle point geometry, which I call the “bag of gold(BG) instanton,” only for the Λ > 0 case. Because of this existence, thermodynamical stability of the system and the entropy bound are absent for Λ > 0, these being universal properties for Λ ≤ 0. In the second part, I investigate the thermodynamical properties of a gravity-scalar system with a φ2 potential. I show that when Λ ≤ 0 and the boundary value of scalar field Jφ is below some value, then the entropy bound and thermodynamical stability do exist. When either condition on the parameters does not hold, however, thermodynamical stability is (partially) broken. The properties of the system and the relation between BG instantons and the breakdown are discussed in detail.

Do They Compute? Dawn of a New Paradigm based on the Information-theoretic View of Black holes, Universe and Various Conceptual Interconnections of Fundamental Physics

The article endeavors to show how thinking about black holes as some form of hyper-efficient, serial computers could help us in thinking about the more fundamental aspects of space-time itself. Black holes as the most exotic and yet simplest forms of gravitational systems also embody quantum fluctuations that could be manipulated to archive hypercomputation, and even if this approach might not be realistic, yet it is important since it has deep connections with various aspects of quantum gravity, the highly desired unification of quantum mechanics and general relativity. The article describes how thinking about black holes as the most efficient kind of computers in the physical universe also paves the way for developing new ideas about such issues as black hole information paradox, the possibility of emulating the properties of curved space-time with the collective quantum behaviors of certain kind of condensate fluids, ideas of holographic spacetime, gravitational thermodynamics and entropic gravity, the role of quantum entanglements and non-locality in the construction of spacetime, spacetime geometry and the nature of gravitation and dark energy and dark matter, etc. to name a few.

Computation is Existence — A Brief Overview of the Multi-faceted Implications of Quantum Mechanical Description of Black holes as hyper computational Entities

The article attempts to deal with the newly emerging paradigm of black hole computers in which adopting a quantum-mechanical perspective of information enables us to assess the computational power of black holes. Viewing space-time itself as a computational entity and black holes as the supreme forms of serial computers can help us to gain insight into the ideas from gravitational thermodynamics and the emergent nature of space-time and gravity. The idea of black holes as computational entities also relates to quantum gravity which views space-time and foamy and fuzzy due to quantum fluctuations and divided into discrete, Planck-scale blocks.

Thermofield double states in group field theory

Group field theories are higher-rank generalizations of matrix/tensor models, and encode the simplicial geometries of quantum gravity. In this paper, we study the thermofield double states in group field theories. The starting point is the equilibrium Gibbs states in group field theory recently found by Kotecha and Oriti, based on which we construct the thermofield double state as a “thermal” vacuum respecting the Kubo–Martin–Schwinger condition. We work with the Weyl [Formula: see text]-algebra of group fields, and a particular type of thermofield double states with single type of symmetry is obtained from the squeezed states on this Weyl algebra. The thermofield double states, when viewed as states on the group field theory Fock vacuum, are condensate states at finite flow parameter [Formula: see text]. We suggest that the equilibrium flow parameters [Formula: see text] of this type of thermofield double states in the group field theory condensate pictures of black hole horizon and quantum cosmology are related to the inverse temperatures in gravitational thermodynamics.

Dynamics of an interacting Barrow holographic dark energy model and its thermodynamic implications

In this paper, using Barrow entropy, we propose an interacting model of Barrow holographic dark energy (BHDE). In particular, we study the evolution of a spatially flat FLRW universe composed of pressureless dark matter and BHDE that interact with each other through a well-motivated interaction term. Considering the Hubble horizon as the IR cut-off, we then study the evolutionary history of important cosmological parameters, particularly, the density parameter, the equation of state parameter, and the deceleration parameter in the BHDE model and find satisfactory behaviors in the model. We perform a detailed study on the dynamics of the field equations by studying the asymptotic behavior of the field equations, while we write the analytic expression for the scale factor with the use of Laurent series. Finally, we study the implications of gravitational thermodynamics in the interacting BHDE model with the dynamical apparent horizon as the cosmological boundary. In particular, we study the viability of the generalized second law by assuming that the apparent horizon is endowed with Hawking temperature and Barrow entropy.

