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Register a new userGravitational decoupling for axially symmetric systems and rotating black holes
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We introduce a systematic and direct procedure to generate hairy rotating black holes by deforming a spherically symmetric seed solution. We develop our analysis in the context of the gravitational decoupling approach, without resorting to the Newman-Janis algorithm. As examples of possible applications, we investigate how the Kerr black hole solution is modified by a surrounding fluid with conserved energy-momentum tensor. We find non-trivial extensions of the Kerr and Kerr-Newman black holes with primary hair. We prove that a rotating and charged black hole can have the same horizon as Kerrs, Schwarzschilds or Reissner-Nordstroms, thus showing possible observational effects of matter around black holes.
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Black holes with hair represented by generic fields surrounding the central source of the vacuum Schwarzschild metric are examined under the minimal set of requirements consisting of i) the existence of a well defined event horizon and ii) the strong or dominant energy condition for the hair outside the horizon. We develop our analysis by means of the gravitational decoupling approach. We find that trivial deformations of the seed Schwarzschild vacuum preserve the energy conditions and provide a new mechanism to evade the no-hair theorem based on a primary hair associated with the charge generating these transformations. Under the above conditions i) and ii), this charge consistently increases the entropy from the minimum value given by the Schwarzschild geometry. As a direct application, we find a non-trivial extension of the Reissner-Nordstrom black hole showing a surprisingly simple horizon. Finally, the non-linear electrodynamics generating this new solution is fully specified.
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).
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.
Perturbations of Kerr spacetime are typically studied with the Teukolsky formalism, in which a pair of invariant components of the perturbed Weyl tensor are expressed in terms of separable modes that satisfy ordinary differential equations. However, for certain applications it is desirable to construct the full metric perturbation in the Lorenz gauge, in which the linearized Einstein field equations take a manifestly hyperbolic form. Here we obtain a set of Lorenz-gauge solutions to the vacuum field equations in terms of homogeneous solutions to the spin-2, spin-1 and spin-0 Teukolsky equations; and completion pieces that represent perturbations to the mass and angular momentum of the spacetime. The solutions are valid in vacuum Petrov type-D spacetimes that admit a conformal Killing-Yano tensor.
An exact solution of Einsteins equations which represents a pair of accelerating and rotating black holes (a generalised form of the spinning C-metric) is presented. The starting point is a form of the Plebanski-Demianski metric which, in addition to the usual parameters, explicitly includes parameters which describe the acceleration and angular velocity of the sources. This is transformed to a form which explicitly contains the known special cases for either rotating or accelerating black holes. Electromagnetic charges and a NUT parameter are included, the relation between the NUT parameter $l$ and the Plebanski-Demianski parameter $n$ is given, and the physical meaning of all parameters is clarified. The possibility of finding an accelerating NUT solution is also discussed.
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