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arXiv · 2501.17283

Innermost Stable Circular Orbits of a Kerr-like Metric with Quadrupole

Fabián Chaverri-Miranda·Francisco Frutos-Alfaro·Diego Solano-Alfaro·Pedro Gómez-Ovares·André Oliva
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Abstract

This paper presents results for the innermost stable circular orbit in a Kerr-like spacetime. The metric employed is an approximation that combines the Kerr metric with the Erez-Rosen metric, expanded in a Taylor series. Consequently, this spacetime incorporates three relativistic multipole moments: mass, spin, and quadrupole moment. Our derivation builds upon the analysis conducted by Chandrasekhar for the Kerr metric. Utilizing the Euler-Lagrange method and Hamiltonian dynamics, we define an effective potential for the radial coordinate. This equation can be used to measure the mass quadrupole through observational methods, as it yields a quadratic polynomial for the quadrupole moment. As anticipated, the limiting cases of this equation correspond to the established cases of Kerr and Schwarzschild spacetimes.

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Fabián Chaverri-Miranda, Francisco Frutos-Alfaro, Diego Solano-Alfaro, Pedro Gómez-Ovares, André Oliva. 2025-01-28. Innermost Stable Circular Orbits of a Kerr-like Metric with Quadrupole. https://arxiv.org/abs/2501.17283

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