Revisiting the gravitational ‘arrow of time’

In this work it is presented the modeling and simulation of energy transfer and fluid flow of a stationary spherical arrangement of particles surrounding a gravitational body such as an astrophysical object that carries the curvature of space-time continuum in general relativity, taking into account the thermodynamics of the second law. This model also predicts the drag of space and time around an astrophysical object as it rotates, with results close to the experimental data reported by other authors. To model the energy transfer of the mass and the fluid flow in the space-time, it is used a 4-dimensional system. In order to make measurements of entropy in the arrow of time (past-present), tensors in General Relativity were used to calculate this thermodynamic quantity and with this, the big bang ́s low entropy condition in phase space of coarse graining (Hawking ́s box), according to Weyl curvature hypothesis (WCH) of Roger Penrose. Contribution of this paper is presented by tensors which carry information that has to do with something as non-distortion effect in fluid flow around the astrophysical object and the low entropy condition that is believed to exist in the past, in the big bang; what leads us to search for a new physical-mathematical science to continue. At this point, the Einstein field equations are out of context, which leads us to conclude that it is necessary a mathematical science that allows us to make calculations to rescue lost information due to collapse of matter to a black hole. This math should allow us to clear up physical phenomena (like origin of the universe) and their relationship, with the objective of unifying theories that lead to a physical science without uncertainties, as at the present time. In this regard, we propose a metric in hyperbolic coodinates to build a physical wormhole shaped object where gravitational bodies can be housed that allow us to link the past entropy with the present entropy according to the second law of thermodynamics, as a kind of mathematical space or alternative model to compensate in some way, the link between WCH and the phase space volume of the Hawking's box, and the link between WCH and the quantum-mechanical state-vector reduction, , proposed by Penrose which still have not been determined by any author. Nomenclature

Quantum Geometrodynamics with intrinsic time development and momentric variables is presented. An underlying SU(3) group structure at each spatial point regulates the theory. The intrinsic time behavior of the theory is analyzed, together with its ground state and primordial quantum fluctuations. Cotton-York potential dominates at early times when the universe was small; the ground state naturally resolves Penrose's Weyl Curvature Hypothesis, and thermodynamic and gravitational `arrows of time' point in the same direction. Ricci scalar potential corresponding to Einstein's General Relativity emerges as a zero-point energy contribution. A new set of fundamental commutation relations without Planck's constant emerges from the unification of Gravitation and Quantum Mechanics.

Our Universe has an arrow of time. In accordance with the second law of thermodynamics, entropy has been increasing ever since the Big Bang. The fact that matter is in thermal equilibrium in the very early Universe, as indicated by the cosmic microwave background, has led to the idea that gravitational entropy must be very low in the beginning. Penrose proposed that gravitational entropy can be quantified by the Weyl curvature, which increases as structures formed. A concrete realization of such a measure is the Clifton-Ellis-Tavakol gravitational entropy, which has been shown to be increasing in quite a number of cosmological models. In this work, we show a counter-example involving a class of inhomogeneous universes that are supported by a chameleon massless scalar field and exhibit anisotropic spacetime shearing effects. In fact, in our model the Clifton-Ellis-Tavakol gravitational entropy is increasing although the magnitude of the Weyl curvature is decreasing; this is due to the growth of the spacetime shear. The topology and the values of the three free parameters of the model are constrained by imposing a positive energy density for the cosmic fluid, and the thermodynamical requirements which follow from the cosmological holographic principle and the second law. It is shown that a negative deceleration parameter and a time decreasing Weyl curvature automatically follow from those conditions. Thus, we argue that our model can account for the formation of some primordial structures, like the Large Quasar Groups, which has required a non-standard evolution of the spatial anisotropies.

The concept of the 'arrow of time' is discussed in relation to thermodynamics, electrodynamics and cosmology Time symmetric electrodynamics, the absorber theory of radiation and quantum transitions receive attention to develop a working theory applicable to a universe with a perfect future absorber and an imperfect past absorber, such as the steady state cosmological model. It is stated that the approach adopted herein establishes a strong connection between the electrodynamic and cosmological arrows of time, and points a way towards linking these arrows with the thermodynamic one.

