Related papers: Analytic solutions of the geodesic equation in axi…
The complete set of analytic solutions of the geodesic equation in a Schwarzschild--(anti) de Sitter space--time is presented. The solutions are derived from the Jacobi inversion problem restricted to the theta--divisor. In its final form…
The complete analytical solutions of the geodesic equations in Kerr-de Sitter and Kerr-anti-de Sitter space-times are presented. They are expressed in terms of Weierstrass elliptic p, zeta, and sigma functions as well as hyperelliptic…
We review the analytical solution methods for the geodesic equations in Kerr-Newman-Taub-NUT-de Sitter spacetimes and its subclasses in terms of elliptic and hyperelliptic functions. A short guide to corresponding literature for general…
The complete set of analytic solutions of the geodesic equation in a Schwarzschild--(anti-)de Sitter space--time is presented. The solutions are derived from the Jacobi inversion problem restricted to the set of zeros of the theta function,…
The complete analytical solutions of the geodesic equation of massive test particles in higher dimensional Schwarzschild, Schwarzschild-(anti)de Sitter, Reissner-Nordstroem and Reissner-Nordstroem-(anti)de Sitter space--times are presented.…
A procedure to find static axially symmetric solutions to the Einstein field equations is presented. We obtained two general solutions and five particular solutions, which depend on the existence conditions for circular and $z$ direction…
In this paper we add a compact dimension to Schwarzschild-(anti-) de sitter and Kerr-(anti-) de sitter spacetimes, which describes (rotating) black string-(anti-) de sitter spacetime. We study the geodesic motion of test particles and light…
The observation of the motion of particles and light near a gravitating object is until now the only way to explore and to measure the gravitational field. In the case of exact black hole solutions of the Einstein equations the…
We study the quantum theory of the Einstein-Maxwell action with a cosmological term in the spherically symmetric space-time, and explored quantum black hole solutions in Reissner-Nordstrom-de Sitter geometry. We succeeded to obtain analytic…
Set of analytic solutions of the geodesic equation in a spherical conformal spacetime is presented. Solutions of this geodesics can be expressed in terms of the Weierstrass {\wp} function and the Kleinian {\sigma} function. Using conserved…
We present the complete set of analytical solutions of the geodesic equation in the five-dimensional Myers-Perry space-time with equal rotation parameter in terms of the Weierstra{\ss}' elliptic and Weierstra{\ss}' zeta and sigma functions.…
Dirac's constraint analysis and the symplectic structure of geodesic equations are obtained for the general cylindrically symmetric stationary spacetime. For this metric, using the obtained first order Lagrangian, the geodesic equations of…
We apply thermodynamics method to generate exact solution with maximum symmetric surface for Einstein equation without solving it. The exact solutions are identified with which people have solved before. The horizons structure of solutions…
We consider the motion of test particles and light rays in a static cylindrically symmetric conformal spacetime given by Said et al [1]. We derive the equations of motion and present their analytical solutions in terms of the Weierstrass…
For an investigation of the physical properties of gravitational fields the observation of massive test particles and light is very useful. The characteristic features of a given space-time may be decoded by studying the complete set of all…
We present the complete set of analytical solutions of the geodesic equation in Taub-NUT space-times in terms of the Weierstrass elliptic function. We systematically study the underlying polynomials and characterize the motion of test…
We consider the motion of test particles in the spacetime of a black hole in f(R) gravity. The complete set of analytic solutions of the geodesic equation in the spacetime of this black hole are presented. The geodesic equations are solved…
We present a menagerie of solutions to the vacuum Einstein equations in six, eight and ten dimensions. These solutions describe spacetimes which are either locally asymptotically adS or locally asymptotically flat, and which have…
In this paper, we propose a survey of the basic geometric properties of Carters Kerr-de Sitter solution to Einsteins equation with positive cosmological constant. In particular, we give simple characterisations of the Kerr-de Sitter analogs…
We revisit the Taub-NUT solution of the Einstein equations without time periodicity condition, showing that the Misner string is still fully transparent for geodesics. In this case, analytic continuation can be carried out through both…