Tidal Effects in Some Regular Black Holes
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I, PARTICLES, FIELDS, GRAVITATION, AND ASTROPHYSICS
Tidal Effects in Some Regular Black Holes1 M. Sharif* and S. Sadiq** Department of Mathematics, University of the Punjab, Quaid-e-Azam Campus, Lahore-54590, Pakistan * e-mail: [email protected] ** e-mail: [email protected] Received July 14, 2017
Abstract—This paper is aimed to study the tidal forces produced by a class of regular black holes. We consider the radial infall of test particle and find radial as well as angular components of tidal forces by taking geodesic deviation equations. We also compute geodesic deviation vector by solving geodesic deviation equation numerically. It is concluded that a particle undergos either compression or stretching in radial or angular direction due to tidal forces. DOI: 10.1134/S1063776118010089
1. INTRODUCTION Gravitational force is the weakest among all fundamental forces of nature and is responsible for the attraction of one body with another. A distribution of non-interacting particles falling freely towards earth will be stretched in the direction of motion and compressed in transverse direction due to the tidal forces produced by gravity. Tidal fields determine the dynamical evolution of galaxies along their trajectories. Gnedin [1] explored the total effect of tidal interactions that are insufficient to transform a spiral galaxy into an elliptical shape and found that in low critical density clusters, tidal heating is stronger. Baiotti et al. [2] found the amplification of tidal effects by higherorder relativistic corrections which are necessary for an accurate phasing of gravitational signal from binary neutron stars. The tidal effects also occur when a body falls towards a black hole (BH) and tends to infinity near the singularity. The gravity of BH generates strong tidal forces which deform and destroy the objects that are close to the BH. In case of Schwarzschild BH [3], a body falling freely undergoes a stretch in radial direction while compression in angular direction due to the tidal effects. Luminet and Marek [4] demonstrated that star may squeeze when periastron of its orbit is sufficiently close to the horizon of BH due to tidal compression acting on the direction orthogonal to the orbital plane of the star. Kostic et al. [5] analyzed the tidal effects of BH on small solid objects that are melted by the strong gravitational field of BH. Kesden [6] examined stellar orbits in the Kerr metric and found that BH spin increases the upper limit on the mass of a black hole capable of tidally disrupting stars. 1 The article is published in the original.
Cheng and Bogdanovi [7] discussed the disruption of a low mass main sequence star as well as a white dwarf by BHs of different masses and calculated the orbital parameters of the debris. Crispino et al. [8] discussed the stretching or compression in radial as well as angular direction for a particle falling freely in Reissner– Nordström (RN) BH and found that the results are in contrast to the Schwarzschild BH. Servin and Kesden [9] studied tidal disrupti
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