Valeria Kagramanova

Solar system effects in Schwarzschild-de Sitter space-time

Abstract The Schwarzschild–de Sitter space–time describes the gravitational field of a spherically symmetric mass in a universe with cosmological constant Λ . Based on this space–time we calculate Solar system effects like gravitational redshift, light deflection, gravitational time delay, perihelion shift, geodetic or de Sitter precession, as well as the influence of Λ on a Doppler measurement, used to determine the velocity of the Pioneer 10 and 11 spacecraft. For Λ = Λ 0 ∼ 10 −52 m −2 the cosmological constant plays no role for all of these effects, while a value of Λ ∼ − 10 −37 m −2 , if hypothetically held responsible for the Pioneer anomaly, is not compatible with the perihelion shift.

Analytical solution of the geodesic equation in Kerr-(anti) de Sitter space-times

All observations in the gravitational domain can be explained by means of Einstein’s General Relativity. While for small scale gravitational effects (e.g. in the solar system) the standard Einstein field equations are sufficient, a consistent description of large scale obervations like the accelerated expansion of the universe can be achieved by the introduction of a cosmological term into the Einstein field equation

Geodesics of electrically and magnetically charged test particles in the Reissner-Nordstroem space-time: Analytical solutions

We present the full set of analytical solutions of the geodesic equations of charged test particles in the Reissner-Nordstroem space-time in terms of the Weierstrass weierp, {sigma}, and {zeta} elliptic functions. Based on the study of the polynomials in the {theta} and r equations, we characterize the motion of test particles and discuss their properties. The motion of charged test particles in the Reissner-Nordstroem space-time is compared with the motion of neutral test particles in the field of a gravitomagnetic monopole. Electrically or magnetically charged particles in the Reissner-Nordstroem space-time with magnetic or electric charges, respectively, move on cones similar to neutral test particles in the Taub-NUT space-times.

Analytic solutions of the geodesic equation in axially symmetric space-times

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 terms of the Kleinian sigma functions.

Particle motion in Horava-Lifshitz black hole space-times

We study the particle motion in the space-time of a Kehagias-Sfetsos black hole which is a static spherically symmetric solution of a Horava-Lifshitz gravity model. This model reduces to general relativity in the infrared limit and deviates slightly from detailed balance. Taking the viewpoint that the model is essentially a (3+1)-dimensional modification of general relativity we use the geodesic equation to determine the motion of massive and massless particles. We solve the geodesic equation exactly by using numerical techniques. We find that neither massless nor massive particles with nonvanishing angular momentum can reach the singularity at r=0. Next to bound and escape orbits that are also present in the Schwarzschild space-time we find that new types of orbits exist: manyworld bound orbits as well as two-world escape orbits. We also discuss observables such as the perihelion shift and the light deflection.

Inversion of a general hyperelliptic integral and particle motion in Hořava–Lifshitz black hole space-times

The description of many dynamical problems such as the particle motion in higher dimensional spherically and axially symmetric space-times is reduced to the inversion of hyperelliptic integrals of all three kinds. The result of the inversion is defined locally, using the algebro-geometric techniques of the standard Jacobi inversion problem and the foregoing restriction to the θ-divisor. For a representation of the hyperelliptic functions the Klein–Weierstras multi-variable σ-function is introduced. It is shown that all parameters needed for the calculations such as period matrices and abelian images of branch points can be expressed in terms of the periods of holomorphic differentials and θ-constants. The cases of genus two, three, and four are considered in detail. The method is exemplified by the particle motion associated with genus one elliptic and genus three hyperelliptic curves. Applications are for instance solutions to the geodesic equations in the space-times of static, spherically symmetric Hořava–Lifshitz black holes.

Charged particle interferometry in Plebański–Demiański black hole spacetimes

The Plebanski–Demianski solution is a very general axially symmetric analytical solution of the Einstein field equations generalizing the Kerr solution. This solution depends on seven parameters which under certain circumstances are related to mass, rotation, cosmological constant, NUT parameter, electric and magnetic charges and acceleration. In this paper we present a general description of matter wave interferometry in the general Plebanski–Demianski black hole spacetime. Particular emphasis is placed on a gauge invariant description of the symmetries of the gauge field. We show that it is possible to have access to all parameters separately except the acceleration. For neutral particles there is only access to a combination of electric and magnetic charge.

Orbits in the field of a gravitating magnetic monopole

Orbits of test particles and light rays are an important tool to study the properties of space-time metrics. Here we systematically study the properties of the gravitational field of a globally regular magnetic monopole in terms of the geodesics of test particles and light. The gravitational field depends on two dimensionless parameters, defined as ratios of the characteristic mass scales present. For critical values of these parameters the resulting metric coefficients develop a singular behavior, which has profound influence on the properties of the resulting space-time and which is clearly reflected in the orbits of the test particles and light rays.

Geodesic Motion in the (Charged) Doubly Spinning Black Ring Spacetime

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 spinning black rings in general, so we concentrate on special cases: null geodesics in the ergosphere and geodesics on the two rotational axes of the (charged) doubly spinning black ring. We present analytical solutions to the geodesic equations for these special cases. Using effective potential techniques we study the motion of test particles and light and discuss the corresponding orbits.

Geodesic motion in the space-time of cosmic strings interacting via magnetic fields

We study the geodesic motion of test particles in the space-time of two Abelian-Higgs strings interacting via their magnetic fields. These bound states of cosmic strings constitute a field theoretical realization of p-q-strings which are predicted by inflationary models rooted in String Theory, e.g. brane inflation. In contrast to previously studied models describing p-q-strings our model possesses a Bogomolnyi-Prasad-Sommerfield (BPS) limit. If cosmic strings exist it would be exciting to detect them by direct observation. We propose that this can be done by the observation of test particle motion in the space-time of these objects. In order to be able to make predictions we have to solve the field equations describing the configuration as well as the geodesic equation numerically. The geodesics can then be classified according to the test particles energy, angular momentum and momentum along the string axis. We find that the interaction of two Abelian-Higgs strings can lead to the existence of bound orbits that would be absent without the interaction. We also discuss the minimal and maximal radius of orbits and comment on possible applications in the context of gravitational wave emission.