Study of energy extraction and epicyclic frequencies in Kerr-MOG (modified gravity) black hole

Parthapratim Pradhan

doi:10.1140/epjc/s10052-019-6907-0

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2024 Impact factor 4.8

Particles and Fields

Open Access

Eur. Phys. J. C (2019) 79: 401
https://doi.org/10.1140/epjc/s10052-019-6907-0

Regular Article - Theoretical Physics

Study of energy extraction and epicyclic frequencies in Kerr-MOG (modified gravity) black hole

Parthapratim Pradhan^*

Department of Physics, Hiralal Mazumdar Memorial College for Women, Dakshineswar, Kolkata, 700035, India

^* e-mail: pppradhan77@gmail.com

Received: 4 April 2019
Accepted: 23 April 2019
Published online: 12 May 2019

Abstract

We investigate the energy extraction by the Penrose process in Kerr-MOG black hole (BH). We derive the gain in energy for Kerr-MOG as $\begin{aligned} \varDelta {{\mathcal {E}}} \le \frac{1}{2}\left( \sqrt{\frac{2}{1+\sqrt{\frac{1}{1+\alpha }-\left( \frac{a}{{{\mathcal {M}}}}\right) ^2}} -\frac{\alpha }{1+\alpha } \frac{1}{\left( 1+\sqrt{\frac{1}{1+\alpha }-\left( \frac{a}{{{\mathcal {M}}}}\right) ^2} \right) ^2}}-1\right) \end{aligned}$ where a is spin parameter, $\alpha$ is MOG parameter and ${{\mathcal {M}}}$ is the Arnowitt–Deser–Misner (ADM) mass parameter. When $\alpha =0$ , we obtain the gain in energy for Kerr BH. For extremal Kerr-MOG BH, we determine the maximum gain in energy is $\varDelta {{\mathcal {E}}} \le \frac{1}{2} \left( \sqrt{\frac{\alpha +2}{1+\alpha }}-1 \right)$ . We observe that the MOG parameter has a crucial role in the energy extraction process and it is in fact diminishes the value of $\varDelta {{\mathcal {E}}}$ in contrast with extremal Kerr BH. Moreover, we derive the Wald inequality and the Bardeen–Press–Teukolsky inequality for Kerr-MOG BH in contrast with Kerr BH. Furthermore, we describe the geodesic motion in terms of three fundamental frequencies: the Keplerian angular frequency, the radial epicyclic frequency and the vertical epicyclic frequency. These frequencies could be used as a probe of strong gravity near the black holes.