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Dynamics of Particles in Time Conformal Reissner-Nordström Black Hole

Farhad Ali, Muhammad Ozair, Takasar Hussain


In this work, we use Noether symmetries to discuss the dynamics of neutral as well as charged particles in the absence/presence of a magnetic field around the Reissner Nordström black hole as well as the time conformal Reissner–Nordström black hole. We investigate the circumstances under which the particle can escape from the vicinity of a black hole after collision with another particle. We analyze the effective potential and effective force of a particle without the magnetic field and in the presence of a magnetic field with angular momentum graphically. Point particle dynamics is very important in the sense that from this type of study one can initiate the study of a more complex motion of extended bodies/celestial bodies. A major area of interest, especially in recent times, is the motion of particles (neutral and charge) in the presence of black holes and naked singularities. Initially, we find the Noether symmetries and the corresponding conservation laws of geodesics of the Reissner–Nordström black hole and the time conformal Reissner–Nordström black hole. We observe that the Reissner–Nordström space time admits the time conformal factor , where  is an arbitrary function of time t and  is very small, causes the perturbation in the given spacetime. The Noether symmetries of the Lagrangian of Reissner–Nordström black hole give the exact conservation laws and do not tell about the radiation of the energy. The time conformal Reissner–Nordström space time has the time conformal Lagrangian, the Noether symmetries of which carry approximate part which corresponds to the losing energy of the black hole. By this procedure we re-scale the energy content of the Reissner-Nordstrom black hole space time. We also investigate the thermal stability, horizons and energy conditions corresponding to time conformal Reissner–Nordström (NR) space time.

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