Maxwell perturbations in a cavity with Robin boundary conditions: two branches of modes with spectrum bifurcation on Schwarzschild black holes

AbstractWe perform a systematic study of the Maxwell quasinormal spectrum in a mirror-like cavity following the generic Robin type vanishing energy flux principle, by starting with the Schwarzschild black holes in this paper. It is shown that, for black holes in a cavity, the vanishing energy flux principle leads to two different sets of boundary conditions. By solving the Maxwell equations with these two boundary conditions both analytically and numerically, we observe two distinct sets of modes. This indicates that the vanishing energy flux principle may be applied not only to asymptotically anti-de Sitter (AdS) black holes but also to black holes in a cavity. In the analytic calculations, the imaginary part of the Maxwell quasinormal modes are derived analytically for both boundary conditions, which match well with the numeric results. While in the numeric calculations, we complete a thorough study on the two sets of the Maxwell spectrum by varying the mirror radius $$r_m$$ r m , the angular momentum quantum number $$\ell $$ ℓ , and the overtone number N. In particular, we proclaim that the Maxwell spectrum may bifurcate for both modes when the mirror is placed around the black hole event horizon, which is analogous to the spectrum bifurcation effects found for the Maxwell fields on asymptotically AdS black holes. This observation provides another example to exhibit the similarity between black holes in a cavity and the AdS black holes.

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Boundary conditions for Maxwell fields in Kerr-AdS spacetimes

International Journal of Modern Physics D ◽

10.1142/s021827181641011x ◽

2016 ◽

Vol 25 (09) ◽

pp. 1641011 ◽

Cited By ~ 4

Author(s):

Mengjie Wang

Keyword(s):

Black Holes ◽

Angular Momentum ◽

Boundary Conditions ◽

Energy Flux ◽

Momentum Flux ◽

De Sitter ◽

Perturbative Methods ◽

Flux Boundary Conditions ◽

Maxwell Fields ◽

New Type

Perturbative methods are useful to study the interaction between black holes and test fields. The equation for a perturbation itself, however, is not complete to study such a composed system if we do not assign physically relevant boundary conditions. Recently we have proposed a new type of boundary conditions for Maxwell fields in Kerr-anti-de Sitter (Kerr-AdS) spacetimes, from the viewpoint that the AdS boundary may be regarded as a perfectly reflecting mirror, in the sense that energy flux vanishes asymptotically. In this paper, we prove explicitly that a vanishing energy flux leads to a vanishing angular momentum flux. Thus, these boundary conditions may be dubbed as vanishing flux boundary conditions.

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Maxwell quasinormal modes on a global monopole Schwarzschild-anti-de Sitter black hole with Robin boundary conditions

The European Physical Journal C ◽

10.1140/epjc/s10052-021-09149-x ◽

2021 ◽

Vol 81 (5) ◽

Author(s):

Mengjie Wang ◽

Zhou Chen ◽

Qiyuan Pan ◽

Jiliang Jing

Keyword(s):

Black Hole ◽

Boundary Conditions ◽

Energy Flux ◽

Maxwell Equations ◽

Normal Modes ◽

Quasinormal Modes ◽

Low Frequency ◽

Global Monopole ◽

De Sitter ◽

Small Black Hole

AbstractWe generalize our previous studies on the Maxwell quasinormal modes around Schwarzschild-anti-de-Sitter black holes with Robin type vanishing energy flux boundary conditions, by adding a global monopole on the background. We first formulate the Maxwell equations both in the Regge–Wheeler–Zerilli and in the Teukolsky formalisms and derive, based on the vanishing energy flux principle, two boundary conditions in each formalism. The Maxwell equations are then solved analytically in pure anti-de Sitter spacetimes with a global monopole, and two different normal modes are obtained due to the existence of the monopole parameter. In the small black hole and low frequency approximations, the Maxwell quasinormal modes are solved perturbatively on top of normal modes by using an asymptotic matching method, while beyond the aforementioned approximation, the Maxwell quasinormal modes are obtained numerically. We analyze the Maxwell quasinormal spectrum by varying the angular momentum quantum number $$\ell $$ ℓ , the overtone number N, and in particular, the monopole parameter $$8\pi \eta ^2$$ 8 π η 2 . We show explicitly, through calculating quasinormal frequencies with both boundary conditions, that the global monopole produces the repulsive force.

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Quasinormal modes of dS and AdS black holes: Feedforward neural network method

International Journal of Geometric Methods in Modern Physics ◽

10.1142/s0219887821501541 ◽

2021 ◽

pp. 2150154

Author(s):

Ali Övgün ◽

İzzet Sakallı ◽

Halil Mutuk

Keyword(s):

Neural Network ◽

Black Holes ◽

Boundary Conditions ◽

Quasinormal Modes ◽

Scalar Fields ◽

Feedforward Neural Network ◽

De Sitter ◽

Neural Network Method ◽

Ads Black Holes ◽

Network Method

In this paper, we show how the quasinormal modes (QNMs) arise from the perturbations of massive scalar fields propagating in the curved background by using the artificial neural networks. To this end, we architect a special algorithm for the feedforward neural network method (FNNM) to compute the QNMs complying with the certain types of boundary conditions. To test the reliability of the method, we consider two black hole spacetimes whose QNMs are well known: [Formula: see text] pure de Sitter (dS) and five-dimensional Schwarzschild anti-de Sitter (AdS) black holes. Using the FNNM, the QNMs of are computed numerically. It is shown that the obtained QNMs via the FNNM are in good agreement with their former QNM results resulting from the other methods. Therefore, our method of finding the QNMs can be used for other curved spacetimes that obey the same boundary conditions.

