Geodesic flows in rotating black hole backgrounds (original) (raw)
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Kinematics of geodesic flows in stringy black hole backgrounds
Physical Review D, 2009
We study the kinematics of timelike geodesic congruences in two and four dimensions in spacetime geometries representing stringy black holes. The Raychaudhuri equations for the kinematical quantities (namely, expansion, shear and rotation) characterising such geodesic flows are written down and subsequently solved analytically (in two dimensions) and numerically (in four dimensions) for specific geodesics flows. We compare between geodesic flows in dual (electric and magnetic) stringy black hole backgrounds in four dimensions, by showing the differences that arise in the corresponding evolutions of the kinematic variables. The crucial role of initial conditions and the spacetime curvature on the evolution of the kinematical variables is illustrated. Some novel general conclusions on caustic formation and geodesic focusing are obtained from the analytical and numerical findings. We also propose a new quantifier in terms of the time (affine parameter) of approach to a singularity, which may be used to distinguish between flows in different geometries. In summary, our quantitative findings bring out hitherto unknown features of the kinematics of geodesic flows, which, otherwise, would have remained overlooked, if we confined ourselves to only a qualitative analysis.
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.
We study the geodesic equations in the space-time of neutral Brans-Dicke Dilaton and BTZ black holes in three dimensions. 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 showed completely also, the geodesic equations are solved in terms of Weierstrass elliptic functions. In addition,with the use of the analytical solution and effective potential technique some trajectories around the black holes are classified.
Rotating black hole spacetimes
1996
of Record A new family of initial data sets, along with a study of their evolutions including apparent horizons, event horizons and gravitational radiation, is presented. These initial data sets represent distorted rotating black holes, and two types of non-rotating black holes with odd-parity radiation distortions. The first has the equatorial plane symmetry of the Kerr spacetime, the second has the equatorial plane symmetry of the "cosmic screw" spacetime.
We perform a detailed study of the geodesic equations in the spacetime of the static and rotating charged black hole corresponding to the Kerr-Newman-(A)dS spacetime. We derive the equations of motion for test particles and light rays and present their solutions in terms of the Weierstrass ℘, ζ, and σ functions as well as the Kleinian σ function. With the help of parametric diagrams and effective potentials, we analyze the geodesic motion and classify the possible orbit types. This spacetime is also a solution of fðRÞ gravity with a constant curvature scalar.
Towards a general description of the interior structure of rotating black holes
Eprint Arxiv 1108 3512, 2011
The purpose of this paper is to present a number of proposals about the interior structure of a rotating black hole that is accreting slowly, but in an arbitrary time-and space-dependent fashion. The proposals could potentially be tested with numerical simulations. Outgoing and ingoing particles free-falling in the parent Kerr geometry become highly focused along the principal outgoing and ingoing null directions as they approach the inner horizon, triggering the mass inflation instability. The original arguments of Barrabés, Israel & Poisson (1990) regarding inflation in rotating black holes are reviewed, and shown to be based on Raychauduri's equation applied along the outgoing and ingoing null directions. It is argued that gravitational waves should behave in the geometric optics limit, and consequently that the spacetime should be almost shear-free. A full set of shear-free equations is derived. A specific line-element is proposed, which is argued should provide a satisfactory approximation during early inflation. Finally, it is argued that super-Planckian collisions between outgoing and ingoing particles will lead to entropy production, bringing inflation to an end, and precipitating collapse.
Evolution of distorted rotating black holes. II. Dynamics and analysis
Physical review, 1995
We have developed a numerical code to study the evolution of distorted, rotating black holes. This code is used to evolve a new family of black hole initial data sets corresponding to distorted "Kerr" holes with a wide range of rotation parameters, and distorted Schwarzschild black holes with oddparity radiation. Rotating black holes with rotation parameters as high as a/m = 0.87 are evolved and analyzed in this paper. The evolutions are generally carried out to about t = 100M , where M is the ADM mass. We have extracted both the even-and odd-parity gravitational waveforms, and find the quasinormal modes of the holes to be excited in all cases. We also track the apparent horizons of the black holes, and find them to be a useful tool for interpreting the numerical results. We are able to compute the masses of the black holes from the measurements of their apparent horizons, as well as the total energy radiated and find their sum to be in excellent agreement with the ADM mass.
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.
Physical Review D, 2016
We perform a detailed study of the geodesic equations in the spacetime of the static and rotating charged black hole corresponding to the Kerr-Newman-(A)dS spacetime. We derive the equations of motion for test particles and light rays and present their solutions in terms of the Weierstrass ℘, ζ and σ functions as well as the Kleinian σ function. With the help of parametric diagrams and effective potentials we analyze the geodesic motion and classify the possible orbit types. This spacetime is also a solution of f (R) gravity with a constant curvature scalar.
Physics Letters B, 2013
The formation of spacetime singularities is a quite common phenomenon in General Relativity and it is regulated by specific theorems. It is widely believed that spacetime singularities do not exist in Nature, but that they represent a limitation of the classical theory. While we do not yet have any solid theory of quantum gravity, toy models of black hole solutions without singularities have been proposed. So far, there are only non-rotating regular black holes in the literature. These metrics can be hardly tested by astrophysical observations, as the black hole spin plays a fundamental role in any astrophysical process. In this letter, we apply the Newman-Janis algorithm to the Hayward and to the Bardeen black hole metrics. In both cases, we obtain a family of rotating solutions. Every solution corresponds to a different matter configuration. Each family has one solution with special properties, which can be written in Kerr-like form in Boyer-Lindquist coordinates. These special solutions are of Petrov type D, they are singularity free, but they violate the weak energy condition for a non-vanishing spin and their curvature invariants have different values at r = 0 depending on the way one approaches the origin. We propose a natural prescription to have rotating solutions with a minimal violation of the weak energy condition and without the questionable property of the curvature invariants at the origin.