Related papers: Analytical solution methods for geodesic motion
We consider Einstein-Weyl gravity with a minimally coupled scalar field in four dimensional spacetime. By using the Minimal Geometric Deformation (MGD) approach, we split the highly nonlinear coupled field equations into two subsystems that…
In this article we study the geodesic motion of test particles and light in the five-dimensional (rotating) black string spacetime. If a compact dimension is added to the four-dimensional Schwarzschild or Kerr spacetime, the new…
The exact solution of Einstein - Maxwell equations for a Schwarzschild black hole immersed in the static spatially homogeneous AdS${}^2\times\mathbb{S}^2$ space-time of Bertotti-Robinson magnetic universe is presented. In this solution, the…
In this article we derive the geodesic equations in the $\text{U(1)}^2$ dyonic rotating black hole spacetime. We present their solutions in terms of the Kleinian $\sigma$-function and in special cases in terms of the Weierstra{\ss} $\wp$-,…
We present a novel method to study interacting orbits in a fixed mean gravitational field associated with a solution of the Einstein field equations. The idea is to consider the Newton gravity among the orbiting particles in a geometry…
The search for solutions of Einstein's equations representing relativistic cosmological models with a discrete matter content has been remarkably fruitful in the last decade. In this review we discuss the progress made in the study of a…
Since the development of Relativity theory, a variety of solutions have been found around Einstein field equations, depending on the time-space. For instance, we can find the axially symmetric space which describes a rotanting black hole.…
In this work, we introduce an analytical approximate black hole solution in Einstein-Cubic gravity. To obtain complete solutions, we construct the near horizon and asymptotic solutions as the first step. Then, the approximate analytic…
Time-like orbits in Schwarzschild space-time are presented and classified in a very transparent and straightforward way into four types. The analytical solutions to orbit, time, and proper time equations are given for all orbit types in the…
In this article we analyze the geodesics of test particles and light in the five dimensional (charged) doubly spinning black ring spacetime. Apparently it is not possible to separate the Hamilton-Jacobi-equation for (charged) doubly…
Detailed observations of phenomena involving black holes, be it via gravitational waves or more traditional electromagnetic means, can probe the strong field regime of the gravitational interaction. The prediction of features in such…
We study new black hole solutions in quantum gravity. We use the Vilkovisky-DeWitt unique effective action to obtain quantum gravitational corrections to Einstein's equations. In full analogy to previous work done for quadratic gravity, we…
We extend a recently developed numerical code to obtain stationary, axisymmetric solutions that describe rotating black hole spacetimes in a wide class of modified theories of gravity. The code utilizes a relaxed Newton-Raphson method to…
By applying the method of moving frames modelling one and two dimensional local anisotropies we construct new solutions of Einstein equations on pseudo-Riemannian spacetimes. The first class of solutions describes non-trivial deformations…
In the standard Einstein's theory the exterior gravitational field of any static and axially symmetric stellar object can be described by means of a single function from which we obtain a metric into a four-dimensional space-time. In this…
We study geodesic motion in expanding spherical impulsive gravitational waves propagating in a Minkowski background. Employing the continuous form of the metric we find and examine a large family of geometrically preferred geodesics. For…
We obtain analytical approximate black hole solutions for higher derivative gravity in the presence of Maxwell electromagnetic source. We construct near horizon and asymptotic solutions and then use these to obtain an approximate analytic…
The study of Kerr geodesics has a long history, particularly for those occurring within the equatorial plane, which is generally well-understood. However, upon comparison with the classification introduced by one of us…
The complete sets of analytic solutions of the geodesic equation in Taub--NUT--(anti-)de Sitter, Kerr--(anti-)de Sitter and also in general Plebanski--Demianski space--times without acceleration are presented. The solutions are given in…
Action-angle coordinates are a tool commonly used in celestial mechanics to systematically parametrize and store general solutions of the equations of motion of astrophysical bodies. I perturbatively construct action-angle coordinates for…