It is known that approximating the Regge-Wheeler Potential with step functions significantly modifies the Schwarzschild black hole quasinormal mode spectrum. Surprisingly, this change in the spectrum has little impact on the ringdown waveform. We examine whether this issue is caused by the jump discontinuities and/or the piecewise constant nature of step functions. We show that replacing the step functions with a continuous piecewise linear function does not qualitatively change the results. However, in contrast to previously published results, we discover that the ringdown waveform can be approximated to arbitrary precision using either step functions or a piecewise linear function. Thus, this approximation process provides a new mathematical tool to calculate the ringdown waveform. In addition, similar to normal modes, the quasinormal modes of the approximate potentials seem to form a complete set that describes the entire time evolution of the ringdown waveform. We also examine smoother approximations to the Regge-Wheeler potential, where the quasinormal modes can be computed exactly, to better understand how different portions of the potential impact various regions of the quasinormal mode spectrum.
Quasinormal modes have played a prominent role in the discussion of perturbations of black holes, and the question arises whether they are as significant as normal modes are for self adjoint systems, such as harmonic oscillators. They can be significant in two ways: Individual modes may dominate the time evolution of some perturbation, and a whole set of them could be used to completely describe this time evolution. It is known that quasinormal modes of black holes have the first property, but not the second. It has recently been suggested that a discontinuity in the underlying system would ma…
Here we consider two phenomena in the vicinity of a black hole deformed by the tidal gravitational force of surrounding matter and by a strong magnetic field: equatorial motion of charged particles and the decay of a test scalar field. We were able to analyze both phenomena with analytical and simple numerical tools, which was unexpected given the low symmetry of the system. We show that both the tidal gravitational force and the magnetic field strongly enhance the release of the binding energy for the matter spiralling into the black hole. In the presence of the magnetic field, the left and r…
We investigate the quasinormal modes (QNMs) of the scalar field coupled to the Einstein's tensor in the non-commutative geometry inspired black hole spacetime. It is found that the lapse function of the non-commutative black hole metric can be represented by a Kummer's confluent hypergeometric function, which can effectively solve the problem that the numerical results of the QNMs are sensitive to the model parameters and make the QNMs values more reliable. We make a careful analysis of the scalar QNM frequencies by using several numerical methods, and find that the numerical results obtained …
We study the Regge-Wheeler and Zerilli equations (RWE and ZE) at the `algebraically special frequency' $Ω$, where these equations admit an exact solution (elaborated here), generating the SUSY relationship between them. The physical significance of the SUSY generator and of the solutions at $Ω$ in general is elucidated as follows. The RWE has no (quasinormal or total-transmission) modes at all; however, $Ω$ is nonetheless `special' in that (a) for the outgoing wave into the horizon one has a `miraculous' cancellation of a divergence expected due to the exponential potential tail, and (b) the b…
We reanalyze the GW150914 post-merger data searching for quasinormal modes beyond the fundamental, quadrupolar mode. There is currently an ongoing disagreement in the literature about whether, and to what extent, the data contains evidence for a quasinormal mode overtone. We use a frequency-domain approach to ringdown data analysis that was recently proposed by the authors. Our analysis has several advantages compared to other analyses performed mainly in the time domain; in particular, the source sky position and the ringdown start time are marginalized over (as opposed to simply being fixed)…
We study the stability of quasinormal modes (QNM) in asymptotically flat black hole spacetimes by means of a pseudospectrum analysis. The construction of the Schwarzschild QNM pseudospectrum reveals the following: (i) the stability of the slowest-decaying QNM under perturbations respecting the asymptotic structure, reassessing the instability of the fundamental QNM discussed by Nollert [H. P. Nollert, About the Significance of Quasinormal Modes of Black Holes, Phys. Rev. D 53, 4397 (1996)] as an "infrared" effect; (ii) the instability of all overtones under small-scale ("ultraviolet") perturba…
Reflectionless and echo modes in asymmetric Damour-Solodukhin wormholes
Escola de Engenharia de Lorena, Universidade de São Paulo（圣保罗大学洛雷纳工程学院）；Center for Gravitation and Cosmology, College of Physical Science and Technology, Yangzhou University（扬州大学物理科学与技术学院引力与宇宙学研究中心）；Faculdade de Engenharia de Guaratinguetá, Universidade Estadual Paulista（圣保罗州立大学瓜拉廷格塔工程学院）；Key Laboratory of Low Dimensional Quantum Structures and Quantum Control of Ministry of Education, Synergetic Innovation Center for Quantum Effects and Applications, and Department of Physics, Hunan Normal University（湖南师范大学物理学院低维量子结构与量子控制教育部重点实验室、量子效应与应用协同创新中心）；Metropolitan State University（大都会州立大学）；Department of Physical Sciences and Applied Mathematics, Vanguard University（先锋大学物理科学与应用数学系）
Ringdown analysis of GW250114 with orthonormal modes
The University of Tokyo（东京大学）；Institute for Cosmic Ray Research, The University of Tokyo（东京大学宇宙射线研究所）；Tokyo Metropolitan University（东京都立大学）；Research Center for the Early Universe (RESCEU), Graduate School of Science, The University of Tokyo（东京大学理学研究系早期宇宙研究中心）
We present a new covariant and gauge-invariant perturbation formalism for dealing with spacetimes having spherical symmetry (or some preferred spatial direction) in the background, and apply it to the case of gravitational wave propagation in a Schwarzschild black hole spacetime. The 1+3 covariant approach is extended to a `1+1+2 covariant sheet' formalism by introducing a radial unit vector in addition to the timelike congruence, and decomposing all covariant quantities with respect to this. The background Schwarzschild solution is discussed and a covariant characterisation is given. We give …
