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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…

We derive a family of exact solutions for bi-metric gravity with an exchange symmetry between the two metrics. In this two-parameter family of solutions the gravitational field is sourced by a time-independent massless scalar field. We find…

We study classical solutions in the Weyl-transverse (WTDiff) gravity. The WTDiff gravity is invariant under both the local Weyl (conformal) transformation and the volume preserving diffeormorphisms (transverse diffeomorphisms) and is known…

Now that English translations of Schwarzschild's original paper exist, that paper has become accessible to more people. Historically, the so-called "standard Schwarzschild solution" was not the original Schwarzschild's work, but it is…

Now that an English translation of Schwarzschild's original work exists, that work has become accessible to more people. Here his original solution to the Einstein field equations is examined and it is noted that it does not contain the…

In this manuscript, we show that the external Schwarzschild metric can be a good approximation of exact black hole solutions of entangled relativity. Since entangled relativity cannot be defined from vacuum, the demonstrations need to rely…

We obtain static, spherically symmetric, and asymptotically flat numerical solutions of massive gravity with a source. Those solutions show, for the first time explicitly, a recovery of the Schwarzschild solution of General Relativity via…

Some solutions of the Einstein equations for the eight-dimensional Riemann extension of the classical four-dimensional Schwarzschild metric are considered.

We study gravitational perturbations of Schwarzschild spacetime by solving a hyperboloidal initial value problem for the Bardeen-Press equation. Compactification along hyperboloidal surfaces in a scri-fixing gauge allows us to have access…

The Schwarzschild-deSitter metric is the known solution of Einstein field equations with cosmological constant term for vacuum spherically symmetric space around a point mass M. Recently it has been reported that in a $Lamda$-dominant world…

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 continue to study the response of black-hole space-times on the presence of additional strong sources of gravity. Restricting ourselves to static and axially symmetric (electro-)vacuum exact solutions of Einstein's equations, we first…

We reconsider space-time singularities in classical Einsteinian general relativity: with the help of several new co-ordinate systems we show that the Schwarzschild solution can be extended beyond the curvature singularity at r=0. The…

Motivated by quantum mechanical considerations we earlier suggested an alternative action for discretised quantum gravity which has a dimension of length. It is the so called "linear" action. The proposed action is a "square root" of the…

We study a set of static solutions of the Einstein equations in presence of a massless scalar field and establish their connection to the Kantowski-Sachs cosmological solutions based on some kind of duality transformations. The physical…

Several rigidity results are proved for critical points of natural Riemannian functionals on the space of metrics on 3-manifolds. Two of these results are as follows. Let (N, g) be a complete Riemannian 3-manifold, satisfying one of the…

We introduce an effective action smoothly extending the standard Einstein-Hilbert action to include un-gravity effects. The improved field equations are solved for the un-graviton corrected Schwarzschild geometry reproducing the Mureika…

Contents: 1) Introduction and a few excursions [A word on the role of explicit solutions in other parts of physics and astrophysics. Einstein's field equations. "Just so" notes on the simplest solutions: The Minkowski, de Sitter and anti-de…

Bending of light rays by gravitational sources is one of the first evidences of the general relativity. When the gravitational souce is a stationary massive object such as a black hole, the bending angle has an integral representation, from…

We consider a wide class of two-dimensional metrics having one Killing vector. The method is proposed for the construction of maximally extended surfaces with the given Riemannian metric which is the analog of the conformal block method for…