Penrose's Weyl Research Articles

On black hole thermodynamics, singularity, and gravitational entropy

Many fundamental issues remain for black hole thermodynamics after almost half a century of its conception. For example, what are the underlying degrees of freedom of a black hole horizon that give rise to said thermodynamical properties? Furthermore, classical black holes also harbor a spacetime singularity. Although it is often believed that quantum gravity would "cure" the singularity, as emphasized by Penrose, this viewpoint requires a deeper examination. In this review, I will examine the possibility that singularities remain in quantum gravity, the roles they may play, and the possible links between singularity and black hole thermodynamics. I will also discuss how -- inspired by Penrose's Weyl curvature hypothesis -- gravitational entropy for a black hole can be defined using curvature invariants, and the surprising implication that the entropy of black holes in different theories of gravity are different manifestations of spacetime curvature, i.e., their underlying microstructures could be different. Finally, I review the "Hookean law" recently established for singly rotating Myers-Perry black holes (including Kerr black holes) that connect black hole fragmentation -- a consequence of the second law of black hole thermodynamics -- with the maximum "Hookean force", as well as with the thermodynamic geometry of Ruppeiner. This also suggests a new way to study black hole microstructures, and hints at the possibility that some black holes are beyond the Hookean regime (and thus have different microstructures). While examining the remarkable connections between black hole thermodynamics, spacetime singularities and cosmic censorship, as well as gravitational entropy, I shall point out some subtleties, provide some new thoughts, and raise some hard but fundamental questions, including whether black hole thermodynamics is really just "ordinary thermodynamics" or something quite different.

On a quantum Weyl curvature hypothesis

Roger Penrose's Weyl curvature hypothesis states that the Weyl curvature is small at past singularities, but not at future singularities. We review the motivations for this conjecture and present estimates for the entropy of our Universe. We then extend this hypothesis to the quantum regime by demanding that the initial state of primordial quantum fluctuations be the adiabatic vacuum in a (quasi-)de Sitter space. We finally attempt a justification of this quantum version from a fundamental theory of quantum gravity and speculate on its consequences in the case of a classically recollapsing universe.

Cosmology of the Symmetrical Relativity versus Spontaneous Creation of the Universe Ex Nihilo

The cosmology of "Spontaneous Creation of the Universe Ex Nihilo" and the cosmology of the Symmetrical Relativity offer proposals to explain the creation and evolution of the universe. In essence they are still very distinct. However, we will argue that there was an antecedent to the big bang. Thus, we will penetrate a trans-Planckian regime, where we find an effective Planck length $L_P^{\prime}\rightarrow 0$. This will lead to more fundamental physical reflections about {\it nothing} in the cosmology of spontaneous creation. From the point of view of spontaneous creation, the step backwards went back to another principle, based on the {\it information}, which led to the big bang. While the spontaneous creation refers to the virtual pre-existence of {\it information}, which would have emerged randomly from {\it nothing}, the cosmology of Symmetrical Relativity does not stop there: we go back to one's own origin by projecting it before the creation of one's own time. From the present perspective, {\it nothing} is a primordial vacuum, whose {\it information} has made the universe by condensing and igniting. It was not randomly created, since the entropy had to vary from infinite (chaos) to zero (big bang) by violating the 2nd.law of thermodynamics in a trans-Planckian regime. {\it Nothing} or chaos with infinite entropy precedes the big bang (null entropy) within a trans-Planckian scenario and it determines the whole plot until the total extinction of the universe. We will show that {\it information}, besides not being born of the universe, also does not develop from it like the computational idea of Artificial Intelligence (AI). Thus, the universe is not simply self-taught as defended by the spontaneous creation. This could shed light on the problem of Penrose's Weyl curvature hypothesis, which considers a null Weyl curvature due to a null entropy in the big bang.

Intrinsic time quantum geometrodynamics

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.

Penrose's Weyl curvature hypothesis and conformally-cyclic cosmology

I discuss two ideas of Roger Penrose and the relation between them: his Weyl curvature hypothesis from thirty years ago and his recent idea for a conformally-cyclic universe, that is a cosmological model with positive cosmological constant in which the conformal metric is cyclic – it can be continued through the future null infinity of one aeon to the big bang of the following aeon.

Gravitational entropy and quantum cosmology

We investigate the evolution of different measures of `gravitationalentropy'in Bianchi type I and Lemaître-Tolman universe models.A new quantity behaving in accordance with the second law ofthermodynamics is introduced. We then go on and investigate whether aquantum calculation of initial conditions for the universe based upon theWheeler-DeWitt equation supports Penrose's Weyl curvatureconjecture, according to which the Ricci part of the curvature dominatesover the Weyl part at the initial singularity of the universe. The theory isapplied to the Bianchi type I universe models with dust and acosmological constant and to the Lemaître-Tolman universe models. Weinvestigate two different versions of the conjecture. First, we investigatea local version which fails to support the conjecture. Thereafter weconstruct a non-local entity which shows more promising behaviourconcerning the conjecture.

Isotropic singularities in cosmological models

Motivated by the ideas of quiescent cosmology and Penrose's Weyl tensor hypothesis concerning the 'big bang', the authors give a geometric (and hence coordinate-independent) definition of the concept of 'isotropic singularity' in a spacetime. The definition generalises previous work on 'quasi-isotropic' and 'Friedman-like' singularities. They discuss simple consequences of the definition. In particular it is shown that an isotropic singularity is a scalar polynomial curvature singularity at which the Weyl tensor is dominated by the Ricci tensor. Finally they impose the Einstein field equations with irrotational perfect fluid source. This enables them to give a detailed description of the geometric structure of an isotropic singularity.

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.