We investigate the status of the gravitational arrow of time in the case of a spherical collapse of a fluid that conducts heat and radiates energy. In particular, we examine the results obtained by W. B. Bonnor in his 1985 paper where he found that the gravitational arrow of time was opposite to the thermodynamic arrow of time. The measure of gravitational epoch function P used by Bonnor was given by the ratio of the Weyl square to the Ricci square. In this paper, we have assumed the measure of gravitational entropy (GE) P 1 to be given by the ratio of the Weyl scalar to the Kretschmann scalar. Our analysis indicates that Bonnor’s result seems to be validated, i.e. the gravitational arrow and the thermodynamic arrow of time point in opposite directions. This strengthens the opinion that the Weyl proposal of GE applies only to the Universe as a whole (provided that we exclude the white holes).

This paper seeks to establish a connexion between the local arrow of time given by the electromagnetic radiation and the cosmological arrow of time given by the expansion of the universe. The Wheeler-Feynman absorber theory of radiation is applied to the expanding cosmological models. First, it is shown that the Schwarzschild-Tetrode-Fokker principle of direct interparticle action can be extended to the general Riemannian space-time. This generalization is considerably simplified in the conformally flat spaces—as all the Robertson—Walker spaces are. In the application of the absorber theory to various cosmological models, the refractive index turns out to play a crucial part. The ambiguities connected with the sign of the imaginary part of the refractive index are resolved if two conditions are fulfilled: (i) a search is made for a self-consistent solution with full retarded (or advanced) solutions (ii) in an elementary theory the origin of the imaginary part of the refractive index is traced to the radiative reaction itself and not to the collisional damping considered by Hogarth. It is shown that full retarded solutions are consistent in the steady-state cosmology and full advanced solutions in the Einstein-de Sitter cosmology. Full advanced solutions are not consistent in the former and full retarded solutions in the latter. Some interesting implications of this result in the C -field approach to the steady-state cosmology are considered.

Traditional discussions about the arrow of time in general involve the concept of entropy. In the cosmological context, the direction past-to-future is usually related to the direction of the gradient of the entropy function of the universe. But the definition of the entropy of the universe is a very controversial matter. Moreover, thermodynamics is a phenomenological theory. Geometrical properties of space-time provide a more fundamental and less controversial way of defining an arrow of time for the universe as a whole. We will call the arrow defined only on the basis of the geometrical properties of space-time, independently of any entropic considerations, “the global arrow of time.” In this paper we will argue that: (i) if certain conditions are satisfied, it is possible to define a global arrow of time for the universe as a whole, and (ii) the standard models of contemporary cosmology satisfy these conditions.

The interior of a static Schwarzschild metric can be written in terms of two functions, similar to some models of anisotropic cosmology. With a suitable choice of canonical variables, we solve the Wheeler-DeWitt equation (WDW) inside the horizon of a Schwarzschild black hole. By imposing classicality near the horizon, and requiring boundedness of the wave function, we get a rather generic solution of the WDW equation, whose steepest-descent solution, i.e., the ridge of the wave function, coincides nicely with the classical trajectory. However, there is an ambiguity in defining the arrow of time which leads to two possible interpretations—(i) if there is only one arrow of time, one can infer that the steepest-descent of the wave function follows the classical trajectory throughout: coming from the event horizon and going all the way down to the singularity, while (ii) if there are two different arrows of time in two separate regimes, it can be inferred that the steepest-descent of the wave function comes inwards from the event horizon in one region while it moves outwards from the singularity in the other region, and there exists an annihilation process of these two parts of the wave function inside the horizon. Adopting the second interpretation could shed light on the information loss paradox: as time goes on, probabilities for histories that include black holes and singularities decay to zero and eventually only trivial geometries dominate.

