We show that the Einstein field equations with a negative cosmological constant can admit black hole solutions whose thermodynamics coincides with that of logotropic fluids, recently investigated to heal some cosmological and astrophysical issues. For this purpose, we adopt the Anton-Schmidt equation of state, which represents a generalized version of logotropic fluids. We thus propose a general treatment to obtain an asymptotic anti-de Sitter metric, reproducing the thermodynamic properties of both Anton-Schmidt and logotropic fluids. Hence, we explore how to construct suitable spacetime functions, invoking an event horizon and fulfilling the null, weak, strong and dominant energy conditions. We further relax the strong energy condition to search for possible additional solutions. Finally, we discuss the optical properties related to a specific class of metrics and show how to construct an effective refractive index depending on the spacetime functions and the thermodynamic quantities of the fluid under study. We also explore possible departures with respect to the case without the fluid.
We consider a spatially flat FLRW universe. We assume that it is filled with dark energy in the form of logotropic dark fluid coupled with dark matter in the form of a perfect fluid having a barotropic equation of state. We employ dynamical system tools to obtain a complete qualitative idea of the evolution of such a universe. It is interesting to note that we ought to consider an approximation for the pressure of the logotropic dark fluid in the form of an infinite series so as to be able to construct the autonomous system required for a dynamical system study. This series form provides us wi…
We here study extended classes of logotropic fluids as \textit{unified dark energy models}. Under the hypothesis of the Anton-Schmidt scenario, we consider the universe obeying a single fluid whose pressure evolves through a logarithmic equation of state. This result is in analogy with crystals under isotropic stresses. Thus, we investigate thermodynamic and dynamical consequences by integrating the speed of sound to obtain the pressure in terms of the density, leading to an extended version of the Anton-Schmidt cosmic fluids. Within this picture, we get significant outcomes expanding the Anto…
A unification of dark matter and dark energy in terms of a logotropic perfect dark fluid has recently been proposed, where deviations with respect to the standard $Λ{\rm CDM}$ model are dependent on a single parameter $B$. In this paper we show that the requirement that the linear growth of cosmic structures on comoving scales larger than $8 h^{-1} \, {\rm Mpc}$ is not significantly affected with respect to the standard $Λ{\rm CDM}$ result provides the strongest constraint to date on the model ($B <6 \times 10^{-7}$), an improvement of more than three orders of magnitude over previous constrai…
We propose a heuristic unification of dark matter and dark energy in terms of a single dark fluid with a logotropic equation of state $P=A\ln(ρ/ρ_P)$, where $ρ$ is the rest-mass density, $ρ_P$ is the Planck density, and $A$ is the logotropic temperature. The energy density $ε$ is the sum of a rest-mass energy term $ρc^2$ mimicking dark matter and an internal energy term $u(ρ)=-P(ρ)-A$ mimicking dark energy. The logotropic temperature is approximately given by $A \simeq ρ_Λc^2/\ln(ρ_P/ρ_Λ)\simeqρ_Λc^2/[123 \ln(10)]$, where $ρ_Λ$ is the cosmological density. More precisely, we obtain $A=2.13\tim…
We determine the k-essence Lagrangian of a relativistic barotropic fluid. The equation of state of the fluid can be specified in different manners depending on whether the pressure is expressed in terms of the energy density (model I), the rest-mass density (model II), or the pseudo rest-mass density for a complex scalar field in the Thomas-Fermi approximation (model III). In the nonrelativistic limit, these three formulations coincide. In the relativistic regime, they lead to different models that we study exhaustively. We provide general results valid for an arbitrary equation of state and s…
We have considered a spatially flat, homogeneous and isotropic FLRW Universe filled with a single fluid, known as logotropic dark fluid (LDF), whose pressure evolves through a logarithmic equation of state. We use the recent Pantheon SNIa and cosmic chronometer datasets to constrain the parameters of this model, the present fraction of dark matter $Ω_{m0}$ and the Hubble constant $H_0$. We find that the mean values of these parameters are $Ω_{m0}=0.288\pm 0.012$ and $H_{0}=69.652\pm 1.698~{\rm km/s/Mpc}$ at the $1σ$ CL. We also find that the LDF model shows a smooth transition from the deceler…
We propose a new class of cosmological unified dark sector models called "{\em Generalized Logotropic Models}". They depend on a free parameter $n$. The original logotropic model [P.H. Chavanis, Eur. Phys. J. Plus {\bf 130}, 130 (2015)] is a special case of our generalized model corresponding to $n=1$. In our scenario, the Universe is filled with a single fluid, a generalized logotropic dark fluid (GLDF), whose pressure $P$ includes higher order logarithmic terms of the rest-mass density $ρ_m$. The total energy density $ε$ is the sum of the rest-mass energy density $ρ_m c^2$ and the internal e…
