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Register a new userThree dimensional distorted black holes: using the Galerkin-Collocation method
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We present an implementation of the Galerkin-Collocation method to determine the initial data for non-rotating distorted three dimensional black holes in the inversion and puncture schemes. The numerical method combines the key features of the Galerkin and Collocation methods which produces accurate initial data. We evaluated the ADM mass of the initial data sets, and we have provided the angular structure of the gravitational wave distribution at the initial hypersurface by evaluating the scalar $Psi_4$ for asymptotic observers.
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We present a new computational framework for the Galerkin-collocation method for double domain in the context of ADM 3+1 approach in numerical relativity. This work enables us to perform high resolution calculations for initial sets of two arbitrary black holes. We use the Bowen-York method for binary systems and the puncture method to solve the Hamiltonian constraint. The nonlinear numerical code solves the set of equations for the spectral modes using the standard Newton-Raphson method, LU decomposition and Gaussian quadratures. We show convergence of our code for the conformal factor and the ADM mass. Thus, we display features of the conformal factor for different masses, spins and linear momenta.
We study the interior of distorted stationary rotating black holes on the example of a Kerr black hole distorted by external static and axisymmetric mass distribution. We show that there is a duality transformation between the outer and inner horizons of the black hole, which is different from that of an electrically charged static distorted black hole. The duality transformation is directly related to the discrete symmetry of the space-time. The black hole horizons area, surface gravity, and angular momentum satisfy the Smarr formula constructed for both the horizons. We formulate the zeroth, the first, and the second laws of black hole thermodynamics for both the horizons of the black hole and show the correspondence between the local and the global forms of the first law. The Smarr formula and the laws of thermodynamics formulated for both the horizons are related by the duality transformation. The distortion is illustrated on the example of a quadrupole and octupole fields. The distortion fields noticeably affect the proper time of a free fall from the outer to the inner horizon of the black hole along the symmetry semi-axes. There is some minimal non-zero value of the quadrupole and octupole moments when the time becomes minimal. The minimal proper time indicates the closest approach of the horizons due to the distortion.
An analytical metric of four-dimensional General Relativity, representing an array of collinear and accelerating black holes, is constructed with the inverse scattering method. The solution can be completely regularised from any conical singularity, thanks to the presence of an external gravitational field. Therefore the multi-black hole configuration can be maintained at equilibrium without the need of string or struts. Some notable subcases such as the accelerating distorted Schwarzschild black hole and the double distorted C-metric are explicitly presented. The Smarr law and the thermodynamics of these systems is studied. The Bonnor-Swaminarayan and the Biv{c}ak-Hoenselaers-Schmidt particle metrics are recovered, through appropriate limits, from the multi-black holes solutions.
We present a single domain Galerkin-Collocation method to calculate puncture initial data sets for single and binary, either in the trumpet or wormhole geometries. The combination of aspects belonging to the Galerkin and the Collocation methods together with the adoption of spherical coordinates in all cases show to be very effective. We have proposed a unified expression for the conformal factor to describe trumpet and spinning black holes. In particular, for the spinning trumpet black holes, we have exhibited the deformation of the limit surface due to the spin from a sphere to an oblate spheroid. We have also revisited the energy content in the trumpet and wormhole puncture data sets. The algorithm can be extended to describe binary black holes.
We consider three-dimensional gravity based on torsion. Specifically, we consider an extension of the so-called Teleparallel Equivalent of General Relativity in the presence of a scalar field with a self-interacting potential, where the scalar field is non-minimally coupled with the torsion scalar. Then, we find asymptotically AdS hairy black hole solutions, which are characterized by a scalar field with a power-law behavior, being regular outside the event horizon and null at spatial infinity and by a self-interacting potential, which tends to an effective cosmological constant at spatial infinity.
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