Talk detail

Participant	Kagramanova, Valeriya
Institution	Carl von Ossietzky University Oldenburg, Department of physics - Carl von Ossietzky Str 9-11 - Oldenburg - Germany - Germany

Session	BH3	Accepted		Order	Time
Talk	Oral abstract	Title	Exact solutions of geodesic equations in general relativity
Co-authors
Abstract	Test particles and light are the best tool to investigate the physical properties of gravitational sources. When the equations of motion are separated, there are two main methods to solve them: analytical and numerical. Finding an analytical solution is an involved task but results in a number of advantages: one gets an exact solution, has arbitrary accuracy and the best possibility to investigate the properties of the orbits and hence of the gravitating body itself in detail. Here we present the analytical solution of the geodesic equations in many well-known black hole space-times starting with 4 dimensions and also discuss their properties. The solution is expressed in terms of the Weierstrass' elliptic or Abelian hyperelliptic functions which requires an advanced knowledge in the theory of functions. The choice of the method depends on the complexity of the considered problem and on the number of parameters characterizing the black hole and the test particle. We integrate differentials of all three kinds with arbitrary genus of the underlying polynomial curve. We also present the analytical expressions for the observable quantities such as the perihelion shift for planetary orbits and light deflection for escape orbits of photons.