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Gyroscopic precession in the vicinity of a static blackhole’s event horizon

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Abstract

In this article, we investigate gyroscopic precession in the vicinity of a spherically symmetric static event horizon. Our goal is to address whether the gyroscopic precession frequency diverges when approaching an event horizon. To do so, we employ the Frenet–Serret formalism of gyroscopic precession, which provides a complete covariant formalism, and extend it to include arbitrary timelike curves. We analyze the precession frequency near the Schwarzschild and Schwarzschild-anti-de-Sitter black holes, using horizon-penetrating Kerr–Schild coordinates to eliminate coordinate singularities near the horizon. Our study shows that a diverging gyroscopic precession frequency is not a universal feature for a trajectory crossing an event horizon. As a counter-example, we construct a timelike curve passing through the event horizon along which the gyroscopic precession frequency remains finite at the horizon.

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Acknowledgements

We want to acknowledge the anonymous reviewers for their valuable suggestions for improving the clarity and presentation of the manuscript.

Funding

PM and RKN acknowledge support from the Ministry of Human Resource Development (MHRD), India, IISER Kolkata and the Center of Excellence in Space Sciences (CESSI).

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Authors and Affiliations

  1. Center of Excellence in Space Sciences India, Indian Institute of Science Education and Research, Campus Road, Mohanpur, Nadia, West Bengal, 741246, India

    Paulami Majumder & K. Rajesh Nayak

  2. Department of Physical Science, IISER Kolkata, Campus Road, Mohanpur, Nadia, West Bengal, 741246, India

    K. Rajesh Nayak

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  1. Paulami Majumder
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Correspondence to K. Rajesh Nayak.

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Majumder, P., Nayak, K.R. Gyroscopic precession in the vicinity of a static blackhole’s event horizon. Gen Relativ Gravit 55, 59 (2023). https://doi.org/10.1007/s10714-023-03108-5

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