Horizon Entropy Research Articles

Non-singular and cyclic universe from the modified GUP

In this paper, we investigate the effects of a new version of the generalized uncertainty principle (modified GUP) on the dynamics of the Universe. As the modified GUP will modify the relation between the entropy and area of the apparent horizon, it will also deform the Friedmann equations within Jacobson's approach. We explicitly find these deformed Friedmann equations governing the modified GUP-corrected dynamics of such a Universe. It is shown that the modified GUP-deformed Jacobson's approach implies an upper bound for the density of such a Universe. The Big Bang singularity can therefore also be avoided using the modified GUP-corrections to horizons' thermodynamics. In fact, we are able to analyze the pre Big Bang state of the Universe. Furthermore, the equations imply that the expansion of the Universe will come to a halt and then will immediately be followed by a contracting phase. When the equations are extrapolated beyond the maximum rate of contraction, a cyclic Universe scenario emerges.

Thermodynamic Analysis of Gravitational Field Equations in Lyra Manifold

Considering the Einstein field equations in Lyra manifold and applying the unified first law of thermodynamics as well as the Clausius relation to the apparent horizon of FRW universe, we find the entropy of apparent horizon in Lyra manifold. In addition, the validity of second law of thermodynamics and its generalized form are also studied. Finally, we use the first law of thermodynamics in order to find the horizon entropy of static spherically symmetric spacetimes. Some results of considering (anti)de-Sitter and Schwarzschild metrics have also been addressed.

Semiclassical Corrections to a Regularized Schwarzschild Metric

A version of the Schwarzschild metric to be valid in microphysics is proposed. The source fluid is anisotropic with $p_{r} = -\rho$ and fluctuating tangential pressures. At large distances with respect to the Compton wavelength associated to the source particle, they do not depend on the mass $m$ of the source and everywhere depend on $\hbar$ and the velocity of light $c$ but not on the Newton constant $G$. The particle may be a black hole for $m \geq m_{P}$ only and when $m = m_{P}$ it becomes an extremal black hole. The Komar energy $W$ of the gravitational fluid is $mc^{2}$ for $\hbar = 0$ and at large distances and vanishes at $r_{0} = 2\hbar/emc$. The WEC is violated when $r < r_{0}/2$ due to the negative tangential pressures. The horizon entropy for the extremal black hole is finite though $W$ and the temperature $T$ are vanishing there.

Heavy fields and gravity

We study the effects of heavy fields on 4D spacetimes with flat, de Sitter and anti-de Sitter asymptotics. At low energies, matter generates specific, calculable higher derivative corrections to the GR action which perturbatively alter the Schwarzschild-(A)dS family of solutions. The effects of massive scalars, Dirac spinors and gauge fields are each considered. The six-derivative operators they produce, such as ∼ R3 terms, generate the leading corrections. The induced changes to horizon radii, Hawking temperatures and entropies are found. Modifications to the energy of large AdS black holes are derived by imposing the first law. An explicit demonstration of the replica trick is provided, as it is used to derive black hole and cosmological horizon entropies. Considering entropy bounds, it’s found that scalars and fermions increase the entropy one can store inside a region bounded by a sphere of fixed size, but vectors lead to a decrease, oddly. We also demonstrate, however, that many of the corrections fall below the resolving power of the effective field theory and are therefore untrustworthy. Defining properties of black holes, such as the horizon area and Hawking temperature, prove to be remarkably robust against higher derivative gravitational corrections.

An alternative path integral for quantum gravity

We define a (semi-classical) path integral for gravity with Neumann boundary conditions in $D$ dimensions, and show how to relate this new partition function to the usual picture of Euclidean quantum gravity. We also write down the action in ADM Hamiltonian formulation and use it to reproduce the entropy of black holes and cosmological horizons. A comparison between the (background-subtracted) covariant and Hamiltonian ways of semi-classically evaluating this path integral in flat space reproduces the generalized Smarr formula and the first law. This "Neumann ensemble" perspective on gravitational thermodynamics is parallel to the canonical (Dirichlet) ensemble of Gibbons-Hawking and the microcanonical approach of Brown-York.

