Weyl Curvature Hypothesis in Light of Quantum Backreaction at Cosmological Singularities or Bounces

The Weyl curvature constitutes the radiative sector of the Riemann curvature tensor and gives a measure of the anisotropy and inhomogeneities of spacetime. Penrose’s 1979 Weyl curvature hypothesis (WCH) assumes that the universe began at a very low gravitational entropy state, corresponding to zero Weyl curvature, namely, the Friedmann–Lemaître–Robertson–Walker (FLRW) universe. This is a simple assumption with far-reaching implications. In classical general relativity, Belinsky, Khalatnikov and Lifshitz (BKL) showed in the 70s that the most general cosmological solutions of the Einstein equation are that of the inhomogeneous Kasner types, with intermittent alteration of the one direction of contraction (in the cosmological expansion phase), according to the mixmaster dynamics of Misner (M). How could WCH and BKL-M co-exist? An answer was provided in the 80s with the consideration of quantum field processes such as vacuum particle creation, which was copious at the Planck time (10−43 s), and their backreaction effects were shown to be so powerful as to rapidly damp away the irregularities in the geometry. It was proposed that the vaccum viscosity due to particle creation can act as an efficient transducer of gravitational entropy (large for BKL-M) to matter entropy, keeping the universe at that very early time in a state commensurate with the WCH. In this essay I expand the scope of that inquiry to a broader range, asking how the WCH would fare with various cosmological theories, from classical to semiclassical to quantum, focusing on their predictions near the cosmological singularities (past and future) or avoidance thereof, allowing the Universe to encounter different scenarios, such as undergoing a phase transition or a bounce. WCH is of special importance to cyclic cosmologies, because any slight irregularity toward the end of one cycle will generate greater anisotropy and inhomogeneities in the next cycle. We point out that regardless of what other processes may be present near the beginning and the end states of the universe, the backreaction effects of quantum field processes probably serve as the best guarantor of WCH because these vacuum processes are ubiquitous, powerful and efficient in dissipating the irregularities to effectively nudge the Universe to a near-zero Weyl curvature condition.

An exploration of the black hole entropy in Gauss–Bonnet gravity via the Weyl tensor

Various proposals for gravitational entropy densities have been constructed from the Weyl tensor. In almost all cases, though, these studies have been restricted to general relativity, and little has been done in modified theories of gravity. However, in this paper, we investigate the simplest proposal for an entropy density constructed from the Weyl tensor in five-dimensional Gauss–Bonnet gravity and find that it fails to reproduce the expected entropy of a black hole.

The cooperation between loop quantum gravity and Entropic gravity

In this paper, we show that bosons can produce bochromatic condensation without an energy layer when the boundary condition $\frac{T}{T_{c}}=z$(when z is complex) is preset. $r_{R}=zr_{A}\left(1-\frac{v^{2}}{c^{2}}\right)^{\frac{1}{2}}$(when z is A complex number). A new form of gravitational potential is obtained by combining the theory of gravitational entropy with loop quantum gravity.

De Sitter entropy as holographic entanglement entropy

We review the results of refs. [1,2], in which the entanglement entropy in spaces with horizons, such as Rindler or de Sitter space, is computed using holography. This is achieved through an appropriate slicing of anti-de Sitter space and the implementation of a UV cutoff. When the entangling surface coincides with the horizon of the boundary metric, the entanglement entropy can be identified with the standard gravitational entropy of the space. For this to hold, the effective Newton's constant must be defined appropriately by absorbing the UV cutoff. Conversely, the UV cutoff can be expressed in terms of the effective Planck mass and the number of degrees of freedom of the dual theory. For de Sitter space, the entropy is equal to the Wald entropy for an effective action that includes the higher-curvature terms associated with the conformal anomaly. The entanglement entropy takes the expected form of the de Sitter entropy, including logarithmic corrections.

