Related papers: Conformal Ricci and Matter Collineations for Two P…
We develop the canonical formalism for a system of $N$ bodies in lineal gravity and obtain exact solutions to the equations of motion for N=2. The determining equation of the Hamiltonian is derived in the form of a transcendental equation,…
The hydrodynamic behaviour of perfect fluid orbiting around black holes in spherically symmetric spacetime for various alternative gravity theories has been investigated. For this purpose we have assumed an uniform distribution for the…
Ideal fluid dynamics is studied as a relativistic field theory with particular importance on its hamiltonian structure. The Schwinger condition, whose integrated version yields the stress tensor conservation, is explicitly verified both in…
In this paper we analyse Abelian diagonal orthogonally transitive spacetimes with spacelike orbits for which the matter content is a stiff perfect fluid. The Einstein equations are cast in a suitable form for determining their geodesic…
We present a brief review of exact solutions of cylindrical symmetric fields in General Relativity produced by different perfect fluid sources. These sources are assumed static, stationary, translating and collapsing. Properties of these…
In this work we explore the consequences that a non-minimal coupling between geometry and matter can have on the dynamics of perfect fluids. It is argued that the presence of a static, axially symmetric pressureless fluid does not imply a…
This paper is devoted to study the charged perfect fluid cylindrical gravitational collapse. For this purpose, we find a new analytical solution of the field equations for non-static cylindrically symmetric spacetime. We discuss physical…
This paper is devoted to the investigation of the consequences of timelike and spacelike matter inheritance vectors in specific forms of energy-momentum tensor, i.e., for string cosmology (string cloud and string fluid) and perfect fluid.…
In Riemannian geometry, the Ricci flow is the analogue of heat diffusion; a deformation of the metric tensor driven by its Ricci curvature. As a step towards resolving the problem of time in quantum gravity, we attempt to merge the Ricci…
We show that complete conformally flat manifolds of dimension n>2 with nonnegative Ricci curvature enjoy nice rigidity properties: they are either flat, or locally isometric to a product of a sphere and a line, or are globally conformally…
A general organizing principle is proposed that can be used to derive the equations of motion describing the near-equilibrium dynamics of causal and thermodynamically stable relativistic systems. The latter are found to display some new…
Alternative gravitational theories described by Lagrangians depending on general functions of the Ricci scalar have been proven to give coherent theoretical models to describe the experimental evidence of the acceleration of universe at…
We present a matrix method for obtaining new classes of exact solutions for Einstein's equations representing static perfect fluid spheres. By means of a matrix transformation, we reduce Einstein's equations to two independent Riccati type…
Einstein's field equations with variable gravitational and cosmological ``constant'' are considered in presence of perfect fluid for Bianchi type-I spacetime. Consequences of the four cases of the phenomenological decay of $\Lambda$ have…
Ricci flow on two dimensional surfaces is far simpler than in the higher dimensional cases. This presents an opportunity to obtain much more detailed and comprehensive results. We review the basic facts about this flow, including the…
The paper aims to study the connection between symmetries and conservation laws for the 2D Ricci flow model. The procedure starts by obtaining a set of multipliers which generates conservation laws. Then, using a general relation which…
We characterize $\eta$-Ricci solitons $(g,\xi,\lambda,\mu)$ in some special cases when the $1$-form $\eta$, which is the $g$-dual of $\xi$, is a harmonic or a Schr\"{o}dinger-Ricci harmonic form. We also provide necessary and sufficient…
Perfect fluid spacetimes admitting a kinematic self-similarity of infinite type are investigated. In the case of plane, spherically or hyperbolically symmetric space-times the field equations reduce to a system of autonomous ordinary…
A formulation of Einstein equations is presented that could yield advantages in the study of collisions of binary compact objects during regimes between linear-nonlinear transitions. The key idea behind this formulation is a separation of…
Conformal Ricci solitons are self similar solutions of the conformal Ricci flow equation. This paper deals with the study of conformal Ricci solitons within the framework of warped product manifolds which extends the notion of usual…