Entropy of Reissner–Nordström–de Sitter black hole

Based on the consideration that the black hole horizon and the cosmological horizon of Reissner-Nordstr\"om black hole in de Sitter space are not independent each other, we conjecture the total entropy of the system should have an extra term contributed from the entanglement between the two horizons, except for the sum of the two horizon entropies. Making use of the globally effective first law and the effective thermodynamic quantities, we derive the total entropy and find that it will diverge as the two horizons tends to coincide.

Temperature and thermodynamic structure of Einstein’s equations for a cosmological black hole

It is expected that the cosmological black holes are the closest realistic solutions of gravitational theories and they evolve with time. Moreover, the natural way of defining thermodynamic entities for the stationary ones is not applicable in the case of a time dependent spacetime. Here we confine our discussion within the Sultana-Dyer metric which is a cosmological black hole solution of Einstein's gravity. In literature, there exists two expressions of horizon temperature -- one is time dependent and the other does not depend on time. To single out the correct one we find the temperature by studying the Hawking effect in the tunnelling formalism. This leads to time dependent structure. After identifying the correct one, the Einstein's equations are written on the horizon and we show that this leads to the first law of thermodynamics. In this process the expressions for horizon entropy and energy, obtained earlier by explicit calculations, are being used. This provides the evidence that Einstein's equations have thermodynamic structure even for a cosmological black hole spacetime. Moreover, this study further clarifies the correctness of the expressions for the thermodynamic quantities; like temperature, entropy and internal energy.

Implications, Consequences and Interpretations of Generalized Entropy in the Cosmological Setups

Recently, it was argued (Eur. Phys. J. C {\bf73}, 2487 (2013)) that the total entropy of a gravitational system should be related to the volume of system instead of the system surface. Here, we show that this new proposal cannot satisfy the unified first law of thermodynamics and the Friedmans equation simultaneously, unless the effects of dark energy candidate on the horizon entropy are considered. In fact, our study shows that some types of dark energy candidate may admit this proposal. Some general properties of required dark energy are also addressed. Moreover, our investigation shows that this new proposal for entropy, while combined with the second law of thermodynamics (as the backbone of Verlinde's proposal), helps us in providing a thermodynamic interpretation for the difference between the surface and bulk degrees of freedom which, according to Padmanabhan's proposal, leads to the emergence of spacetime and thus the universe expansion. In fact, our investigation shows that the entropy changes of system may be equal to the difference between the surface and bulk degrees of freedom falling from surface into the system volume. Briefly, our results signal us that this new proposal for entropy may be in agreement with the thermodynamics laws, the Friedmann equation, Padmanabhan's holographic proposal for the emergence of spacetime and therefore the universe expansion. In fact, this new definition of entropy may be used to make a bridge between Verlinde's and Padmanabhan's proposals.

Thermodynamics of flat FLRW universe in Rastall theory

In this paper, after referring to the Rastall theory, we address some of its cosmological consequences. Moreover, bearing the Clausius relation in mind, using Friedman equations in Rastall theory and the Cai-Kim temperature, we obtain a relation for the apparent horizon entropy of a flat FLRW universe. In addition, we impose the entropy positivity condition on the obtained relation for the horizon entropy, to find some constraints on the Rastall parameters. Moreover, we investigate the second and generalized second laws of thermodynamics. The results of considering a dominated prefect fluid with constant state parameter are also addressed helping us familiarize with the Rastall theory.

Black hole thermodynamics as seen through a microscopic model of a relativistic Bose gas

Equations of gravity when projected on spacetime horizons resemble Navier–Stokes equation of a fluid with a specific equation of state [T. Damour, Surface effects of black hole physics, in Proc. M. Grossman Meeting (North Holland, 1982), p. 587, T. Padmanabhan, Phys. Rev. D 83 (2011) 044048, arXiv:gr-qc/1012.0119, S. Kolekar and T. Padmanabhan, Phys. Rev. D 85 (2011) 024004, arXiv:gr-qc/1012.5421]. We show that this equation of state describes massless ideal relativistic gas. We use these results, and build an explicit and simple molecular model of the fluid living on the Schwarzschild and Reissner–Nordström black hole horizons. For the spin zero Bose gas, our model makes two predictions: (i) The horizon area/entropy is quantized as given by Bekenstein’s quantization rule, (ii) The model explains the correct type of proportionality between horizon area and entropy. However, for the physically relevant range of parameters, the proportionality constant is never equal to [Formula: see text].