Black hole evolution in quantum-gravitational framework

We found black hole evolution on a quantum-gravitational scattering framework with an aim to tackle the black hole information paradox. With this setup, various pieces of the system information are explicit from the start and unitary evolution is manifest throughout. The scattering amplitudes factorize into the perturbative part and nonperturbative part. The nonperturbative part is dominated by an instanton-type contribution, i.e., a black hole analogue of the Coleman-De Luccia’s bounce solution, and we propose that the Hawking radiation be identified with the particles generated by the vacuum decay. Our results indicate that the black hole degrees of freedom are entangled not only with the Hawking modes but also with the pre-Hawking modes. The Wald’s entropy charge measures their entanglement. The full quantum-gravitational entropy is defined as the vev of the Wald entropy charge. With this definition a shifted Page-like curve is generically generated and its quantum extension is readily defined.

An investigation on gravitational entropy of cosmological models

In this paper, we investigate the entropy of the free gravitational field for a given epoch for some well-known isotropic and anisotropic cosmologies. We use the definition of gravitational entropy proposed by Clifton, Ellis and Tavakol, where the 2-index square root of the 4-index Bel–Robinson tensor is taken to be the energy– momentum tensor for the free gravity. We examine whether in the vicinity of the initial singularity, the ratio of energy density of free gravity to that of matter density goes to zero, validating Penrose conjecture on Weyl curvature. Whenever this is true, the gravitational entropy increases monotonically with time, leading to structure formation. For the models considered by us, we identify the conditions for which the Weyl curvature hypothesis is valid, and the assumptions under which it is validated, or otherwise.

On Regular Black Holes at Finite Temperature

The Thermo Field Dynamics (TFD) formalism is used to investigate the regular black holes at finite temperature. Using the Teleparalelism Equivalent to General Relativity (TEGR), the gravitational Stefan-Boltzmann law and the gravitational Casimir effect at zero and finite temperature are calculated. In addition, the first law of thermodynamics is considered. Then, the gravitational entropy and the temperature of the event horizon of a class of regular black holes are determined.

On the gravitational entropy of accelerating black holes

In this paper, we have examined the validity of a proposed definition of gravitational entropy in the context of accelerating black hole solutions of the Einstein field equations, which represent the realistic black hole solutions. We have adopted a phenomenological approach proposed in Rudjord et al. [Phys. Scr. 77, 055901 (2008)] and expanded by Romero et al. [Int. J. Theor. Phys. 51, 925 (2012)], in which the Weyl curvature hypothesis is tested against the expressions for the gravitational entropy. Considering the [Formula: see text]-metric for the accelerating black holes, we have evaluated the gravitational entropy and the corresponding entropy density for four different types of black holes, namely, nonrotating black hole, nonrotating charged black hole, rotating black hole and rotating charged black hole. We end up by discussing the merits of such an analysis and the possible reason of failure in the particular case of rotating charged black hole and comment on the possible resolution of the problem.

Gravitational entropy of wormholes with exotic matter and in galactic halos

In this work, we study and compare the features of gravitational entropy near the throat of transversable wormholes formed by exotic matter and wormholes in galactic halos. We have verified that gravitational entropy and entropy density of these wormholes in regions near their throats are indistinguishable for objects of same throat, despite the fact that they are described by different metrics and by distinct energy–momentum tensors. We have found that the gravitational entropy density diverges near the throat for both cases, probably due to a nontrivial topology at this point, however, allowing the interesting interpretation that a maximum flux of information can be carried through the throat of these wormholes. In addition, we have found that both are endowed with an entropic behaviour similar to Hawking–Bekenstein’s entropy of nonrotating and null charge black holes.

Black Hole Entropy from Non-Commutative Geometry and Spontaneous Localisation

In our recently proposed theory of quantum gravity, a black hole arises from the spontaneous localisation of an entangled state of a large number of atoms of space-time-matter [STM]. Prior to localisation, the non-commutative curvature of an STM atom is described by the spectral action of non-commutative geometry. By using the techniques of statistical thermodynamics from trace dynamics, we show that the gravitational entropy of a Schwarzschild black hole results from the microstates of the entangled STM atoms and is given (subject to certain assumptions) by the classical Euclidean gravitational action. This action, in turn, equals the Bekenstein-Hawking entropy (Area/$4{L_P}^2$) of the black hole. We argue that spontaneous localisation is related to black-hole evaporation through the fluctuation-dissipation theorem.