Related papers: Self-gravitating fluid solutions of Shape Dynamics
We analyse the gravitational behaviour of a relativistic heat conducting fluid in a shear-free spherically symmetric spacetime. We show that the isotropy of pressure is a consistency condition which realises a second order nonlinear…
In this paper we investigate a class of solutions of Einstein equations for the plane-symmetric perfect fluid case with shear and vanishing acceleration. If these solutions have shear, they must necessarily be non-static. We examine the…
We discuss the total collision singularities of the gravitational N-body problem on shape space. Shape space is the relational configuration space of the system obtained by quotienting ordinary configuration space with respect to the…
In this work we shall investigate the occurrence of future cosmological finite-time singularities in the dynamical system corresponding to two cosmological theories, namely that of vacuum $f(R)$ gravity and that of three fluids. The vacuum…
Stimulated by the methods applied for the observational determination of masses in the central regions of the AGNs, we examine the conditions under which, in the interior of a gravitating perfect fluid source, the geodesic motions and the…
Perfect fluid space-times admitting a three-dimensional Lie group of conformal motions containing a two-dimensional Abelian Lie subgroup of isometries are studied. Demanding that the conformal Killing vector be proper (i.e., not homothetic…
We study a 2D potential flow of an ideal fluid with a free surface with decaying conditions at infinity. By using the conformal variables approach, we study a particular solution of Euler equations having a pair of square-root branch points…
In this paper we provide a classification of plane symmetric kinematic self-similar perfect fluid and dust solutions. In the perfect fluid and dust cases, kinematic self-similar vectors for the tilted, orthogonal and parallel cases have…
The static vacuum spherically symmetric solutions of massive gravity theories possess two integration constant: the mass M and a scalar charge S. The presence of this scalar charge reflects the modification of the gravitational interaction…
The evolution of electromagnetic and thermodynamic fields in a non-ideal fluid are studied in the framework of ultrarelativistic transverse magnetohydrodynamics (MHD), which is essentially characterized by electric and magnetic fields being…
We study properties of static spherically symmetric solutions in $f(\mathbb T)$ gravity. Based on our previous work on generalising Bianchi identities for this kind of theories, we show how this search of solutions can be reduced to the…
Mathematical modeling of gravitating configurations of physical fields is one of the priority directions of the modern theory of gravity. Most of the exact solutions constructed within the framework of the general relativity are static or…
A perfect fluid, spatially flat cosmology in a $f(T)$ model, derived from a recently proposed general Born-Infeld type theory of gravity is studied. Four dimensional cosmological solutions are obtained assuming the equation of state…
Static spherically symmetric solutions to the Einstein-Euler equations with prescribed central densities are known to exist, be unique and smooth for reasonable equations of state. Some criteria are also available to decide whether…
Einstein's field equations for spatially self-similar locally rotationally symmetric perfect fluid models are investigated. The field equations are rewritten as a first order system of autonomous ordinary differential equations.…
Relational particle dynamics include the dynamics of pure shape and cases in which absolute scale or absolute rotation are additionally meaningful. These are interesting as regards the absolute versus relative motion debate as well as…
In this paper we investigate spherically symmetric vacuum solutions of $f(R)$ gravity in a higher dimensional spacetime. With this objective we construct a system of non-linear differential equations, whose solutions depend on the explicit…
New exact vacuum solutions with various singularities in the plane-symmetric spacetime are shown, and they are applied to the analysis of inhomogeneous cosmological models and colliding gravitational waves. One of the singularities can be…
We outline the content and theoretical support for the proposal of "hydrodynamics on (mini)superspace" (or a non-linear extension of quantum cosmology) as an effective framework for quantum gravity in a cosmological context. The basis for…
This paper is a study of the effects of anisotropic matter sources on the qualitative evolution of spatially homogenous cosmologies of Bianchi type VIII. The analysis is based on a dynamical system approach and makes use of an anisotropic…