In a previous paper we have introduced a new cosmological model that we called the logotropic model. The logotropic model is able to account, without free parameter, for the constant surface density of the dark matter halos, for their mass-radius relation, and for the Tully-Fisher relation. In this paper, we explore other consequences of this model. By advocating a form of "strong cosmic coincidence" we predict that the present proportion of dark energy in the Universe is $Ω_{\rm de,0}=e/(1+e)\simeq 0.731$ which is close to the observed value. We also remark that the surface density of dark ma…
We here propose a new class of barotropic factor for matter, motivated by properties of isotropic deformations of crystalline solids. Our approach is dubbed Anton-Schmidt's equation of state and provides a non-vanishing, albeit small, pressure term for matter. The corresponding pressure is thus proportional to the logarithm of universe's volume, i.e. to the density itself since $V\propto ρ^{-1}$. In the context of solid state physics, we demonstrate that by only invoking standard matter with such a property, we are able to frame the universe speed up in a suitable way, without invoking a dark …
We consider a class of cosmological fluids that possess properties analogous to those of crystalline solids undergoing isotropic deformations. Our research is based on a modified log-corrected power-law equation of state in the presence of a bulk viscosity. This formalism represents a class of so-called logotropic fluids, and allows explaining an accelerating late-time universe. In order to obtain a more detailed picture of its evolution, we add in our model a coupling of the log-corrected power-law fluid to dark matter, and study various interacting forms between them. We solve the system of …
The low-energy dynamics of relativistic continuous media is given by a shift-symmetric effective theory of four scalar fields. These scalars describe the embedding in spacetime of the medium and play the role of Stückelberg fields for spontaneously broken spatial and time translations. Perfect fluids are selected imposing a stronger symmetry group or reducing the field content to a single scalar. We explore the relation between the field theory description of perfect fluids to thermodynamics. By drawing the correspondence between the allowed operators at leading order in derivatives and the th…
We show that there is a correspondence between cosmology from non-extensive thermodynamics and cosmology with fluids of redefined and generalized equation of state. We first establish the correspondence in the case of basic non-extensive thermodynamics, and then we proceed by investigating the more consistent case, from the quantum field theoretical point of view, of varying exponent, namely depending on the scale. The obtained duality provides a way of explaining the complicated phenomenological forms of the effective fluid equation-of-state parameters that are being broadly used in the liter…
We provide a proof of the necessary and sufficient condition on the profile of the temperature, chemical potential, and angular velocity for a charged perfect fluid in dynamic equilibrium to be in thermodynamic equilibrium not only in fixed but also in dynamical electromagnetic and gravitational fields. In passing, we also present the corresponding expression for the first law of thermodynamics for such a charged star.
According to maximum entropy principle, it has been proved that the gravitational field equations could be derived by the extrema of total entropy for perfect fluid, which implies that thermodynamic relations contain information of gravity. In this manuscript, we obtain a criterion for thermodynamical stability of an adiabatic, self-gravitating perfect fluid system by the second variation of total entropy. We show, for Einstein's gravity with spherical symmetry spacetime, that the criterion is consistent with that for dynamical stability derived by Chandrasekhar and Wald. We also find that the…
In this paper we have investigated the limits imposed by thermodynamics on a dark energy fluid. We have obtained the heat capacities and the compressibilities for a dark energy fluid. The thermal and mechanical stabilities require these quantities to be positive. We have shown that dark energy fluids must satisfy the stability conditions and that such requirement put difficulties in the cosmic fluid models with negative constant EoS parameters. We have also shown that the observational constraints imposed by SN Ia, BAO and $H(z)$ data on a general dark energy fluid with a time-dependent EoS pa…
We revisit the analogy between a minimally coupled scalar field in general relativity and a perfect fluid, correcting previous identifications of effective temperature and chemical potential. This provides a useful complementary picture for the first-order thermodynamics of scalar-tensor gravity, paving the way for the Einstein frame formulation (which eluded previous attempts) and raises interesting questions to further develop the analogy.