Thermodynamic descriptions of polytropic gas and its viscous type as dark energy candidates

In this paper, at first, we focus on a Friedmann–Robertson–Walker (FRW) universe in which the dark energy candidate satisfies the polytropic equation of state and study thermodynamics of dark energy. Bearing the thermal fluctuation theorem in mind, we establish a relation between the thermal fluctuation of the system and mutual interaction between the dark energy and dark matter. Generalization to a viscous polytropic gas is also investigated. We point to a condition for decaying the dark energy candidate into the dark matter needed for alleviating the coincidence problem. The effects of dark energy candidates and their interactions with other parts of the cosmos on the horizon entropy as well as the second law of thermodynamics are also addressed. Our study suggests a correction term besides the Bekenstein entropy, which carries the information of the dark energy candidate, its interaction with other parts of the cosmos, and its viscosity.

Thermodynamical Study of FRW Universe in Quasi-Topological Theory

By applying the unified first law of thermodynamics on the apparent horizon of FRW universe, we get the entropy relation for the apparent horizon in quasi-topological gravity theory. Throughout the paper, the results of considering the Hayward-Kodama and Cai-Kim temperatures are also addressed. Our study shows that whenever there is no energy exchange between the various parts of cosmos, we can get an expression for the apparent horizon entropy in quasi-topological gravity, which is in agreement with other attempts that followed different approaches. The effects of a mutual interaction between the various parts of cosmos on the apparent horizon entropy as well as the validity of second law of thermodynamics in quasi-topological gravity are perused.

Thermodynamics of nonsingular bouncing universes

Homogeneous and isotropic, nonsingular, bouncing world models are designed to evade the initial singularity at the beginning of the cosmic expansion. Here, we study the thermodynamics of the subset of these models governed by general relativity. Considering the entropy of matter, radiation and that the entropy of the apparent horizon is proportional to its area, we argue that these models do not respect the generalised second law of thermodynamics, also away from the bounce.

Entropy of Causal Horizons

We analyze spacetimes with horizons and study the thermodynamic aspects of causal horizons, suggesting that the resemblance between gravitational and thermodynamic systems has a deeper quantum mechanical origin. We find that the observer dependence of such horizons is a direct consequence of associating a temperature and entropy to a spacetime. The geometrical picture of a horizon acting as a one-way membrane for information flow can be accepted as a natural interpretation of assigning a quantum field theory to a spacetime with boundary, ultimately leading to a close connection with thermodynamics.

Thermodynamic Analysis of the Static Spherically Symmetric Field Equations in Rastall Theory

The restrictions on the Rastall theory due to application of the Newtonian limit to the theory are derived. In addition, we use the zero-zero component of the Rastall field equations as well as the unified first law of thermodynamics to find the Misner-Sharp mass content confined to the event horizon of the spherically symmetric static spacetimes in the Rastall framework. The obtained relation is calculated for the Schwarzschild and de-Sitter back holes as two examples. Bearing the obtained relation for the Misner-Sharp mass in mind together with recasting the one-one component of the Rastall field equations into the form of the first law of thermodynamics, we obtain expressions for the horizon entropy and the work term. Finally, we also compare the thermodynamic quantities of system, including energy, entropy, and work, with their counterparts in the Einstein framework to have a better view about the role of the Rastall hypothesis on the thermodynamics of system.

Thermodynamics of universe with a varying dark energy component

We consider a Friedmann–Robertson–Walker (FRW) universe filled by a dark energy (DE) candidate together with other possible sources which may include the baryonic and nonbaryonic matters. Thereinafter, we consider a situation in which the cosmos sectors do not interact with each other. By applying the unified first law of thermodynamics on the apparent horizon of the FRW universe, we show that the DE candidate may modify the apparent horizon entropy and thus the Bekenstein limit. Moreover, we generalize our study to the models in which the cosmos sectors have a mutual interaction. Our final result indicates that the mutual interaction between the cosmos sectors may add an additional term to the apparent horizon entropy leading to modify the Bekenstein limit. Relationships with previous works have been addressed throughout the paper. Finally, we investigate the validity of the second law of thermodynamics and its generalized form in the interacting and noninteracting cosmoses.

