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Register a new userGravitational shockwaves on rotating black holes
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We present an exact solution of Einsteins equation that describes the gravitational shockwave of a massless particle on the horizon of a Kerr-Newman black hole. The backreacted metric is of the generalized Kerr-Schild form and is Type II in the Petrov classification. We show that if the background frame is aligned with shear-free null geodesics, and if the background Ricci tensor satisfies a simple condition, then all nonlinearities in the perturbation will drop out of the curvature scalars. We make heavy use of the method of spin coefficients (the Newman-Penrose formalism) in its compacted form (the Geroch-Held-Penrose formalism).
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We construct analytical and regular solutions in four-dimensional General Relativity which represent multi-black hole systems immersed in external gravitational field configurations. The external field background is composed by an infinite multipolar expansion, which allows to regularise the conical singularities of an array of collinear static black holes. A stationary rotating generalisation is achieved by adding independent angular momenta and NUT parameters to each source of the binary configuration. Moreover, a charged extension of the binary black hole system at equilibrium is generated. Finally, we show that the binary Majumdar-Papapetrou solution is consistently recovered in the vanishing external field limit. All of these solutions reach an equilibrium state due to the external gravitational field only, avoiding in this way the presence of any string or strut defect.
In the teleparallel equivalent of general relativity the energy density of asymptotically flat gravitational fields can be naturaly defined as a scalar density restricted to a three-dimensional spacelike hypersurface $Sigma$. Integration over the whole $Sigma$ yields the standard ADM energy. After establishing the reference space with zero gravitational energy we obtain the expression of the localized energy for a Kerr black hole. The expression of the energy inside a surface of constant radius can be explicitly calculated in the limit of small $a$, the specific angular momentum. Such expression turns out to be exactly the same as the one obtained by means of the method preposed recently by Brown and York. We also calculate the energy contained within the outer horizon of the black hole for {it any} value of $a$. The result is practically indistinguishable from $E=2M_{ir}$, where $M_{ir}$ is the irreducible mass of the black hole.
We obtain rotating black hole solutions to the novel 3D Gauss-Bonnet theory of gravity recently proposed. These solutions generalize the BTZ metric and are not of constant curvature. They possess an ergoregion and outer horizon, but do not have an inner horizon. We present their basic properties and show that they break the universality of thermodynamics present for their static charged counterparts, whose properties we also discuss. Extending our considerations to higher dimensions, we also obtain novel 4D Gauss-Bonnet rotating black strings.
We identify a set of Hertz potentials for solutions to the vector wave equation on black hole spacetimes. The Hertz potentials yield Lorenz gauge electromagnetic vector potentials that represent physical solutions to the Maxwell equations, satisfy the Teukolsky equation, and are related to the Maxwell scalars by straightforward and separable inversion relations. Our construction, based on the GHP formalism, avoids the need for a mode ansatz and leads to potentials that represent both static and non-static solutions. As an explicit example, we specialise the procedure to mode-decomposed perturbations of Kerr spacetime and in the process make connections with previous results.
We construct slowly rotating black-hole solutions of Einsteinian cubic gravity (ECG) in four dimensions with flat and AdS asymptotes. At leading order in the rotation parameter, the only modification with respect to the static case is the appearance of a non-vanishing $g_{tphi}$ component. Similarly to the static case, the order of the equation determining such component can be reduced twice, giving rise to a second-order differential equation which can be easily solved numerically as a function of the ECG coupling. We study how various physical properties of the solutions are modified with respect to the Einstein gravity case, including its angular velocity, photon sphere, photon rings, shadow, and innermost stable circular orbits (in the case of timelike geodesics).
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