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A new form of the Kerr-Newman solution is presented. The solution involves a time coordinate which represents the local proper time for a charged massive particle released from rest at spatial infinity. The chosen coordinates ensure that…

General Relativity and Quantum Cosmology · Physics 2023-02-15 Michael Hobson

Under the hypothesis of asymptotic safety of gravity, the static, spherically symmetric black hole solutions in the infrared limit are corrected by non-perturbative effects. Specifically, the metric is modified by the running of…

General Relativity and Quantum Cosmology · Physics 2015-06-05 Dao-Jun Liu , Bin Yang , Yong-Jia Zhai , Xin-Zhou Li

The black hole as the thermodynamical system in equilibrium possesses the periodicity of motion in imaginary time, that allows us to formulate the quasi-classical rule of quantization. The rule yields the equidistant spectrum for the…

General Relativity and Quantum Cosmology · Physics 2007-05-23 V. V. Kiselev

Scalar, vector and tensor perturbations on the Kerr spacetime are governed by equations that can be solved by separation of variables, but the same is not true in generic stationary and axisymmetric geometries. This complicates the…

General Relativity and Quantum Cosmology · Physics 2023-10-03 Rajes Ghosh , Nicola Franchini , Sebastian H. Völkel , Enrico Barausse

This paper contains the second part of a two-part series on the stability and instability of extreme Reissner-Nordstrom spacetimes for linear scalar perturbations. We continue our study of solutions to the linear wave equation on a suitable…

General Relativity and Quantum Cosmology · Physics 2015-05-30 Stefanos Aretakis

This is the last part of our proof of the nonlinear stability of the Kerr family for small angular momentum, i.e $|a|/m\ll 1$, in which we deal with the nonlinear wave type estimates needed to complete the project. More precisely we provide…

Analysis of PDEs · Mathematics 2022-05-31 Elena Giorgi , Sergiu Klainerman , Jeremie Szeftel

The purpose of this paper is to investigate the stabilization of a one-dimensional coupled wave equations with non smooth localized viscoelastic damping of Kelvin-Voigt type and localized time delay. Using a general criteria of…

Analysis of PDEs · Mathematics 2020-07-17 Mohammad Akil , Haidar Badawi , Ali Wehbe

We study the instability of small AdS black holes with two independent rotation parameters in minimal five-dimensional gauged supergravity to massless scalar perturbations. We analytically solve the Klein-Gordon equation for low-frequency…

High Energy Physics - Theory · Physics 2009-03-12 Alikram N. Aliev , Özgür Delice

Normal modes, quasi-normal modes and super-radiant modes are studied to clarify the total dynamics for complex scalar fields in Kerr anti-de Sitter black hole spacetime. Orthonormal relations and quasi-orthonormal relations are obtained for…

General Relativity and Quantum Cosmology · Physics 2009-05-06 Masakatsu Kenmoku

The Klein-Gordon equation for a massive scalar field in the background of a rapidly-rotating Kerr black hole is studied analytically. In particular, we derive a simple formula for the stationary (marginally-stable) resonances of the field…

General Relativity and Quantum Cosmology · Physics 2015-06-18 Shahar Hod

We consider the Cauchy problem for the scalar wave equation in the Kerr geometry for smooth initial data supported outside the event horizon. We prove that the solutions decay in time in L^\infty_loc. The proof is based on a representation…

General Relativity and Quantum Cosmology · Physics 2017-08-29 Felix Finster , Niky Kamran , Joel Smoller , Shing-Tung Yau

We provide a rigorous definition of quasinormal modes for the Kerr black hole. They are obtained as the discrete set of poles of the meromorphically continued cutoff resolvent. The construction combines the method of complex scaling near…

Analysis of PDEs · Mathematics 2025-07-23 Thomas Stucker

Motivated by the recent work on a new physical interpretation of quasinormal modes by Maggiore, we utilize this new proposal to the interesting case of Kerr black hole. In particular, by modifying Hod's idea, the resulting black hole…

General Relativity and Quantum Cosmology · Physics 2008-12-18 Elias C. Vagenas

We present a short review of the analytical aspects of recent progress in the study of black hole spectral instability and its potential observational consequences. This topic, inspired by earlier foundational works, has attracted…

General Relativity and Quantum Cosmology · Physics 2026-01-13 Shui-Fa Shen , Guan-Ru Li , Ramin G. Daghigh , Jodin C. Morey , Michael D. Green , Wei-Liang Qian , Rui-Hong Yue

We study the quasinormal modes of Boulware-Deser-Wheeler black hole in Einstein-Gauss-Bonnet gravity theory within the hyperboloidal framework. The effective potentials for the test Klein-Gordon field and gravitational perturbations of…

General Relativity and Quantum Cosmology · Physics 2025-08-18 Li-Ming Cao , Liang-Bi Wu , Yu-Sen Zhou

We construct growing mode solutions to the uncharged and charged Klein-Gordon equations on the sub-extremal Reissner-Nordstr\"om--anti-de-Sitter (AdS) spacetime under reflecting (Dirichlet or Neumann) boundary conditions. Our result applies…

General Relativity and Quantum Cosmology · Physics 2026-05-19 Weihao Zheng

In this paper, we investigate the stability of the linear wave equation where one part of the boundary, which is seen as a lower-dimensional Riemannian manifold, is governed by a coupled wave equation, while the other part is subject to a…

Analysis of PDEs · Mathematics 2022-09-23 Nicolas Vanspranghe

We study the dispersive properties for the wave equation in the Kerr space-time with small angular momentum. The main result of this paper is to establish Strichartz estimates for solutions of the aforementioned equation. As an application,…

Analysis of PDEs · Mathematics 2009-10-09 Mihai Tohaneanu

One of the central goals of the newborn field of gravitational wave astronomy is to test gravity in the highly nonlinear, strong field regime characterizing the spacetime of black holes. In particular, "black hole spectroscopy" (the…

General Relativity and Quantum Cosmology · Physics 2017-10-04 Kostas Glampedakis , George Pappas , Hector O. Silva , Emanuele Berti

We consider solutions of the massless scalar wave equation $\Box_g\psi=0$, without symmetry, on fixed subextremal Kerr backgrounds $(\mathcal M, g)$. It follows from previous analyses in the Kerr exterior that for solutions $\psi$ arising…

General Relativity and Quantum Cosmology · Physics 2020-04-22 Anne T. Franzen