Related papers: Particle dynamics in spherically symmetric electro…
Geodesic equations of timelike and null charged particles in the Ernst metric are studied. We consider two distinct forms of the Ernst solution where the Maxwell potential represents either a uniform electric or magnetic field. Circular…
When solving the equations of General Relativity in a symmetric sector, it is natural to consider the same symmetry for the geometry and stress-energy. This implies that for static and isotropic spacetimes, the most general natural…
In computational relativity, critical behaviour near the black hole threshold has been studied numerically for several models in the last decade. In this paper we present a spatial Galerkin method, suitable for finding numerical solutions…
A general formalism for understanding the thermodynamics of horizons in spherically symmetric spacetimes is developed. The formalism reproduces known results in the case of black hole spacetimes. But its power lies in being able to handle…
Starting from the equations of motion in a 1 + 1 static, diagonal, Lorentzian spacetime, such as the Schwarzschild radial line element, I find another metric, but with Euclidean signature, which produces the same geodesics x(t). This…
We determine the exact solution of the Einstein field equations for the case of a spherically symmetric shell of liquid matter, characterized by an energy density which is constant with the Schwarzschild radial coordinate $r$ between two…
We find simple expressions for velocity of massless particles in dependence of the distance $r$ in Schwarzschild coordinates. For massive particles these expressions put an upper bound for the velocity. Our results apply to static…
We study the motion of a spinning particle with gravimagnetic moment in Schwarzschild-like spacetimes with a metric $ds^2=-f(r) dt^2 + f^{-1}(r) dr^2 + r^2 d\Omega^2$, specifically we deal with Schwarzschild, Reissner-Nordstrom black holes…
Here we construct new solution for the Einstein equations -- some analog of the Schwarzschild metric in anti--de Sitter--Beltrami space in the $c\to \infty$ limit ($R$-space). In this case we derive an adiabatic invariant for finite…
We present the full set of analytical solutions of the geodesic equations of charged test particles in the Reissner-Nordstr\"om space-time in terms of the Weierstra{\ss} $\wp$, $\sigma$ and $\zeta$ elliptic functions. Based on the study of…
The study investigates orbital motion of test particles near compact objects described by solutions involving massless scalar fields, electromagnetic fields, and nonlinear electrodynamics. Specifically, we analyze orbital dynamics in the…
A general form of a metric preserving all symmetries of a spherically symmetric gravitational field and angular momentum in spherical coordinates is obtained. Such metric may have $g_{01}(r)\neq 0$. The Newtonian limit uniquely defines…
We investigate the vacuum and charged spherically symmetric static solutions of the Einstein equations on cosmological background. The background metric is not flat, but curved, with constant - curvature spatial sections. Both vacuum and…
We derive the complete set of geodesic equations for massive and massless, charged test particles of a five-dimensional, rotating and charged solution of the Einstein-Maxwell-Chern-Simons field equations in five-dimensional minimal gauged…
This work is a purely syntactic geometric exploration of some few elements, which are our axioms, that in last instance it is the set of differential equations whose solutions give the geodesic lines of the Schwarzschild spacetime. We…
The equations of motion for $N$ non-relativistic particles attracting according to Newton's law are shown to correspond to the equations for null geodesics in a $(3N+2)$-dimensional Lorentzian, Ricci-flat, spacetime with a covariantly…
In this work we present all the possible solutions for a static cylindrical symmetric spacetime in the Einstein-Aether (EA) theory. As far as we know, this is the first work in the literature that considers cylindrically symmetric solutions…
Recently, an analytical study of radial and circular orbits for null and time-like geodesics that propagate in the spacetime produced by a Schwarzschild black hole associated with cloud of strings, in a universe filled by quintessence, has…
In this article, we have examined the existence of a static spherically symmetric solution in the Scalar Tensor Vector Gravity (STVG) and investigated its horizon distances to develop boundary limitations for our test particle. We have…
We establish a one-to-one correspondence between static spacetimes and Riemannian manifolds that maps causal geodesics to geodesics, as suggested by L. C. Epstein. We then explore constant curvature spacetimes - such as the de Sitter and…