Related papers: Point massive particle in General Relativity
We present a stationary generalization of the static $q-$metric, the simplest generalization of the Schwarzschild solution that contains a quadrupole parameter. It possesses three independent parameters that are related to the mass,…
A general procedure to find static and axially symmetric, interior solutions to the Einstein equations is presented. All the so obtained solutions, verify the energy conditions for a wide range of values of the parameters, and match…
The paper deals with a special kind of problems that appear in solutions of Einstein's field equations for extended bodies: many structure-dependent terms appear in intermediate calculations that cancel exactly in virtue of the local…
In this article, a special static spherically symmetric perfect fluid solution of Einstein's equations is provided. Though pressure and density both diverge at the origin, their ratio remains constant. The solution presented here fails to…
We study spherically symmetric configurations of the quadratic $f(R)$ gravity in the Einstein frame. In case of a purely gravitational system, we have determined the global qualitative behavior of the metric and the scalaron field for all…
Kerr-Schild solutions to the vacuum Einstein equations are considered from the viewpoint of integral equations. We show that, for a class of Kerr-Schild fields, the stress-energy tensor can be regarded as a total divergence in Minkowski…
We study spherically symmetric spacetimes in Einstein-aether theory in three different coordinate systems, the isotropic, Painlev\`e-Gullstrand, and Schwarzschild coordinates, in which the aether is always comoving, and present both…
The so called gamma metric corresponds to a two-parameter family of axially symmetric, static solutions of Einstein's equations found by Bach. It contains the Schwarzschild solution for a particular value of one of the parameters, that…
We find the most general, spherically symmetric solution in a special class of tetrad theory of gravitation. The tetrad gives the Schwarzschild metric. The energy is calculated by the superpotential method and by the Euclidean continuation…
In this work, we have obtained exact solutions of Einstein equations for static and axially symmetric magnetized matter, specifically in plane-symmetric and almost-plane symmetric cases. Although these solutions impose constraints on the…
Motivated by conventional gauge theories, we consider a theory of gravity in which the Einstein-Hilbert action is replaced by a term that is quadratic in the Riemann tensor. We focus on cosmological solutions to the field equations in flat,…
The static spherically symmetric solution for (R +- {\mu}^4/R) model of f(R)gravity is investigated. We obtain the metric for space-time in the solar system that reduces to the Schwarzschild metric, when {\mu} tends to zero. For the…
Firstly, I give the reason why is wrong my previously made assumption that the volume integral over the pressure may not be zero in a system where the gravitation plays no role in holding the system together. Secondly, in the first…
In gravitational Higgs mechanism graviton components acquire mass via spontaneous diffeomorphism breaking by scalar vacuum expectation values. We point out that in the massless limit the resulting theory is not Einstein-Hilbert gravity…
We study a numerical solution to Einstein's equation for a compact object composed of null particles. The solution avoids quantum scale regimes and hence neither relies upon nor ignores the interaction of quantum mechanics and gravitation.…
In this work we study static spherically symmetric solutions of effective field equations related to local and nonlocal higher-derivative gravity models, based on their associated effective delta sources. This procedure has been applied to…
The Schwarzschild-de Sitter solution in the Einstein theory with a positive cosmological constant $\Lambda=m^2/\alpha$ becomes an exact solution to the dRGT non-linear massive gravity theory with the mass parameter $m$ when the theory…
The Einstein equations are non-linear and the particles of which the gravitational effect is described by these equations are lastly unknown. If renormalizable fields are assumed, then results are obtained only in the case of a at space.…
The solution of Einstein field equations for static spherically symmetric spacetime metric with anisotropic internal stresses has been obtained. The matter has vanishing complexity and a spacetime metric that satisfies the Karmarkar…
We show that, unlike vacuum General Relativity, Einstein-scalar theories allow balanced static, neutral, asymptotically flat, double-black hole solutions, for scalar field models minimally coupled to gravity, with appropriate…