scholarly journals Quasinormal Modes in Extremal Reissner–Nordström Spacetimes

2021 ◽  
Author(s):  
Dejan Gajic ◽  
Claude Warnick
Keyword(s):  
Wave Equation ◽  
Event Horizon ◽  
Hilbert Spaces ◽  
Quasinormal Modes ◽  
Meromorphic Continuation ◽  
De Sitter ◽  
Null Infinity ◽  
Asymptotically Flat ◽  
Black Hole Spacetimes ◽  
New Framework

AbstractWe present a new framework for characterizing quasinormal modes (QNMs) or resonant states for the wave equation on asymptotically flat spacetimes, applied to the setting of extremal Reissner–Nordström black holes. We show that QNMs can be interpreted as honest eigenfunctions of generators of time translations acting on Hilbert spaces of initial data, corresponding to a suitable time slicing. The main difficulty that is present in the asymptotically flat setting, but is absent in the previously studied asymptotically de Sitter or anti de Sitter sub-extremal black hole spacetimes, is that $$L^2$$ L 2 -based Sobolev spaces are not suitable Hilbert space choices. Instead, we consider Hilbert spaces of functions that are additionally Gevrey regular at infinity and at the event horizon. We introduce $$L^2$$ L 2 -based Gevrey estimates for the wave equation that are intimately connected to the existence of conserved quantities along null infinity and the event horizon. We relate this new framework to the traditional interpretation of quasinormal frequencies as poles of the meromorphic continuation of a resolvent operator and obtain new quantitative results in this setting.

scholarly journals Energy of test objects on black hole spacetimes: A brief review

2015 ◽  
Vol 24 (14) ◽  
pp. 1550103 ◽  
Author(s):  
Alejandro Corichi
Keyword(s):  
Black Hole ◽  
Asymptotic Region ◽  
Gravitational Potential Energy ◽  
De Sitter ◽  
Conservation Of Energy ◽  
Asymptotically Flat ◽  
Black Hole Spacetimes ◽  
Test Particles ◽  
Exterior Regions ◽  
Test Objects

In this paper, we review the issue of defining energy for test particles on a background stationary spacetime. We revisit different notions of energy as defined by different observers. As is well-known, the existence of a timelike isometry allows for the notion of total conserved energy to be well defined. We use this well-known quantity to show that a gravitational potential energy can be consistently defined. As examples, we study the case of the exterior regions of an asymptotically flat black hole and of the [Formula: see text] Schwarzschild–de Sitter (SdS) case, where an asymptotic region is not available. We then consider the situation in which the test particle is absorbed by the black hole and analyze the energetics in detail. In particular, we show that the notion of horizon energy as defined by the isolated horizons formalism provides a satisfactory notion of energy compatible with the particle’s total conserved energy. With these choices, there is a global conservation of energy. Finally, we comment on a recent proposal to define energy of the black hole as seen by a nearby observer at rest, for which this feature is lost.

Logarithmic corrections in the asymptotic expansion for the radiation field along null infinity

2019 ◽  
Vol 16 (01) ◽  
pp. 1-34 ◽  
Author(s):  
Yannis Angelopoulos ◽  
Stefanos Aretakis ◽  
Dejan Gajic
Keyword(s):  
Radiation Field ◽  
Late Time ◽  
Spherically Symmetric ◽  
Null Infinity ◽  
Asymptotically Flat ◽  
Black Hole Spacetimes ◽  
Logarithmic Corrections ◽  
Time Asymptotics ◽  
Physics Literature ◽  
Field Of Solutions

We obtain the second-order late-time asymptotics for the radiation field of solutions to the wave equation on spherically symmetric and asymptotically flat backgrounds including the Schwarzschild and sub-extremal Reissner–Nordström families of black hole spacetimes. These terms appear as logarithmic corrections to the leading-order asymptotic terms which were rigorously derived in our previous work. Such corrections have been heuristically and numerically derived in the physics literature in the case of a non-vanishing Newman–Penrose constant. In this case, our results provide a rigorous confirmation of the existence of these corrections. On the other hand, the precise logarithmic corrections for spherically symmetric compactly supported initial data (and hence, with a vanishing Newman–Penrose constant) explicitly obtained here appear to be new.

