Kinematics of geodesic flows in stringy black hole backgrounds (original) (raw)
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Geodesic flows in rotating black hole backgrounds
Physical Review D, 2012
We study the kinematics of timelike geodesic congruences, in the spacetime geometry of rotating black holes in three (the BTZ) and four (the Kerr) dimensions. The evolution (Raychaudhuri) equations for the expansion, shear and rotation along geodesic flows in the such spacetimes are obtained. For the BTZ case, the equations are solved analytically. The effect of the negative cosmological constant on the evolution of the expansion (θ), for congruences with and without an initial rotation (ω 0) is noted. Subsequently, the evolution equations, in the case of a Kerr black hole in four dimensions are written and solved numerically, for some specific geodesics flows. It turns out that, for the Kerr black hole, there exists a critical value of the initial expansion below (above) which we have focusing (defocusing). We delineate the dependencies of the expansion, on the black hole angular momentum parameter, a, as well as on ω 0. Further, the role of a and ω 0 on the time (affine parameter) of approach to singularity (defocusing/focusing) is studied. While the role of ω 0 on the time to singularity is as expected, the effect of a leads to an interesting new result.
Geodesic flows around charged black holes in two dimensions
Astrophysics and Space Science, 2015
We study the evolution of timelike geodesics for two dimensional black hole spacetimes arising in string theory and general theory of relativity by solving the Raychaudhuri equation for expansion scalar as an initial value problem. The possibility of geodesic focusing/defocusing is then examined accordingly with different settings of black hole parameters. In view of the geodesic focusing/defocusing, the critical value of expansion scalar is also calculated in each case. The effect of the charge and the cosmological constant on the evolution of expansion scalar for timelike geodesics is discussed in detail.
Geodesics and Geodesic Deviation in a Stringy Charged Black Hole
arXiv (Cornell University), 2007
The radial motion along null geodesics in the charged black hole space-times, in particular, the Reissner-Nordström and stringy charged black holes are studied. We analyze the properties of the effective potential. The circular photon orbits in these space-times are investigated. We find that the radius of circular photon orbits in both charged black holes are different and differ from that given in Schwarzschild space-time. We Study the physical effects of the gravitational field between two test particles in stringy charged black hole and compare the results with that given in Schwarzschild and Reissner-Nordström black holes.
Geodesic motions in extraordinary string geometry
General Relativity and Gravitation, 2011
The geodesic properties of the extraordinary vacuum string solution in (4+1) dimensions are analyzed by using Hamilton-Jacobi method. The geodesic motions show distinct properties from those of the static one. Especially, any freely falling particle can not arrive at the horizon or singularity. There exist stable null circular orbits and bouncing timelike and null geodesics. To get into the horizon or singularity, a particle need to follow a non-geodesic trajectory. We also analyze the orbit precession to show that the precession angle has distinct features for each geometry such as naked singularity, black string, and wormhole.
Physical Review D, 2010
We study the geodesic equations in the space-time of a Schwarzschild black hole pierced by an infinitely thin cosmic string and give the complete set of analytical solutions of these equations for massive and massless particles, respectively. The solutions of the geodesic equations can be classified according to the particle's energy and angular momentum, the ratio between the component of the angular momentum aligned with the axis of the string and the total angular momentum, the deficit angle of the space-time and as well the horizon radius (or mass) of the black hole. For bound orbits of massive test particles we calculate the perihelion shift, we discuss light deflection and comment on the Newtonian limit.
Geodesics of the hyperbolically symmetric black hole
Physical review, 2020
We carry out a systematic study on the motion of test particles in the region inner to the horizon of a hyperbolically symmetric black hole. The geodesic equations are written and analyzed in detail. The obtained results are contrasted with the corresponding results obtained for the spherically symmetric case. It is found that test particles experience a repulsive force within the horizon, which prevents them to reach the center. These results are obtained for radially moving particles as well as for particles moving in the θ − R subspace. To complement our study we calculate the precession of a gyroscope moving along a circular path (non-geodesic) within the horizon. We obtain that the precession of the gyroscope is retrograde in the rotating frame, unlike the precession close to the horizon (R = 2m + ǫ) in the Schwarzschild spacetime, which is forward.
Black hole dynamics in general relativity
Pramana, 2007
Basic features of dynamical black holes in full, non-linear general relativity are summarized in a pedagogical fashion. Qualitative properties of the evolution of various horizons follow directly from the celebrated Raychaudhuri equation.
Constants of geodesic motion in higher-dimensional black-hole spacetimes
Physical Review D, 2007
In [Phys. Rev. Lett. 98, 061102 (2007)], we announced the complete integrability of geodesic motion in the general higher-dimensional rotating black-hole spacetimes. In the present paper we prove all the necessary steps leading to this conclusion. In particular, we demonstrate the independence of the constants of motion and the fact that they Poisson commute. The relation to a different set of constants of motion constructed in [J. High Energy Phys. 02 (2007) 004] is also briefly discussed.
Investigation the geodesic motion of three dimensional rotating black holes
Chinese Journal of Physics, 2020
We study the geodesic equations in the space-time of neutral Brans-Dicke Dilaton black hole in three dimensions and BTZ black hole. We use the process of separation of the Hamilton-Jacobi equation to obtain the constants of motion. The whole analytical solution of the geodesic equations in the space-times of the intended black holes are shown completely. Moreover, the geodesic equations are solved in terms of Weierstrass elliptic functions. Furthermore, with use of the analytical solution and effective potential technique some trajectories around the black holes are classified. Meanwhile, by analytical solution, effective potential and considering the zeroes of underlying polynomials, some possible orbits are plotted. Finally, we compare our results with Cruz et. al. [17] and we indicate the benefits of the analytical method which is applied in this paper.
Universe
Geodesics (by definition) have an intrinsic 4-acceleration zero. However, when expressed in terms of coordinates, the coordinate acceleration d 2 x i /dt 2 can very easily be non-zero, and the coordinate velocity dx i /dt can behave unexpectedly. The situation becomes extremely delicate in the near-horizon limit-for both astrophysical and idealised black holes-where an inappropriate choice of coordinates can quite easily lead to significant confusion. We shall carefully explore the relative merits of horizon-penetrating versus horizon-non-penetrating coordinates, arguing that in the near-horizon limit the coordinate acceleration d 2 x i /dt 2 is best interpreted in terms of horizon-penetrating coordinates.