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We obtain a geometrical inequality involving the ADM mass, the angular momentum and the size of an ordinary, axially symmetric object. We use the monotonicity of the Geroch quasi-local energy on 2-surfaces along the inverse mean curvature…
We discuss the averaging problem in general relativity, using the form of the macroscopic gravity equations in the case of spherical symmetry in volume preserving coordinates. In particular, we calculate the form of the correlation tensor…
We use the idea of the symmetry between the spacetime coordinates x^\mu and the energy-momentum p^\mu in quantum theory to construct a momentum space quantum gravity geometry with a metric s_{\mu\nu} and a curvature P^\lambda_{\mu\nu\rho}.…
A range of cosmological observations demonstrate an accelerated expansion of the Universe, and the most likely explanation of this phenomenon is a cosmological constant. Given the importance of understanding the underlying physics, it is…
In an expanding universe the vacuum energy density \rho_{\Lambda} is expected to be a dynamical quantity. In quantum field theory in curved space-time \rho_{\Lambda} should exhibit a slow evolution, determined by the expansion rate of the…
Continuum equations are ubiquitous in physical modelling of elastic, viscous, and viscoelastic systems. The equations of continuum mechanics take nontrivial forms on curved surfaces. Although the curved surface formulation of the continuum…
The problem of deforming geometries is particularly important in the context of constructing new exact solutions of Einstein's equation. This issue often appears when extensions of the general relativity are treated, for instance in brane…
Two forms are suggested for the energy-momentum source term associated with an aggregate of dark matter (with the properties described in Paper I). Both have large pressure-like components which dominate the density terms. Using one form a…
Spacetime must be foliable by spacelike surfaces for the quantum mechanics of matter fields to be formulated in terms of a unitarily evolving state vector defined on spacelike surfaces. When a spacetime cannot be foliated by spacelike…
The Friedmann equation is derived for a Newtonian universe. Changing mass density to energy density gives exactly the Friedmann equation of general relativity. Accounting for work done by pressure then yields the two Einstein equations that…
Doubly special relativity has been studied for the last twenty years as a way to go beyond the special relativistic kinematics, trying to capture residual effects of a quantum gravity theory. In particular, in doubly special relativity the…
While the simple picture of a spatially flat, matter plus cosmological constant universe fits current observation of the accelerated expansion, strong consideration has also been given to models with dynamical vacuum energy. We examine the…
As evidenced by a great number of works, it is common practice to assume that the Universe is flat. However, the majority of studies which make use of observational data to constrain the curvature density parameter are premised on the…
A number of recent proposals for a quantum theory of gravity are based on the idea that spacetime geometry and gravity are derivative concepts and only apply at an approximate level. There are two fundamental challenges to any such…
The space-time length R between a moving source and the observation point is calculated in order to substitute with it the spatial distance D, normally used in the Newton's law of gravitation, as well as in any inverse-square-law.…
The investigations presented in this study are directed at relativistic modifications of the uncertainty relation derived from the curvature of the background spacetime. These findings generalize previous work which is recovered in the…
A suitable derivative of Einstein's equations in the framework of the teleparallel equivalent of general relativity (TEGR) yields a continuity equation for the gravitational energy-momentum. In particular, the time derivative of the total…
A deformation of special relativistic kinematics (possible signal of a theory of quantum gravity at low energies) leads to a modification of the notion of spacetime. At the classical level, this modification is required when one considers a…
We present new numerical cosmological solutions of the Einstein Field Equations. The spacetime is spherically symmetric with a source of dust and radiation approximated as a perfect fluid. The dust and radiation are necessarily non-comoving…
There has been considerable interest over the past years in investigating the role of gravity in quantum phenomenon such as entanglement and decoherence. In particular, gravitational time dilation is believed to decohere superpositions of…