Out of several possible extensions of general relativity, the scalar-tensor theory is the most popular for several reasons. Since the quantum description of gravity is yet to be formulated properly, the understanding of a gravitational theory remains incomplete until the study of thermodynamic and fluid-gravity aspects, which provides an alternative viewpoint to understand the gravitational theory. In this review, we study these features (thermodynamics and the fluid gravity analogy) in a rigorous and yet in a concise manner for the scalar-tensor gravity, which has been revealed in our recent …
We establish the nonlocal generalization of the Israel-Stewart model for the relativistic causal thermodynamics of the cosmic fluid, which evolves in the homogeneous isotropic Universe. Based on the second law of thermodynamics we derive the integro-differential master equation for the nonequilibrium pressure scalar and reduce it to the differential equation of the second order in time derivatives. We show that this master equation can be considered as the relativistic analog of the Burgers equation, which is known in the classical theory of viscoelasticity. We obtain the nonlinear key equatio…
A new entropic gravity inspired derivation of general relativity from thermodynamics is presented. This generalizes, within Einstein gravity, the "Thermodynamics of Spacetime" approach by T. Jacobson, which relies on the Raychaudhuri evolution equation. Here the rest of the first law of thermodynamics is incorporated by using the Damour-Navier-Stokes equation, known from the membrane paradigm for describing fluid dynamics on the horizon.
In this paper, we study thermodynamics and thermodynamic geometry of a black hole surrounded by the perfect fluid in Rastall theory. In particular, we calculate the physical quantity like mass, temperature and heat capacity of the system for two different cases. From the resulting heat capacity, we emphasize stability of the system. Following Weinhold, Ruppiner, Quevedo and HPEM formalism, thermodynamic geometry of this black hole in Rastall gravity is also analyzed. We find that the singular points of the curvature scalar of Ruppeiner and HPEM metrics entirely coincides with zero points of th…
Holographic cosmology with logarithmic equation of state based on a new generalized entropy
Norwegian University of Science and Technology（挪威科技大学）；Tomsk State Pedagogical University (TSPU)（托木斯克国立师范大学）；International Centre of Gravity and Cosmos, Tomsk State University of Control Systems and Radio electronics (TUSUR)（托木斯克州立控制系统与电子大学国际引力与宇宙学中心）
In this paper, we study the model of $f(T, B)$ gravity with viscous fluid in flat-FRW metric, in which $T$ and $B$ are torsion scalar and boundary term, respectively. We obtain the Friedmann equations in the framework of modified teleparallel gravity by tetrad components. We consider an interacting model between matter and dark energy so that universe dominates by viscous fluid. Then, we write the corresponding cosmological parameters in terms of the redshift parameter, and, we parameterize the Hubble parameter with experimental data. In what follows, we plot the corresponding cosmological par…
We present a new approach to the problem of the thermodynamical equilibrium of a quantum relativistic fluid in a curved spacetime in the limit of small curvature. We calculate the mean value of local operators by expanding the four-temperature Killing vector field in Riemann normal coordinates about the same spacetime point and we derive corrections with respect to the flat spacetime expressions. Thereby, we clarify the origin of the terms proportional to Riemann and Ricci tensors introduced in general hydrodynamic expansion of the stress-energy tensor.
We analyze the interpretation of the spherically symmetric perfect fluid solutions that admit a flat synchronization orthogonal to the fluid flow as a thermodynamic perfect fluid in local thermal equilibrium. The ideal gas sonic condition is examined for this family of metrics, and the macroscopic conditions for physical reality are accurately tested for some specific solutions.
The search for thermodynamic admissibility moreover reveals a fundamental difference between liquids and gases in relativistic fluid dynamics, as the reversible convection mechanism is much simpler for liquids than for gases. In relativistic fluid mechanics, positive entropy production is known to be insufficient for guaranteeing stability. Much more restrictive criteria for thermodynamic admissibility have become available in nonequilibrium thermodynamics. We here perform a linear stability analysis for a model of relativistic hydrodynamics that is based on the GENERIC (general equation for t…
This paper is devoted to investigate the thermodynamic stability of a generic cosmological fluid known as Van der Waals fluid in the context of flat FRW universe. It is treated as a perfect fluid that obeys the equation of state $P=\frac{γρ}{1-βρ}-αρ^{2}, 0\leqγ<1$, where $ρ$ stands for energy density and $P$ stands for pressure of the fluid. In this regard, we discuss the behavior of physical parameters to analyze the evolution of the universe. We investigate whether the cosmological scenario fulfills the third law of thermodynamics using specific heat formalism. Next we discuss the thermal e…
The present work deals with homogeneous and isotropic FLRW model of the Universe having a system of non-interacting diffusive cosmic fluids with barotropic equation of state (constant or variable equation of state parameter). Due to diffusive nature of the cosmic fluids, the divergence of the energy momentum tensor is chosen to be proportional to the diffusive current. The thermodynamic stability analysis of individual fluids is done and the stability conditions are expressed as restrictions on the equation of state parameter.
