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Three-dimensional gravity coupled to pressureless dust is a field theory with one local degree of freedom. In the canonical framework, the dust-time gauge encodes this physical degree of freedom as a metric function. We find that the…
Albert Einstein's General Relativity (GR) from 1916 has become the widely accepted theory of gravity and been tested observationally to a very high precision at different scales of energy and distance. At the same time, there still remain…
Solutions of the stationary axisymmetric Einstein equations describing the interior of circularly rotating dust are investigated in order to study their potential applicability as galaxy models. It is shown that such interior solutions…
The general relativistic non--linear dynamics of a self--gravitating collisionless fluid with vanishing vorticity is studied in synchronous and comoving -- i.e. {\em Lagrangian} -- coordinates. Writing the equations in terms of the metric…
Canonical analysis of a recently proposed [1] linear+quadratic curvature gravity model in D=3 displays its pure fourth derivative quadratic branch as a ghost-free (massless) excitation. Hence it both negates an old no-go theorem and is…
The Raychaudhuri equations for the expansion, shear and vorticity are generalized in a spacetime with torsion for timelike as well as null congruences. These equations are purely geometrical like the original Raychaudhuri equations and…
This is the second in a series of papers on the construction of explicit solutions to the stationary axisymmetric Einstein equations which can be interpreted as counter-rotating disks of dust. We discuss the class of solutions to the…
We present an idealised model of gravitational collapse, describing a collapsing rotating cylindrical shell of null dust in flat space, with the metric of a spinning cosmic string as the exterior. We find that the shell bounces before…
We give a model of the higher-dimensional spherically symmetric gravitational collapse of a dust cloud in Einstein-Gauss-Bonnet gravity. A simple formulation of the basic equations is given for the spacetime $M \approx M^2 \times K^{n-2}$…
In this paper, the following two propositions are proven under the dominant energy condition for the matter field in the higher-dimensional spherically symmetric spacetime in Einstein-Gauss-Bonnet gravity in the presence of a cosmological…
A class of exact general relativistic rotating thick disks surrounded by rotating dust is constructed by applying the ``displace, cut, fill and reflect'' method on the van Stockum class of metrics. Two particular solutions are considered in…
We study gravitational collapse in effective loop quantum gravity, focusing on non-marginally bound configurations in Lema\^itre-Tolman-Bondi spacetimes. In the homogeneous limit we recover the effective dynamics of loop quantum cosmology…
The vacuum solution of Einstein's theory of general relativity provides a rotating metric with a ring singularity, which is covered by the inner and outer horizons, and an ergo region. In this paper, we will discuss how ghost-free,…
We describe the irrotational dust component of the universe in terms of a relativistic gradient expansion and transform the resulting synchronous metric to a Newtonian coordinate system. The two metrics are connected via a space-like…
Symmetries of spacetimes with null dust field as a source compatible with asymptotic flatness are studied by using the Bondi-Sachs-van der Burg formalism. It is shown that in an axially symmetric spacetime with null dust field in which at…
We develop an algebraic equation to describe the collapse and possible bounce of dust in quantum-inspired gravity models with spherical symmetry from knowledge of the vacuum solution. Starting from a wide class of spherically symmetric…
In this work we investigate some non-Newtonian effects in exact solutions of the Einstein equations, which describe stationary and axisymmetric configurations of self-gravitating dust. A distinctive feature of these solutions is the…
Using a framework based on the 1+3 formalism, we show that a source represented by a geodesic, dissipative, rotational dust, endowed with axial and reflection symmetry, violates regularity conditions at the center of the fluid distribution,…
We present an explicit exact solution of Einstein's equations for an inhomogeneous dust universe with cylindrical symmetry. The spacetime is extremely simple but nonetheless it has new surprising features. The universe is ``closed'' in the…
When tetrad (metric) fields are not invertible, the standard canonical formulation of gravity cannot be adopted as it is. Here we develop a Hamiltonian theory of gravity for non-invertible tetrad. In contrast to Einstein gravity, this phase…