Quantum dissipative processes and gravitational entropy of the universe

We discuss the meaning of gravitational entropy of the universe when quantum dissipative processes like cosmological particle production are important and propose to use the entropy generated in these processes as a measure of the change in gravitational entropy of the spacetime dynamics. Penrose's Weyl Curvature Hypothesis is re-examined in this generalized context. It is shown that gravitational entropy defined as such can actually decrease in the quantum regime by the action of vacuum viscosity. The theoretical and cosmological implications of this postulate is discussed.     

Density contrast indicators in cosmological dust models

We discuss ways of quantifying structuration in relativistic cosmological settings, by employing a family of covariant density constrast indicators. We study the evolution of these indicators with time in the context of inhomogeneous Szekeres models. We find that different observers (having either different spatial locations or different indicators) see different evolutions for the density contrast, which may or may not be monotonically increasing with time. We also find that monotonicity seems to be related to the initial conditions of the model, which may be of potential interest in connection with debates regarding gravitational entropy and the arrow of time.     

Gravitational entropy of Kerr black holes

Classical invariants of General Relativity can be used to approximate the entropy of the gravitational field. In this work, we study two proposed estimators based on scalars constructed out from the Weyl tensor, in Kerr spacetime. In order to evaluate Clifton, Ellis and Tavakol’s proposal, we calculate the gravitational energy density, gravitational temperature, and gravitational entropy of the Kerr spacetime. We find that in the frame we consider, Clifton et al.’s estimator does not reproduce the Bekenstein–Hawking entropy of a Kerr black hole. The results are compared with previous estimates obtained by the authors using the Rudjord–Gr \(\varnothing \) n–Hervik approach. We conclude that the latter represents better the expected behaviour of the gravitational entropy of black holes.     

Holographic dark energy: Quantum correlations against thermodynamical description

Classical and quantum entropic properties of holographic dark energy (HDE) are considered in view of the fact that its entropy is far more restrictive than the entropy of a black hole of the same size. In cosmological settings (in which HDE is promoted to a plausible candidate for being the dark energy of the universe), HDE should be viewed as a combined state composed of the event horizon and the stuff inside the horizon. By any interaction of the subsystems, the horizon and the interior become entangled, raising thereby a possibility that their quantum correlations be responsible for the almost purity of the combined state. Under this circumstances, the entanglement entropy is almost the same for both subsystems, being also of the same order as the thermal (coarse grained) entropy of the interior or the horizon. In the context of thermodynamics, however, only additive coarse grained entropies matter, so we use these entropies to test the generalized second law (GSL) of gravitational thermodynamics in this framework. While we find that the original Li's model passes the GSL test for a special choice of parameters, in a saturated model with the choice for the IR cutoff in the form of the Hubble parameter, the GSL always breaks down.     

Baryogenesis in f(R,T) Gravity

We study gravitational baryogenesis in the context of f(R, T) gravity where the gravitational Lagrangian is given by a generic function of the Ricci scalar R and the trace of the stress-energy tensor T. We explore how this type of modified gravity is capable to shed light on the issue of baryon asymmetry in a successful manner. We consider various forms of baryogenesis interaction and discuss the effect of these interaction terms on the baryon to entropy ratio in this setup. We show that baryon asymmetry during the radiation era of the expanding universe can be non-zero in this framework. Then, we calculate the baryon to entropy ratio for some specific f(R, T) models and by using the observational data, we give some constraints on the parameter spaces of these models.     

Baryogenesis in f(R,T) Gravity

We study gravitational baryogenesis in the context of f(R, T) gravity where the gravitational Lagrangian is given by a generic function of the Ricci scalar R and the trace of the stress-energy tensor T. We explore how this type of modified gravity is capable to shed light on the issue of baryon asymmetry in a successful manner. We consider various forms of baryogenesis interaction and discuss the effect of these interaction terms on the baryon to entropy ratio in this setup. We show that baryon asymmetry during the radiation era of the expanding universe can be non-zero in this framework. Then, we calculate the baryon to entropy ratio for some specific f(R, T) models and by using the observational data, we give some constraints on the parameter spaces of these models.     

Relativity,thermodynamics and entropic forces

A recent assertion that inertial and gravitational forces are entropic forces is discussed. A more conventional approach is stressed herein, whereby entropy is treated as a result of relative motion between observers in different frames of reference. It is demonstrated that the entropy associated with inertial and gravitational forces is dependent upon the well known lapse function of general relativity. An interpretation of the temperature and entropy of an accelerating body is then developed, and used to relate the entropic force to Newton's second law of motion. The entropic force is also derived in general coordinates. An expression of the gravitational entropy of in‐falling matter is then derived by way of Schwarzschild coordinates. As a final consideration, the entropy of a weakly gravitating matter distribution is shown to be proportional to the self‐energy and the stress‐energy‐momentum content of the matter distribution.     

Essay: The Quantum Gravitational Black Hole Is Neither Black Nor White

Understanding the end state of black hole evaporation, the microscopic origin of black hole entropy, the information loss paradox, and the nature of the singularity arising in gravitational collapse - these are outstanding challenges for any candidate quantum theory of gravity. Recently, a midisuperspace model of quantum gravitational collapse has been solved using a lattice regularization scheme. It is shown that the mass of an eternal black hole follows the Bekenstein spectrum, and a related argument provides a fairly accurate estimate of the entropy. The solution also describes a quantized mass-energy distribution around a central black hole, which in the WKB approximation, is precisely Hawking radiation. The leading quantum gravitational correction makes the spectrum non-thermal, thus providing a plausible resolution of the information loss problem.     