Instability of super-entropic black holes in extended thermodynamics

The charged black hole of Bañados, Teitelbiom and Zanelli is studied in extended gravitational thermodynamics where there is a dynamical pressure and volume. It is a simple example of a super-entropic black hole, violating the reverse isoperimetric inequality. It is proven that this property implies that its specific heat at constant volume is negative, signaling a new kind of fundamental instability for black holes. It is conjectured that this instability is present for other super-entropic black holes, and this is demonstrated numerically for a large family of known solutions.

Holographic heat engines as quantum heat engines

Certain solutions of Einstein’s equations in anti-de Sitter spacetime can be engineered, using extended gravitational thermodynamics, to yield ‘holographic heat engines’, devices that turn heat into useful mechanical work. On the other hand, there are constructions (both experimental and theoretical) where a series of operations is performed on a small quantum system, defining what are known as ‘quantum heat engines’. We propose that certain holographic heat engines can be considered models of quantum heat engines, and the possible fruitfulness of this connection is discussed. Motivated by features of quantum heat engines that take a quantum system through analogues of certain classic thermodynamic cycles, some black hole Otto and Diesel cycles are presented and explored for the first time. In the expected regime of overlap, our Otto efficiency formulae are of the form exhibited by quantum and classical heat engines.

Gravitational thermodynamics of causal diamonds in (A)dS

The static patch of de Sitter spacetime and the Rindler wedge of Minkowski spacetime are causal diamonds admitting a true Killing field, and they behave as thermodynamic equilibrium states under gravitational perturbations. We explore the extension of this gravitational thermodynamics to all causal diamonds in maximally symmetric spacetimes. Although such diamonds generally admit only a conformal Killing vector, that seems in all respects to be sufficient. We establish a Smarr formula for such diamonds and a ``first law" for variations to nearby solutions. The latter relates the variations of the bounding area, spatial volume of the maximal slice, cosmological constant, and matter Hamiltonian. The total Hamiltonian is the generator of evolution along the conformal Killing vector that preserves the diamond. To interpret the first law as a thermodynamic relation, it appears necessary to attribute a negative temperature to the diamond, as has been previously suggested for the special case of the static patch of de Sitter spacetime. With quantum corrections included, for small diamonds we recover the ``entanglement equilibrium'' result that the generalized entropy is stationary at the maximally symmetric vacuum at fixed volume, and we reformulate this as the stationarity of free conformal energy with the volume not fixed.

Physical generalizations of the Rényi entropy

We present a new type of generalization of the Rényi entropy that follows naturally from its representation as a thermodynamic quantity. We apply it to the case of [Formula: see text]-dimensional conformal field theories (CFTs) reduced on a region bounded by a sphere. It is known how to compute their Rényi entropy as an integral of the thermal entropy of hyperbolic black holes in [Formula: see text]-dimensional anti-de Sitter spacetime. We show how this integral fits into the framework of extended gravitational thermodynamics, and then point out the natural generalization of the Rényi entropy that suggests itself in that light. In the field theory terms, the new generalization employs aspects of the physics of Renormalization Group (RG) flow to define a refined version of the reduced vacuum density matrix. For [Formula: see text], it can be derived directly in terms of twist operators in field theory. The framework presented here may have applications beyond this context, perhaps in studies of both quantum and classical information theoretic properties of a variety of systems.

Holographic heat engines, entanglement entropy, and renormalization group flow

We explore a fruitful connection between the physics of conformal field theories (CFTs) in -dimensional Minkowski spacetime and the extended gravitational thermodynamics of hyperbolic black holes in -dimensional anti-de Sitter spacetime. The CFTs are reduced on a region bounded by a sphere. We show that renormalization group flows between CFTs are specific thermodynamic processes in the plane, where the irreversibility of coarse-graining flows from the ultraviolet to the infrared corresponds to the second law of thermodynamics, preventing heat from flowing from low temperature to high. We observe that holographic heat engines using the black holes as a working substance correspond to specific combinations of CFT flows and deformations. We construct three special engines whose net heat and work can be described in terms of changes of entanglement entropy across the sphere. Engine efficiencies emerge as simple functions of the ratio of the number of degrees of freedom of two CFTs.