scholarly journals Gravitational Quasinormal Modes of Regular Phantom Black Hole

2017 ◽  
Vol 2017 ◽  
pp. 1-19 ◽  
Author(s):  
Jin Li ◽  
Kai Lin ◽  
Hao Wen ◽  
Wei-Liang Qian
Keyword(s):  
Black Hole ◽  
Scalar Field ◽  
Quasinormal Modes ◽  
De Sitter ◽  
Asymptotically Flat ◽  
Gravitational Perturbations ◽  
Phantom Scalar ◽  
Quantum Interpretation ◽  
The Stability ◽  
Phantom Scalar Field

We investigate the gravitational quasinormal modes (QNMs) for a type of regular black hole (BH) known as phantom BH, which is a static self-gravitating solution of a minimally coupled phantom scalar field with a potential. The studies are carried out for three different spacetimes: asymptotically flat, de Sitter (dS), and anti-de Sitter (AdS). In order to consider the standard odd parity and even parity of gravitational perturbations, the corresponding master equations are derived. The QNMs are discussed by evaluating the temporal evolution of the perturbation field which, in turn, provides direct information on the stability of BH spacetime. It is found that in asymptotically flat, dS, and AdS spacetimes the gravitational perturbations have similar characteristics for both odd and even parities. The decay rate of perturbation is strongly dependent on the scale parameterb, which measures the coupling strength between phantom scalar field and the gravity. Furthermore, through the analysis of Hawking radiation, it is shown that the thermodynamics of such regular phantom BH is also influenced byb. The obtained results might shed some light on the quantum interpretation of QNM perturbation.

scholarly journals A Non-degenerate Scattering Theory for the Wave Equation on Extremal Reissner–Nordström

2020 ◽  
Vol 380 (1) ◽  
pp. 323-408
Author(s):  
Yannis Angelopoulos ◽  
Stefanos Aretakis ◽  
Dejan Gajic
Keyword(s):  
Black Hole ◽  
Wave Equation ◽  
Event Horizon ◽  
Scattering Theory ◽  
Physical Space ◽  
Extremal Black Hole ◽  
Null Infinity ◽  
Interior Region ◽  
Exterior Region ◽  
Black Hole Interior

Abstract It is known that sub-extremal black hole backgrounds do not admit a (bijective) non-degenerate scattering theory in the exterior region due to the fact that the redshift effect at the event horizon acts as an unstable blueshift mechanism in the backwards direction in time. In the extremal case, however, the redshift effect degenerates and hence yields a much milder blueshift effect when viewed in the backwards direction. In this paper, we construct a definitive (bijective) non-degenerate scattering theory for the wave equation on extremal Reissner–Nordström backgrounds. We make use of physical-space energy norms which are non-degenerate both at the event horizon and at null infinity. As an application of our theory we present a construction of a large class of smooth, exponentially decaying modes. We also derive scattering results in the black hole interior region.

scholarly journals Massive Dirac quasinormal modes in Schwarzschild–de Sitter black holes: Anomalous decay rate and fine structure

2021 ◽  
Vol 103 (6) ◽  
Author(s):  
Almendra Aragón ◽  
Ramón Bécar ◽  
P. A. González ◽  
Yerko Vásquez
Keyword(s):  
Black Holes ◽  
Fine Structure ◽  
Decay Rate ◽  
Quasinormal Modes ◽  
De Sitter

scholarly journals Hamiltonian charges in the asymptotically de Sitter spacetimes

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Maciej Kolanowski ◽  
Jerzy Lewandowski
Keyword(s):  
Phase Space ◽  
Initial Data ◽  
Exact Solutions ◽  
Gravitational Waves ◽  
Physical Meaning ◽  
De Sitter ◽  
Killing Vectors ◽  
Asymptotically Flat ◽  
Angular Momenta ◽  
The One

Abstract We generalize a notion of ‘conserved’ charges given by Wald and Zoupas to the asymptotically de Sitter spacetimes. Surprisingly, our construction is less ambiguous than the one encountered in the asymptotically flat context. An expansion around exact solutions possessing Killing vectors provides their physical meaning. In particular, we discuss a question of how to define energy and angular momenta of gravitational waves propagating on Kottler and Carter backgrounds. We show that obtained expressions have a correct limit as Λ → 0. We also comment on the relation between this approach and the one based on the canonical phase space of initial data at ℐ+.

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