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Register a new userA geometric framework for black hole perturbations
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Authors
An{i}l Zenginou{g}lu
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Black hole perturbation theory is typically studied on time surfaces that extend between the bifurcation sphere and spatial infinity. From a physical point of view, however, it may be favorable to employ time surfaces that extend between the future event horizon and future null infinity. This framework resolves problems regarding the representation of quasinormal mode eigenfunctions and the construction of short-ranged potentials for the perturbation equations in frequency domain.
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Linearized perturbations of a Schwarzschild black hole are described, for each angular momentum $ell$, by the well-studied discrete quasinormal modes (QNMs), and in addition a continuum. The latter is characterized by a cut strength $q(gamma>0)$ for frequencies $omega = -igamma$. We show that: (a) $q(gammadownarrow0) propto gamma$, (b) $q(Gamma) = 0$ at $Gamma = (ell+2)!/[6(ell-2)!]$, and (c) $q(gamma)$ oscillates with period $sim 1$ ($2Mequiv1$). For $ell=2$, a pair of QNMs are found beyond the cut on the unphysical sheet very close to $Gamma$, leading to a large dipole in the Greens function_near_ $Gamma$. For a source near the horizon and a distant observer, the continuum contribution relative to that of the QNMs is small.
We study linear gravitational perturbations of Schwarzschild spacetime by solving numerically Regge-Wheeler-Zerilli equations in time domain using hyperboloidal surfaces and a compactifying radial coordinate. We stress the importance of including the asymptotic region in the computational domain in studies of gravitational radiation. The hyperboloidal approach should be helpful in a wide range of applications employing black hole perturbation theory.
We study the spectrum of the bound state perturbations in the interior of the Schwarzschild black hole for the scalar, electromagnetic and gravitational perturbations. Demanding that the perturbations to be regular at the center of the black hole determines the spectrum of the bound state solutions. We show that our analytic expression for the spectrum is in very good agreement with the imaginary parts of the high overtone quasi normal mode excitations obtained for the exterior region. We also present a simple scheme to calculate the spectrum numerically to good accuracies.
We derive a set of coupled equations for the gravitational and electromagnetic perturbation in the Reissner-Nordstrom geometry using the Newman Penrose formalism. We show that the information of the physical gravitational signal is contained in the Weyl scalar function $Psi_4$, as is well known, but for the electromagnetic signal the information is encoded in the function $chi$ which relates the perturbations of the radiative Maxwell scalars $varphi_2$ and the Weyl scalar $Psi_3$. In deriving the perturbation equations we do not impose any gauge condition and our analysis contains as a limiting case the results obtained previously for instance in Chandrashekhars book. In our analysis, we also include the sources for the perturbations and focus on a dust-like charged fluid distribution falling radially into the black hole. Finally, by writing the functions on a basis of spin weighted spherical harmonics and the Reissner-Nordstrom spacetime in Kerr-Schild type coordinates a hyperbolic system of coupled partial differential equations is presented and numerically solved. In this way, we solve completely a system which generates a gravitational signal as well as an electromagnetic/gravitational one, which sets the basis to find correlations between them and thus facilitating the gravitational wave detection via the electromagnetic signal.
In this work, we have calculated the polar gravitational quasinormal modes for a quantum corrected black hole model, that arises in the context of Loop Quantum Gravity, known as Self-Dual Black Hole. In this way, we have calculated the characteristic frequencies using the WKB approach, where we can verify a strong dependence with the Loop Quantum Gravity parameters. At the same time we check that the Self-Dual Black Hole is stable under polar gravitational perturbations, we can also verify that the spectrum of the polar quasinormal modes differs from the axial one cite{Cruz:2015bcj}. Such a result tells us that isospectrality is broken in the context of Self Dual Black Holes.
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