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Gravitational Field of a Spinning Mass as an Example of Algebraically Special Metrics

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Abstract

Algebraically special solutions of Einstein's empty-space field ; equations that are characterized by the existence of a geodesic and shear-free ; ray congruence are considered. A class of solutions is presented for which the ; congruence is diverging and is not necessarily hypersurface orthogonal. (C.E.S.);
... The Kerr-Newman metric is an exact solution of the Einstein-Maxwell equation, which describes stationary spacetime with the angular momentum and the electric charge. In 1963, Kerr first found the metric of a spinning object in a gravitational field [17], which is a generalization of the Schwarzschild metric. Two years later, Newman et al. obtained the metric that can describe both rotating and charged spacetime [18]. ...
... This can be used to constrain physical quantities of the black hole in a cavity. We turn to consider the three equations mentioned above: the horizon radius determined by ∆ = 0 in Eq. (17), the angular momentum J = M a and the entropy in Eq. (27). Solving these equations yields ...
Preprint
The quasi-local energy of a Kerr-Newman black hole in a finite spherical cavity with fixed radius is derived from the Hamiltonian, and the first law of thermodynamics is constructed accordingly. In a canonical ensemble, the black hole could undergo a van der Waals-like phase transition. The temperature where the phase transition occurs decreases with the increase of the angular momentum or the charge. Our results imply that the thermodynamics of a Kerr-Newman black hole in a cavity shows extensive similarities to the one in AdS spacetime.
... Theory-agnostic metrics can often be written down in a relatively convenient form, but do not have a physical theory behind them and can be difficult to interpret. They can, however, be used without reservation for null tests of GR, where parametrized deviations from the BH solutions of GR (often the rotating one known as the Kerr solution [25]) provide a handle on violations of GR via the no-hair theorem. ...
Preprint
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... When a bosonic wave is impinging upon a rotating black hole, the wave reflected by the event horizon will be amplified if the wave frequency ω lies in the following superradiant regime [7,9,13,15,16] ...
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Thesis
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