The recently proposed inflationary Universe scenario1–4 explains several of the mysteries of modern cosmology. I argue here that it also provides a natural explanation for the origin of time asymmetry (‘time's arrow’) in the Universe. The new feature which inflation injects into this long-standing problem is the temporary dominance of the cosmological term in the gravitational field equations, which acts as a sort of repulsive gravity. This term generates huge quantities of energy and radiation (or matter) entropy, while drastically reducing the entropy density of the gravitational field. It thus establishes a large gap between the radiation entropy and the gravitational entropy, which gravity is now trying to close.

FSC is shown to be an excellent model of Penrose’s Weyl curvature hypothesis and his concept of gravitational entropy. The assumptions of FSC allow for the minimum entropy at the inception of the cosmic expansion and rigorously define a cosmological arrow of time. This is in sharp contrast to inflationary models, which appear to violate the second law of thermodynamics within the early universe. Furthermore, by virtue of the same physical assumptions applying at any cosmic time t, the perpetually-flat FSC model predicts the degree of scale invariance observed in the CMB anisotropy pattern, without requiring an explosive and exceedingly brief inflationary epoch. Penrose’s concepts, as described in this paper, provide support for the idea that FSC models gravitational entropy and Verlinde’s emergent gravity theory.

A viable alternative to cosmological inflation is provided by the combined theory of quiescent cosmology and the Weyl curvature hypothesis. We augment the conformal framework of this theory by incorporating the spacetime property of self-similarity. A generalisation of the conformal Killing equation is developed as a definition of asymptotic self-similarity for use in the framework; we derive several propositions and theorems that facilitate the application of this definition, and demonstrate asymptotic self-similarity for FLRW and other models. We also detail the conditions under which self-similarity is preserved by conformal transformations, and investigate its relationship to other symmetry properties in the framework.

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.

There is a mounting evidence that our universe is propelled into an accelerated expansion driven by Dark Energy. The simplest form of Dark Energy is a cosmological constant Λ, which is woven into the fabric of spacetime. For this reason it is often referred to as vacuum energy. It has the “strange” property of maintaining a constant energy density despite the expanding volume of the universe. Universes whose energy ismade of Λ posses an event horizon with and eternally finite constant temperature and entropy, and are known as DeSitter geometries. Since the entropy of DeSitter spaces remains a finite constant, then the meaning of a thermodynamic arrow of time becomes unclear. Here we explore the consequences of a fundamental cosmological constant Λ for our universe. We show that when the gravitational entropy of a pure DeSitter state ultimately dominates over the matter entropy, then the thermodynamic arrow of time in our universe may reverse in scales of order a Hubble time. We find that due to the dynamics of gravity and entanglement with other domain, a finite size system such as a DeSitter patch with horizon size H 0 -1 has a finite lifetime ∆t. This phenomenon arises from the dynamic gravitational instabilities that develop during a DeSitter epoch and turn catastrophic. A reversed arrow of time is in disagreementwith observations. Thus we explore the possibilities that: Nature may not favor a fundamental Λ, or else general relativity may be modified in the infrared regime when Λ dominates the expansion of the Universe.

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.

Macroscopic irreversible processes emerge from fundamental physical laws of reversible character. The source of the local irreversibility seems to be not in the laws themselves but in the initial and boundary conditions of the equations that represent the laws. In this work we propose that the screening of currents by black hole event horizons determines, locally, a preferred direction for the flux of electromagnetic energy. We study the growth of black hole event horizons due to the cosmological expansion and accretion of cosmic microwave background radiation, for different cosmological models. We propose generalized McVittie co-moving metrics and integrate the rate of accretion of cosmic microwave background radiation onto a supermassive black hole over cosmic time. We find that for flat, open, and closed Friedmann cosmological models, the ratio of the total area of the black hole event horizons with respect to the area of a radial co-moving space-like hypersurface always increases. Since accretion of cosmic radiation sets an absolute lower limit to the total matter accreted by black holes, this implies that the causal past and future are not mirror symmetric for any spacetime event. The asymmetry causes a net Poynting flux in the global future direction; the latter is in turn related to the ever increasing thermodynamic entropy. Thus, we expose a connection between four different "time arrows": cosmological, electromagnetic, gravitational, and thermodynamic.