Apparent Horizon and Gravitational Thermodynamics of Universe in the Eddington-Born-Infeld Theory

The thermodynamics of Universe in the Eddington-Born-Infeld (EBI) theory was restudied by utilizing the holographic-style gravitational equations that dominate the dynamics of the cosmical apparent horizon ΥA and the evolution of Universe. We started in rewriting the EBI action of the Palatini approach into the Bigravity-type action with an extra metric qμν. With the help of the holographic-style dynamical equations, we discussed the property of the cosmical apparent horizon ΥA including timelike, spacelike, and null characters, which depends on the value of the parameter of state wm in EBI Universe. The unified first law for the gravitational thermodynamics and the total energy differential for the open system enveloped by ΥA in EBI Universe were obtained. Finally, applying the positive-heat-out sign convention, we derived the generalized second law of gravitational thermodynamics in EBI Universe.

Super inflation mechanism and dark energy from a cosmological entropy perspective

Various approaches are developed that provide a unification of the early inflationary epoch of the universe and dark energy (cosmic accelerating expansion case). In one respect, we express this unification in a universal thermodynamic framework within the context of F ( T , T G ) role=presentation> F ( T , T G ) F ( T , T G ) F\left( T,T_{G} \right) gravity, where T role=presentation> T T T represents the torsion invariant and T G role=presentation> T G T G T_{G} is the teleparallel equivalent of the Gauss--Bonnet term. For a Friedmann-Robertson-Walker universe model bounded by the dynamical apparent horizon, we explore the generalized second law of gravitational thermodynamics (GSLT). Finally, we discuss the super inflation mechanism, the deceleration case (radiation and dust regions), and the late time cosmic acceleration of the universe into the validity of the GSLT that we obtain.

Gravitational pressure, apparent horizon and thermodynamics of FLRW universe in the teleparallel gravity

In the context of the teleparallel equivalent of general relativity the concept of gravitational pressure and gravitational energy-momentum arisen in a natural way. In the case of a Friedmann-Lemaitre-Robertson-Walker space FLRW we obtain the total energy contained inside the apparent horizon and the radial pressure over the apparent horizon area. We use these definitions to written a thermodynamics relation $T_{A}dS_{A} = dE_{A}+P_{A}dV_{A}$ at the apparent horizon, where $E_{A}$ is the total energy inside the apparent horizon, $V_{A}$ is the areal volume of the apparent horizon, $P_{A}$ is the radial pressure over the apparent horizon area, $S_{A}$ is the entropy which can be assumed as one quarter of the apparent horizon area only for a non stationary apparent horizon. We identify $T_{A}$ as the temperature at the surface of the apparent horizon. We shown that for all expanding accelerated FLRW model of universe the radial pressure is positive.

Modified dark matter: Relating dark energy, dark matter and baryonic matter

Modified dark matter (MDM) is a phenomenological model of dark matter, inspired by gravitational thermodynamics. For an accelerating universe with positive cosmological constant ([Formula: see text]), such phenomenological considerations lead to the emergence of a critical acceleration parameter related to [Formula: see text]. Such a critical acceleration is an effective phenomenological manifestation of MDM, and it is found in correlations between dark matter and baryonic matter in galaxy rotation curves. The resulting MDM mass profiles, which are sensitive to [Formula: see text], are consistent with observational data at both the galactic and cluster scales. In particular, the same critical acceleration appears both in the galactic and cluster data fits based on MDM. Furthermore, using some robust qualitative arguments, MDM appears to work well on cosmological scales, even though quantitative studies are still lacking. Finally, we comment on certain nonlocal aspects of the quanta of modified dark matter, which may lead to novel nonparticle phenomenology and which may explain why, so far, dark matter detection experiments have failed to detect dark matter particles.