General Relativity And Quantum Cosmology

We give a detailed account of the Hamiltonian GNH analysis of the parametrized unimodular extension of the Holst action. The purpose of the paper is to derive, through the clear geometric picture furnished by the GNH method, a simple Hamiltonian formulation for this model and explain why it is difficult to arrive at it in other approaches. We will also show how to take advantage of the field equations to anticipate the simple form of the constraints that we find in the paper.

In the context of the dynamics and stability of black holes in modified theories of gravity, we derive the Teukolsky equations for massless fields of all spins in general spherically-symmetric and static metrics. We then compute the short-ranged potentials associated with the radial dynamics of spin 1 and spin 1/2 fields, thereby completing the existing literature on spin 0 and 2. These potentials are crucial for the computation of Hawking radiation and quasi-normal modes emitted by black holes. In addition to the Schwarzschild metric, we apply these results and give the explicit formulas for the radial potentials in the case of charged (Reissner--Nordström) black holes, higher-dimensional black holes, and polymerized black holes arising from loop quantum gravity. These results are in particular relevant and applicable to a large class of regular black hole metrics. The phenomenological applications of these formulas will be the subject of a companion paper.

We analyze the Hawking evaporation process of Reissner-Nordström black holes. It is shown that the characteristic radiation quanta emitted by the charged black holes may turn near-extremal black-hole spacetimes into horizonless naked singularities. The present analysis therefore reveals the intriguing possibility that the semi-classical Hawking evaporation process of black holes may violate the fundamental Penrose cosmic censorship conjecture.

Recently, a class of stationary black hole solutions with non-killing horizon in the asymptotic AdS bulk space was constructed to describe the far from equilibrium heat transport and particle transport from the boundary black holes via AdS/CFT correspondence. In this study, we calculate the spectrum of Hawking radiation of the black funnel solution. Our results indicate that the spectrum and the temperatures as well as the chemical potentials of the non-equilibrium black funnel do depend on one of the spatial coordinates. This is different from the equilibrium black holes with killing horizon, where the temperatures are uniform. Therefore, the black hole with non-killing horizon can be overall in non-equilibrium steady state while the Hawking temperature of the black funnel can be viewed as the local temperature and the corresponding Hawking radiation can be regarded as being in the local equilibrium with the horizon of the black funnel. By AdS/CFT, we discuss some possible implications of our results of local Hawking temperature for the non-equilibrium thermodynamics of dual conformal field theory. We further discuss the nonequilibrium thermodynamics of the black funnel, where the first law can be formulated as the entropy production rate being equal to the sum of the changes of the entropies from the system (black funnel) and environments while the second law is given by the entropy production being larger than or equal to zero. We found the time arrow emerged from the nonequilibrium black hole heat and particle transport dissipation. We also discuss how the nonequilibrium dissipation may influence the evaporation process of the black funnel.

In this paper, by studying the Einstein-Bohr's photon box for weighting a photon, we find that the effective Newton constant can be proposed by the extended uncertainty principle and extended generalized uncertainty principle. We obtain the modified Hawking temperature, mass, specific heat, and entropy by using the modified Schwarzschild metric.

We consider the Hawking-Ellis (Segre-Plebanski) classification of stress-energy tensors, both in the test-field limit, and in the presence of back-reaction governed by the usual Einstein equations. For test fields it is not too difficult to get a type~IV stress-energy via quantum vacuum polarization effects. (For example, consider the Unruh quantum vacuum state for a massless scalar field in the Schwarzschild background.) However, in the presence of back-reaction driven by the ordinary Einstein equations the situation is often much more constrained. For instance: (1) in any static spacetime the stress-energy is always type I in the domain of outer communication, and on any horizon that might be present; (2) in any stationary axisymmetric spacetime the stress-energy is always type I on any horizon that might be present; (3) on any Killing horizon that is extendable to a bifurcation 2-surface the stress-energy is always type I; (4) in any stationary axisymmetric spacetime the stress-energy is always type I on the axis of symmetry; (5) some of the homogeneous Bianchi cosmologies are guaranteed to be Hawking-Ellis type I (for example, all the Bianchi type I cosmologies, all the FLRW cosmologies, and all the "single mode" Bianchi cosmologies). That is, in very many physically interesting situations once one includes back-reaction the more unusual stress-energy types are automatically excluded.

The Hawking radiation would make microscopic black holes evaporate rapidly which excludes them from many astrophysical considerations. However, it has been argued that the quantum nature of space would alter this behaviour: the temperature of a Planck-size black hole vanishes and what is left behind is a Planck-mass remnant with a cross-section on the order of 10 ??0 m 2 which makes direct detection nearly impossible. Such black hole remnants have been identified as possible dark matter candidates. Here we argue that the final stage of the evaporation has a recoil effect which would give the microscopic black hole velocity on the order of 10 ?? c which is in disagreement with the cold dark matter cosmological model.

A heuristic method to find asymptotic solutions to a system of non-linear wave equations near null infinity is proposed. The non-linearities in this model, dubbed good-bad-ugly, are known to mimic the ones present in the Einstein field equations (EFE) and we expect to be able to exploit this method to derive an asymptotic expansion for the metric in General Relativity (GR) close to null infinity that goes beyond first order as performed by Lindblad and Rodnianski for the leading asymptotics. For the good-bad-ugly model, we derive formal expansions in which terms proportional to the logarithm of the radial coordinate appear at every order in the bad field, from the second order onward in the ugly field but never in the good field. The model is generalized to wave operators built from an asymptotically flat metric and it is shown that it admits polyhomogeneous asymptotic solutions. Finally we define stratified null forms, a generalization of standard null forms, which capture the behavior of different types of field, and demonstrate that the addition of such terms to the original system bears no qualitative influence on the type of asymptotic solutions found.

Quantum fluctuations endow spacetime with a foamy texture. The degree of foaminess is dictated by blackhole physics to be of the holographic type. Applied to cosmology, the holographic foam model predicts the existence of dark energy with critical energy density in the current (late) universe, the quanta of which obey infinite statistics. Furthermore we use the deep similarities between turbulence and the spacetime foam phase of strong quantum gravity to argue that the early universe was in a turbulent regime when it underwent a brief cosmic inflation with a "graceful" transition to a laminar regime. In this scenario, both the late and the early cosmic accelerations have their origins in spacetime foam.

In this paper, we extend the treatment of asymptotically decelerating spatially flat FLRW spacetimes initiated in [1]. We show that a certain class of those metrics is ruled by the asymptotic algebra bm s s , which belongs to a one-parameter family of deformations of bms . Furthermore, we enlarge our ansatz to include Diff( S 2 ) transformations whose asymptotic algebra gbm s s is a one parameter deformation of gbms . Therefore, the holographic algebras bm s s and gbm s s in FLRW can be related to their flat counterparts through a cosmological holographic flow. Finally, we introduce a logarithmic ansatz in order to account for cosmological black holes, which does not generally satisfy the peeling property but preserves the asymptotic algebra.