General Relativity And Quantum Cosmology

We examine the influence of the dispersion relation on the Unruh effect by Lorentz boosting the phase of Minkowski vacuum fluctuations endowed with an arbitrary dispersion relation. We find that, unlike what happens with a linear dispersion relation exhibited by massless fields, thermality is lost for general dispersion relations. We show that thermality emerges with a varying "apparent" Davies-Unruh temperature depending on the acceleration of the observer and on the degree of departure from linearity of the dispersion relation. The approach has the advantage of being intuitive and able to pinpoint why such a loss of thermality occurs and when such a deviation from thermality becomes significant. We discuss the link of our results with the well-known fundamental difference between the thermalization theorem and the concept of Rindler noise. We examine the possible experimental validation of our results based on a successful setup for testing the classical analogue of the Unruh effect recently described in the literature.

The propagators for the Faddeev-Popov (FP) ghosts in Yang-Mills theory and perturbative gravity in the covariant gauge are infrared (IR) divergent in de Sitter spacetime. An IR cutoff in the momentum space to regularize these divergences breaks the de Sitter invariance. These IR divergences are due to the spatially constant modes in the Yang-Mills case and the modes proportional to the Killing vectors in the case of perturbative gravity. It has been proposed that these IR divergences can be removed, with the de Sitter invariance preserved, by first regularizing them with an additional mass term for the FP ghosts and then taking the massless limit. In the Yang-Mills case, this procedure has been shown to correspond to requiring that the physical states, and the vacuum state in particular, be annihilated by some conserved charges in the Landau gauge. In this paper we show that there are similar conserved charges in perturbative gravity in the covariant Landau gauge in de Sitter spacetime and that the IR-regularization procedure described above also correspond to requiring that the vacuum state be annihilated by these charges with a natural definition of the interacting vacuum state.

Regular black holes with nonsingular cores have been considered in several approaches to quantum gravity, and as agnostic frameworks to address the singularity problem and Hawking's information paradox. While in a recent work we argued that the inner core is destabilized by linear perturbations, opposite claims were raised that regular black holes have in fact stable cores. To reconcile these arguments, we discuss a generalization of the geometrical framework, originally applied to Reissner--Nordtsröm black holes by Ori, and show that regular black holes have an exponentially growing Misner--Sharp mass at the inner horizon. This result can be taken as an indication that stable nonsingular black hole spacetimes are not the definitive endpoint of a quantum gravity regularization mechanism, and that nonperturbative backreaction effects must be taken into account in order to provide a consistent description of the quantum-gravitational endpoint of gravitational stellar collapse.

We consider a Lorentz violating scalar field cosmological model given by the modified Einstein-aether theory defined in Weyl integrable geometry. The existence of exact and analytic solutions is investigated for the case of a spatially flat Friedmann--Lema\^ıtre--Robertson--Walker background space. We show that the theory admits cosmological solutions of special interests. In addition, we prove that the cosmological field equations admit the Lewis invariant as a second conservation law, which indicates the integrability of the field equations.

We consider the interaction between the Earth's gravitational field and a superconductor in the fluctuation regime. Exploiting the weak field expansion formalism and using time dependent Ginzburg-Landau formulation, we show a possible short-time alteration of the gravitational field in the vicinity of the superconductor.

In [M. Zych et al., Nat. Commun. 2, 505 (2011)], the authors predicted that the interferometric visibility is affected by a gravitational field in way that cannot be explained without the general relativistic notion of proper time. In this work, we take a different route and start deriving the same effect using the unitary representation of the local Lorentz transformation in the Newtonian Limit. In addition, we show that the effect on the interferometric visibility due to gravity persists in different spacetime geometries. However, the influence is not necessarily due to the notion of proper time. For instance, by constructing a `astronomical' Mach-Zehnder interferometer in the Schwarzschild spacetime, the influence on the interferometric visibility can be due to another general relativistic effect, the geodetic precession. Besides, by using the unitary representation of the local Lorentz transformation, we show that this behavior of the interferometric visibility is general for an arbitrary spacetime, provided that we restrict the motion of the quanton to a two-dimensional spacial plane.

We obtain well behaved interior solutions describing hydrostatic equilibrium of anisotropic relativistic stars in scale-dependent gravity, where Newton's constant is allowed to vary with the radial coordinate throughout the star. Assuming i) a linear equation-of-state in the MIT bag model for quark matter, and ii) a certain profile for the energy density, we integrate numerically the generalized structure equations, and we compute the basic properties of the strange quark stars, such as mass, radius and compactness. Finally, we demonstrate that stability criteria as well as the energy conditions are fulfilled. Our results show that a decreasing Newton's constant throughout the objects leads to slightly more massive and more compact stars.

The Alcubierre warp drive is an exotic solution in general relativity. It allows for superluminal travel at the cost of enormous amounts of matter with negative mass density. For this reason, the Alcubierre warp drive has been widely considered unphysical. In this study, we develop a model of a general warp drive spacetime in classical relativity that encloses all existing warp drive definitions and allows for new metrics without the most serious issues present in the Alcubierre solution. We present the first general model for subluminal positive-energy, spherically symmetric warp drives; construct superluminal warp-drive solutions which satisfy quantum inequalities; provide optimizations for the Alcubierre metric that decrease the negative energy requirements by two orders of magnitude; and introduce a warp drive spacetime in which space capacity and the rate of time can be chosen in a controlled manner. Conceptually, we demonstrate that any warp drive, including the Alcubierre drive, is a shell of regular or exotic material moving inertially with a certain velocity. Therefore, any warp drive requires propulsion. We show that a class of subluminal, spherically symmetric warp drive spacetimes, at least in principle, can be constructed based on the physical principles known to humanity today.

It is conjectured that stationary black holes are characterized by the inverse hoop relation A??C 2 /? , where A and C are respectively the black-hole surface area and the circumference length of the smallest ring that can engulf the black-hole horizon in every direction. We explicitly prove that generic Kerr-Newman-(anti)-de Sitter black holes conform to this conjectured area-circumference relation.

This paper proposes a toy model where, in the Einstein equations, the right-hand side is modified by the addition of a term proportional to the symmetrized partial contraction of the Ricci tensor with the energy-momentum tensor, while the left-hand side remains equal to the Einstein tensor. Bearing in mind the existence of a natural length scale given by the Planck length, dimensional analysis shows that such a term yields a correction linear in h to the classical term, that is instead just proportional to the energy-momentum tensor. One then obtains an effective energy-momentum tensor that consists of three contributions: pure energy part, mechanical stress and thermal part. The pure energy part has the appropriate property for dealing with the dark sector of modern relativistic cosmology. Such a theory coincides with general relativity in vacuum, and the resulting field equations are here solved for a Dunn and Tupper metric, for departures from an interior Schwarzschild solution as well as for a Friedmann-Lemaitre-Robertson-Walker universe.