Generalized Second Law of Thermodynamics in Parabolic LTB Inhomogeneous Cosmology**Supported financially by Research Institute for Astronomy & Astrophysics of Maragha (RIAAM), Iran

We study thermodynamics of the parabolic Lemaitre–Tolman–Bondi (LTB) cosmology supported by a perfect fluid source. This model is the natural generalization of the flat Friedmann–Robertson–Walker (FRW) universe, and describes an inhomogeneous universe with spherical symmetry. After reviewing some basic equations in the parabolic LTB cosmology, we obtain a relation for the deceleration parameter in this model. We also obtain a condition for which the universe undergoes an accelerating phase at the present time. We use the first law of thermodynamics on the apparent horizon together with the Einstein field equations to get a relation for the apparent horizon entropy in LTB cosmology. We find out that in LTB model of cosmology, the apparent horizon's entropy could be feeded by a term, which incorporates the effects of the inhomogeneity. We consider this result and get a relation for the total entropy evolution, which is used to examine the generalized second law of thermodynamics for an accelerating universe. We also verify the validity of the second law and the generalized second law of thermodynamics for a universe filled with some kinds of matters bounded by the event horizon in the framework of the parabolic LTB model.

Entropy function from the gravitational surface action for an extremal near horizon black hole

It is often argued that {\it all the information of a gravitational theory is encoded in the surface term of the action}; which means one can find several physical quantities just from the surface term without incorporating the bulk part of the action. This has been observed in various instances; e.g. derivation of the Einstein's equations, surface term calculated on the horizon leads to entropy, etc. Here I investigate the role of it in the context of entropy function and entropy of extremal near horizon black holes. Considering only the Gibbons-Hawking-York (GHY) surface term to define an entropy function for the extremal near horizon black hole solution, it is observed that the extremization of such function leads to the exact value of the horizon entropy. This analysis again supports the previous claim that there exists a ``{\it holographic}'' nature in the gravitational action -- surface term contains the information of the bulk.

Generalized holographic Ricci dark energy and generalized second law of thermodynamics in Bianchi Type I universe

Generalized second law of thermodynamics in the Bianchi type I universe with the generalized holographic Ricci dark energy model is studied in this paper. The behavior of dark energy's equation of state parameter indicates that it is matter-like in the early time of the universe but phantom-like in the future. By analysing the evolution of the deviations of state parameter and the total pressure of the universe, we find that for an anisotropic Bianchi type I universe, it transits from a high anisotropy stage to a more homogeneous stage in the near past. Using the normal entropy given by Gibbs' law of thermodynamics, it is proved that the generalized second law of thermodynamics does not always satisfied throughout the history of the universe when we assume the universe is enclosed by the generalized Ricci scalar radius $R_{gr}$. It becomes invalid in the near past to the future, and the formation of the galaxies will be helpful in explaining such phenomenon, for that the galaxies's formation is an entropy increase process. The negative change rates of the horizon entropy and internal entropy occur in different period indicates that the influences of galaxies formation is wiped from internal to the universe's horizon.

RG flow and thermodynamics of causal horizons in AdS

Causal horizons in pure Poincare $AdS$ are Killing horizons generated by dilatation vector. Renormalization group (RG) flow breaks the dilatation symmetry and makes the horizons dynamical. We propose that the boundary RG flow is dual to the thermodynamics of the causal horizon. As a check of our proposal we show that the gravity dual of the boundary $c$-theorem is the second law of thermodynamics obeyed by causal horizons. The holographic $c$-function is the Bekenstein-Hawking entropy (density) of the dynamical causal horizon. We explicitly construct the $c$-function in a generic class of RG-flow geometries and show that it interpolates monotonically between the UV and IR central charges as a result of the second law.