Periapsis and gravitomagnetic precessions of stellar orbits in Kerr and Kerr-de Sitter black hole spacetimes

The exact solution for the motion of a test particle in a non-spherical polar orbit around a Kerr black hole is derived. Exact novel expressions for frame dragging (Lense-Thirring effect), periapsis advance and the orbital period are produced. The resulting formulae, are expressed in terms of Appell's first hypergeometric function $F_1$, Jacobi's amplitude function, and Appell's $F_1$ and Gau\ss hypergeometric function respectively. The exact expression for frame dragging is applied for the calculation of the Lense-Thirring effect for the orbits of S-stars in the central arcsecond of our Galaxy assuming that the galactic centre is a Kerr black hole, for various values of the Kerr parameter including those supported by recent observations. In addition, we apply our solutions for the calculation of frame dragging and periapsis advance for stellar non-spherical polar orbits in regions of strong gravitational field close to the event horizon of the galactic black hole, e.g. for orbits in the central milliarcsecond of our galaxy. Such orbits are the target of the GRAVITY experiment. We provide examples with orbital periods in the range of 100min - 54 days. Detection of such stellar orbits will allow the possibility of measuring the relativistic effect of periapsis advance with high precision at the strong field realm of general relativity. Further, an exact expression for the orbital period of a test particle in a non-circular equatorial motion around a Kerr black hole is produced. We also derive exact expressions for the periapsis advance and the orbital period for a test particle in a non-circular equatorial motion in the Kerr field in the presence of the cosmological constant in terms of Lauricella's fourth hypergeometric function $F_D$.Comment: LaTeX file, 46 pages, typos fixed, substantial changes, version published in Classical and Quantum Gravity, Vol 24 (2007) 1775-180

The geodesic structure of the Schwarzschild Anti-de Sitter black hole

In the present work we found the geodesic structure of an AdS black hole. By means of a detailed analyze of the corresponding effective potentials for particles and photon, we found all the possible motions which are allowed by the energy levels. Radial and non radial trajectories were exactly evaluated for both geodesics. The founded orbits were plotted in order to have a direct visualization of the allowed motions. We show that the geodesic structure of this black hole presents new type of motions not allowed by the Schwarzschild spacetime.Comment: 17 pages, 11 figure

Particle motion and gravitational lensing in the metric of a dilaton black hole in a de Sitter universe

We consider the metric exterior to a charged dilaton black hole in a de Sitter universe. We study the motion of a test particle in this metric. Conserved quantities are identified and the Hamilton-Jacobi method is employed for the solutions of the equations of motion. At large distances from the black hole the Hubble expansion of the universe modifies the effective potential such that bound orbits could exist up to an upper limit of the angular momentum per mass for the orbiting test particle. We then study the phenomenon of strong field gravitational lensing by these black holes by extending the standard formalism of strong lensing to the non-asymptotically flat dilaton-de Sitter metric. Expressions for the various lensing quantities are obtained in terms of the metric coefficients.Comment: 8 pages, RevTex, 1 eps figures; discussion improved; typos corrected; references adde

Particle motion in the field of a five-dimensional charged black hole

In this paper, we have investigated the geodesics of neutral particles near a five-dimensional charged black hole using a comparative approach. The effective potential method is used to determine the location of the horizons and to study radial and circular trajectories. This also helps us to analyze the stability of radial and circular orbits. The radius of the innermost stable circular orbits have also been determined. Contrary to the case of massive particles for which, the circular orbits may have up to eight possible values of specific radius, we find that the photons will only have two distinct values for the specific radii of circular trajectories. Finally we have used the dynamical systems analysis to determine the critical points and the nature of the trajectories for the timelike and null geodesics.Comment: 15 pages, accepted for publication in Astrophysics and Space Scienc

Frame dragging and bending of Light in Kerr and Kerr-(anti) de Sitter spacetimes

The equations of general relativity in the form of timelike and null geodesics that describe motion of test particles and photons in Kerr spacetime are solved exactly including the contribution from the cosmological constant. We then perform a systematic application of the exact solutions obtained to the following cases. The exact solutions derived for null, spherical, polar and non-polar orbits are applied for the calculation of frame dragging (Lense-Thirring effect) for the orbit of a photon around the galactic centre, assuming that the latter is a Kerr black hole for various values of the Kerr parameter including those supported by recent observations. Unbound null polar orbits are investigated, and an analytical expression for the deviation angle of a polar photon orbit from the gravitational Kerr field is derived. In addition, we present the exact solution for timelike and null equatorial orbits. In the former case, we derive an analytical expression for the precession of the point of closest approach (perihelion, periastron) for the orbit of a test particle around a rotating mass whose surrounding curved spacetime geometry is described by the Kerr field. In the latter case, we calculate an exact expression for the deflection angle for a light ray in the gravitational field of a rotating mass (the Kerr field). We apply this calculation for the bending of light from the gravitational field of the galactic centre for various values of the Kerr parameter and the impact factor.Comment: LaTeX file, 45 pages 1 figure, typos fixed, v3 published in Classical and Quantum Gravity 22 (2005) 4391-442

From b→sγb \to s \gamma to the LSP Detection Rates in Minimal String Unification Models

We exploit the measured branching ratio for $b \rightarrow s\gamma$ to derive lower limits on the sparticle and Higgs masses in the minimal string unification models. For the LSP('bino'), chargino and the lightest Higgs, these turn out to be 50, 90 and 75 GeV respectively. Taking account of the upper bounds on the mass spectrum from the LSP relic abundance, we estimate the direct detection rate for the latter to vary from 10^{-1} to 10^{-4} events/kg/day. The muon flux, produced by neutrinos from the annihilating LSP's, varies in the range 10^{-2} - 10^{-9} muons/m^2/day.Comment: Latex, 20 page