Related papers: Solution of the Helmholtz equation for spin-2 fiel…
The exact static and spherically symmetric solutions of the vacuum field equations for a Higgs Scalar-Tensor theory (HSTT) are derived in Schwarzschild coordinates. It is shown that in general there exists no Schwarzschild horizon and that…
We consider static, spherically symmetric, electrically or/and magnetically charged configurations of a minimally coupled scalar field with an arbitrary potential $V(\phi)$ in general relativity. Using the inverse problem method, we obtain…
We derive an exact solution to the Einstein's equations with a stress-energy tensor corresponding to an opposite-sign scalar field, and show that such a solution describes the internal region of a rotating wormhole. We also derive an static…
There are a number of publications on relativistic objects dealing either with black holes or naked singularities in the center. Here we show that there exist static spherically symmetric solutions of Einstein equations with a strongly…
After dimensional reduction the stationary spherically symmetric sector of Einstein's gravity is identified with an SL(2,R)/SO(2) Sigma model coupled to a one dimensional gravitational remnant. The space of classical solutions consists of a…
We critically examine the Roberts homothetic solution for the spherically symmetric Einstein-scalar field equations in double null coordinates, and show that the Roberts solution indeed solves the field equations only for one non-trivial…
Extensions of Einstein gravity with quadratic curvature terms in the action arise in most effective theories of quantised gravity, including string theory. This article explores the set of static, spherically symmetric and asymptotically…
We propose a low-rank method for solving the Helmholtz equation. Our approach is based on the WaveHoltz method, which computes Helmholtz solutions by applying a time-domain filter to the solution of a related wave equation. The wave…
We explain how to use smooth bivariate splines of arbitrary degree to solve the exterior Helmholtz equation based on a Perfectly Matched Layer (PML) technique. In a previous study (cf. [26]), it was shown that bivariate spline functions of…
In [18], fundamental solutions for the generalized bi-axially symmetric Helmholtz equation were constructed in $R_2^ + = \left\{ {\left( {x,y} \right):x > 0,y > 0} \right\}.$ They contain Kummer's confluent hypergeometric functions in three…
In this paper, we present the point symmetry group of three-dimensional homogeneous Helmholtz equation, when we consider the cylindrical coordinate system. In continuation, we present a complete set of functionally independent invariants of…
A static spherically symmetric metric in Einstein-scalar-tensor gravity theory with a scalar field potential $V[\phi]$ is non-singular for all real values of the coordinates. It does not have a black hole event horizon and there is no…
We find static spherically symmetric solutions of scale invariant $R^2$ gravity. The latter has been shown to be equivalent to General Relativity with a positive cosmological constant and a scalar mode. Therefore, one expects that solutions…
It is shown that the first biharmonic boundary value problem on a topologically trivial domain in 3D is equivalent to three (consecutively to solve) second-order problems. This decomposition result is based on a Helmholtz-like decomposition…
New solutions to the static, spherically symmetric Einstein-Yang-Mills-Higgs equations with the Higgs field in the triplet resp. doublet representation are presented. They form continuous families parametrized by $\alpha=M_W/M_Pl$ ($M_W$…
We present a detailed study of the spherically symmetric solutions in Lorentz breaking massive gravity. There is an undetermined function $\mathcal{F}(X, w_1, w_2, w_3)$ in the action of St\"{u}ckelberg fields…
There are constructed exact solutions of the quantum-mechanical equation for a spin S=1 particle in 2-dimensional Riemannian space of constant positive curvature, spherical plane, in presence of an external magnetic field, analogue of the…
We study spherically symmetric black hole solutions in a four-parameter Einstein-Cartan-type class of theories, called "torsion bigravity". These theories offer a geometric framework (with a metric and an independent torsionfull connection)…
Spherically symmetric static empty space solutions are studied in f(R) theories of gravity. We reduce the set of modified Einstein's equations to a single equation and show how one can construct exact solutions in different f(R) models. In…
Spin-Polarised cylinders with and without axial magnetic fields are obtained as particular families of solutions of Einstein-Cartan gravity (EC).The first solution represents a spin-polarised cylinder in teleparallel gravity.The second…