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We resolve the entire gravitational field;i.e. the Riemann curvature into its electric and magnetic parts. In general, the vacuum Einstein equation is symmetric in active and passive electric parts. However it turns out that the…
In this paper we study black string solutions considering the Lifshitz anisotropic scaling. We have shown that a new class of asymptotically Lifshitz solutions can be generated by an Einstein-Maxwell-Dilaton theory with a cosmological…
In this work, we investigate the existence of analytic solutions of static scalar fields on Lifshitz spacetimes. We evade Derrick's theorem on curved spacetimes by breaking general covariance and use first-order formalism to obtain…
In this paper we utilize symmetries in order to exhibit exact solutions to Einstein's equation of a perfect fluid on a static manifold all of whose spatial factor belongs to the conformal class of a Riemannian space of constant curvature.
In this paper we provide a method capable of producing an infinite number of solutions for Einstein's equation on static spacetimes with perfect fluid as a matter field. All spacetimes of this type which are symmetric with respect to a…
When exploring equations of nonlinear electrodynamics in effective medium formed by mutually parallel external electric and magnetic fields, we come to special static axial-symmetric solutions of two types. The first are comprised of fields…
Based on the rigid positive energy theorem we proved the uniqueness of static spherically symmetric traversable wormholes with two asymptotically flat ends, being the higher-dimensional solutions of Einstein scalar phantom field. The proof…
By means of Banach fixed point theorem , the uniqueness of Boltzmann Equation generalizaled Solutions in Sobolev spaces in $L^1(\mathbb{R}^+\times \mathbb{R}^n\times \mathbb{R}^n)$, can be proved as well as Boltzmann Equation renormalized…
Schrodinger's equation for a single particle is proved from the assumption that dynamics can be formulated in a space whose curvature is the electromagnetic force.
We analyse the issue of uniqueness of solutions of the static vacuum Einstein equations with prescribed geometric or Bartnik boundary data. Large classes of examples are constructed where uniqueness fails. We then discuss the implications…
We study the appearance of multiple solutions to certain decompositions of Einstein's constraint equations. Pfeiffer and York recently reported the existence of two branches of solutions for identical background data in the extended…
We study the stability of general relativistic static thick disks, as an application we consider the thick disk generated by applying the ``displace, cut, fill and reflect" method, usually known as the image method, to the Schwarzschild…
We reexamine the Israel-type proof of the uniqueness theorem of the static spacetime outside the photon surface in the Einstein-conformal scalar system. We derive in a systematic fashion a new divergence identity which plays a key role in…
This paper consists of two parts. In the first part we describe the recent works on the inverse problems for the wave equation in $(n+1)$-dimensional space equipped with pseudo-Riemannian metric with Lorentz signature. We study the…
The deep reason why the equations describing axial and polar perturbations of Schwarzschild black holes have the same spectrum is far from trivial. In this article, we revisit the original proof and try to make it clearer. Still focusing on…
An exact solution for the field of a charge in a uniformly accelerated noninertial frame of reference (NFR) alongside the "Equivalent Situation Postulate" allows one to find space-time structure as well as fields from arbitrarily shaped…
We have studied spacetime structures of static solutions in the $n$-dimensional Einstein-Gauss-Bonnet-Maxwell-$\Lambda$ system. Especially we focus on effects of the Maxwell charge. We assume that the Gauss-Bonnet coefficient $\alpha$ is…
Extensions of Einstein gravity with higher-order derivative terms arise in string theory and other effective theories, as well as being of interest in their own right. In this paper we study static black-hole solutions in the example of…
According to the Einstein hole argument, vacuum metric solutions are equivalent only if they correspond to the same energy--momentum tensor in the source region. In this paper it is shown that singular coordinates that are used to show…
We study static spherically symmetric solutions to the vacuum field equations of quadratic gravity in the presence of a cosmological constant $\Lambda$. Motivated by the trace no-hair theorem, we assume the Ricci scalar to be constant…