Ratios of magnetic charge to charge and of magnetic mass to mass

It is shown that, unlike the case of (vacuum) solutions describing isolated bodies, conformal Killing fields are not excluded by the structure of vacuum gravitational magnetic monopoles at null infinity. The resulting dilation must be constant. This brings support to the viewpoint that such solutions might have a role to play in the understanding of gravitational entropy and time's arrow. If, in addition, a Maxwellian magnetic monopole (Dirac string singularity) is available, the ratio of the total magnetic charge (magnetic mass) over the total electric charge (mass) can be identified. This common feature between the gravitational and the electromagnetic interaction finds its origin in the space-time topology.     

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.     

An interpretation for the entropy of a black hole

We investigate the meaning of the entropy carried away by Hawking radiations from a black hole. We propose that the entropy for a black hole measures the uncertainty of the information about the black hole forming matter’s precollapsed configurations, self-collapsed configurations, and inter-collapsed configurations. We find that gravitational wave or gravitational radiation alone cannot carry all information about the processes of black hole coalescence and collapse, while the total information locked in the hole could be carried away completely by Hawking radiation as tunneling.     

Poisson-Vlasov: stochastic representation and numerical codes

In this paper, we examine the effects of the gravitational field on the dynamical evolution of the cavity-field entropy and the creation of the Schr?dinger-cat state in the Jaynes-Cummings model. We consider a moving two-level atom interacting with a single mode quantized cavity-field in the presence of a classical homogeneous gravitational field. Based on an su(2) algebra, as the dynamical symmetry group of the model, we derive the reduced density operator of the cavity-field which includes the effects of the atomic motion and the gravitational field. Also, we obtain the exact solution and the approximate solution for the system-state vector, and examine the atomic dynamics. By considering the temporal evolution of the cavity-field entropy as well as the dynamics of the Q-function of the cavity-field we study the effects of the gravitational field on the generation of the Schr?dinger-cat states of the cavity-field by using the Q-function, field entropy and approximate solution for the system-state vector. The results show that the gravitational field destroys the generation of the Schr?dinger-cat state of the cavity-field.     

Life,gravity and the second law of thermodynamics

We review the cosmic evolution of entropy and the gravitational origin of the free energy required by life. All dissipative structures in the universe including all forms of life, owe their existence to the fact that the universe started in a low entropy state and has not yet reached equilibrium. The low initial entropy was due to the low gravitational entropy of the nearly homogeneously distributed matter and has, through gravitational collapse, evolved gradients in density, temperature, pressure and chemistry. These gradients, when steep enough, give rise to far from equilibrium dissipative structures (e.g., galaxies, stars, black holes, hurricanes and life) which emerge spontaneously to hasten the destruction of the gradients which spawned them. This represents a paradigm shift from “we eat food” to “food has produced us to eat it”.     

Tunnelling with a negative cosmological constant

The point of this paper is to see what light new results in hyperbolic geometry may throw on gravitational entropy and whether gravitational entropy is relevant for the quantum origin of the universe. We introduce some new gravitational instantons which mediate the birth from nothing of closed universes containing wormholes and suggest that they may contribute to the density matrix of the universe. We also discuss the connection between their gravitational action and the topological and volumetric entropies introduced in hyperbolic geometry. These coincide for hyperbolic 4-manifolds, and increase with increasing topological complexity of the 4-manifold. We raise the question of whether the action also increases with the topological complexity of the initial 3-geometry, measured either by its 3-volume or its Matveev complexity. We point out, in distinction to the non-supergravity case, that universes with domains of negative cosmological constant separated by supergravity domain walls cannot be born from nothing. Finally we point out that our wormholes provide examples of the type of Perpetual Motion machines envisaged by Frolov and Novikov.     

Proof of a universal lower bound on the shear viscosity to entropy density ratio

It has been conjectured, on the basis of the gauge-gravity duality, that the ratio of the shear viscosity to the entropy density should be universally bounded from below by 1/4π$1/4\pi$ in units of the Planck constant divided by the Boltzmann constant. Here, we prove the bound for any ghost-free extension of Einstein gravity and the field-theory dual thereof. Our proof is based on the fact that, for such an extension, any gravitational coupling can only increase from its Einstein value. Therefore, since the shear viscosity is a particular gravitational coupling, it is minimal for Einstein gravity. Meanwhile, we show that the entropy density can always be calibrated to its Einstein value. Our general principles are demonstrated for a pair of specific models, one with ghosts and one without.     

Gravitational Entropy in Cosmological Models

We discuss whether an appropriately defined dimensionless scalar function might be an acceptable candidate for the gravitational entropy, by explicitly considering Szekeres and Bianchi type VI _h models that admit an isotropic singularity. We also briefly discuss other possible gravitational entropy functions, including an appropriate measure of the velocity dependent Bel-Robinson tensor. PACS: 04.20.-q 95.30.Sf 98.80.Jk     

Modified entropic gravitation in superconductors

Verlinde recently developed a theoretical account of gravitation in terms of an entropic force. The central element in Verlinde’s derivation is information and its relation with entropy through the holographic principle. The application of this approach to the case of superconductors requires to take into account that information associated with superconductor’s quantum vacuum energy is not stored on Planck size surface elements, but in four volume cells with Planck-Einstein size. This has profound consequences on the type of gravitational force generated by the quantum vacuum condensate in superconductors, which is closely related with the cosmological repulsive acceleration responsible for the accelerated expansion of the Universe. Remarkably this new gravitational type force depends on the level of breaking of the weak equivalence principle for cooper pairs in a given superconducting material, which was previously derived by the author starting from similar principles. It is also shown that this new gravitational force can be interpreted as a surface force. The experimental detection of this new repulsive gravitational-type force appears to be challenging.