This article presents the study of a multi-species fluid characterised by a freeze-out or break-away of one or more species. Whereas single-fluid approximation suffices for modelling of the pre {\it freeze-out} period, multi-fluid approximation is required for the post freeze-out period. Embedded in this is a transition period where neither one of the two approximations is singly appropriate. We examine the thermodynamics of this fluid and find that the second law holds before, during and after the freeze-out. Our application to cosmological modelling involving interacting dark-section species…
Thermodynamics on the cosmological apparent horizon of a flat Friedmann-Lemaitre-Robertson-Walker metric has been investigated with Bekenstein entropy and Hawking temperature on the horizon, and Unruh temperature for the fluid inside the horizon. This temperature is experienced by a radial comoving observer infinitesimally close to the horizon due to the pressure exerted by the fluid bounded by the horizon. An expression for the entropy of the fluid has been obtained which is found to be proportional to the volume of the thermodynamic system which implies that the Unruh temperature of the flui…
We investigate the emergent universe scenario in the presence of interacting fluids. The non-linear equation of state (EoS) considered in the general theory of relativity for obtaining emergent universe is effectively a cosmological model with a composition of three fluids. In this paper we consider two models to realize viable cosmological scenarios, {\it viz.}, (i) a two-fluid model with interaction of a pressureless fluid with the fluid having the non-linear EoS needed for the emergent universe, and (ii) a three-fluid model with interaction among the three fluids which originate from the Eo…
We demonstrate that the thermodynamics of a perfect fluid describing baryonic matter can, in certain limits, lead to an equation of state similar to that of dark energy. We keep the cosmic fluid equation of state quite general by just demanding that the speed of sound is positive and less than the speed of light. In this framework, we discuss some propositions by looking at the asymptotic behavior of the cosmic fluid.
Based on Reissner-Nordstrom-anti-de Sitter(RN-AdS) black hole surrounded by perfect fluid dark matter, we study the thermodynamics and phase transition by extending the phase space defined by the charge square $Q^{2}$ and the conjugate quantity $ψ$, where $ψ$ is a function of horizon radius. The first law of thermodynamics and the equation of state are derived in the form $Q^{2}=Q^{2}(T,ψ)$. By investigating the critical behaviour of perfect fluid dark matter around Reissner-Nordstrom-anti-de Sitter black hole, we find that these thermodynamics system are similar to Van der Waals system, and c…
This article extends the single-fluid relativistic irreversible thermodynamics theory of {\it M{ü}ller}, {\it Israel} and {\it Stewart} (hereafter the {MIS} theory) to a multi-fluid system with inherent species interactions. This is illustrated in a two-fluid toy-model where an effective complex 4-velocity plays the role of a primary dynamical parameter. We find that an observer who resides in the {\it real}-part of this universe will notice that their knowledge of the universe parametrized using {\it real}, rather than {\it imaginary}, quantities are insufficient to fully determine properties…
The present work deals with three alternative generalized Bekenstein-Hawking formulation of thermodynamical parameters namely entropy and temperature for the universal thermodynamical system bounded by a horizon in the frame work of inhomogeneous perfect fluid Lemaitre-Tolman-Bondi (LTB) model of the Universe. For the first choice, the first law of thermodynamics holds only for the trivial de Sitter case of the LTB model while we need restriction on the evolution of the horizon radius for the validity of the generalized second law of thermodynamics. However, for the other two choices, the firs…
The work deals with the thermodynamical aspects of the cosmic substratum which is dissipative in nature. For homogeneous and isotropic model of the Universe this dissipative phenomenon is effective bulk viscous pressure in nature and is related to the particle creation mechanism. Finally, the stability criteria for the thermal equilibrium has been analyzed and are presented in tabular form restricting the particle creation parameter or the variation of the equation of state parameter with the volume.