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Phase Structure and Quasinormal Modes of AdS Black Holes in Rastall Theory

Advances in High Energy Physics ◽

10.1155/2020/8039183 ◽

2020 ◽

Vol 2020 ◽

pp. 1-9

Author(s):

De-Cheng Zou ◽

Ming Zhang ◽

Ruihong Yue

Keyword(s):

Phase Transition ◽

Black Holes ◽

Quasinormal Modes ◽

Massless Scalar ◽

Extended Phase Space ◽

De Sitter ◽

Extended Phase ◽

Large Black Hole ◽

Ads Black Holes ◽

Scalar Perturbations

We discuss the P−V criticality and phase transition in the extended phase space of anti-de Sitter(AdS) black holes in four-dimensional Rastall theory and recover the Van der Waals (VdW) analogy of small/large black hole (SBH/LBH) phase transition when the parameters ωs and ψ satisfy some certain conditions. Later, we further explore the quasinormal modes (QNMs) of massless scalar perturbations to probe the SBH/LBH phase transition. It is found that it can be detected near the critical point, where the slopes of the QNM frequencies change drastically in small and large black holes.

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Anomalous decay rate of quasinormal modes in Schwarzschild-dS and Schwarzschild-AdS black holes

Journal of High Energy Physics ◽

10.1007/jhep08(2020)120 ◽

2020 ◽

Vol 2020 (8) ◽

Author(s):

Almendra Aragón ◽

P.A. González ◽

Eleftherios Papantonopoulos ◽

Yerko Vásquez

Keyword(s):

Black Holes ◽

Scalar Field ◽

Decay Rate ◽

Critical Mass ◽

Quasinormal Modes ◽

De Sitter ◽

Field Mass ◽

Massive Scalar Field ◽

Ads Black Holes ◽

Sitter Background

Abstract Recently an anomalous decay rate of the quasinormal modes of a massive scalar field in Schwarzschild black holes backgrounds was reported in which the longest-lived modes are the ones with higher angular number, for a scalar field mass smaller than a critical value, while that beyond this value the behaviour is inverted. In this work, we extend the study to other asymptotic geometries, such as, Schwarzschild-de Sitter and Schwarzschild-AdS black holes. Mainly, we found that such behaviour and the critical mass are present in the Schwarzschild-de Sitter background. Also, we found that the value of the critical mass increases when the cosmological constant increases and also when the overtone number is increasing. On the other hand, despite the critical mass is not present in Schwarzschild-AdS black holes backgrounds, the decay rate of the quasinormal modes always exhibits an anomalous behaviour.

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IS THERE CLASSICAL SUPER-RADIANCE ON KERR-NEWMAN-ANTI-DE SITTER BLACK HOLES?

International Journal of Modern Physics A ◽

10.1142/s0217751x02012090 ◽

2002 ◽

Vol 17 (20) ◽

pp. 2782-2782

Author(s):

ELIZABETH WINSTANLEY

Keyword(s):

Black Holes ◽

Boundary Conditions ◽

Killing Vector ◽

De Sitter ◽

Transparent Boundary Conditions ◽

Asymptotically Flat ◽

Ads Black Holes ◽

Definition Of ◽

Conditions At Infinity ◽

Positive Frequency

Since the formulation of the AdS/CFT correspondence 1, there has been great interest in space-times which are asymptotically anti-de Sitter, and the properties of the Kerr-Newman-anti-de Sitter (KN-AdS) space-time in various dimensions have been extensively studied 2. However, the properties of classical or quantum fields propagating on this background have not been widely studied, and, in particular, the question of whether super-radiance occurs has not been addressed. This is an important issue since a detailed understanding of classical super-radiance is necessary before tackling quantum field theory on rotating black hole geometries 3. We considered a classical scalar field on the KN-AdS background 4, and examined the form of the separated field modes. Given the structure of infinity in asymptotically anti-de Sitter space-times, we paid particular attention to the boundary conditions at infinity. Unlike the situation for asymptotically flat Kerr-Newman black holes 5, super-radiance is not inevitable. It depends partly on our choice of boundary condition at infinity. For reflective boundary conditions at infinity, there is no super-radiance. On the other hand, if we consider transparent boundary conditions at infinity, then the presence of super-radiance depends on our choice of positive frequency. For those KN-AdS black holes possessing a globally time-like Killing vector, then the natural definition of positive frequency implies that there are no super-radiant modes. For other KN-AdS black holes, then this same definition of positive frequency again leads to no super-radiance.

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