Separable wave equations for gravitoelectromagnetic perturbations of rotating charged black strings

Miranda, Alex S.; Morgan, Jaqueline; Kandus, Alejandra; Zanchin, Vilson T.

doi:10.1088/0264-9381/32/23/235002

Cited by 11 publications

(16 citation statements)

References 97 publications

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“…In the limit of a → 0, the transverse and longitudinal perturbations, labeled by (−) and (+) in Ref. [80], correspond respectively to the odd (axial) and even (polar) perturbations under the parity transformation ϕ → −ϕ. As shown along this work, the (T ) sector gives rise to shear modes in the hydrodynamic regime, while the (L) sector gives rise to sound wave modes.…”

Section: Fundamental Equations For the Gravitational Perturbationsmentioning

confidence: 60%

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From quasinormal modes of rotating black strings to hydrodynamics of a moving CFT plasma

et al. 2018

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A certain identification of points in a planar Schwarzschild-anti de Sitter (AdS) black hole generates a four-dimensional static black string. In turn, a rotating black string can be obtained from a static one by means of a local boost along the compact direction. On the basis of the gauge/gravity duality, these black strings are dual to rotating thermal states of a strongly interacting conformal field theory (CFT) that lives on a cylinder. In this work, we obtain the complete quasinormal mode (QNM) spectrum of the gravitational perturbations of rotating black strings. Analytic solutions for the dispersion relations are found in the hydrodynamic limit, characterized by fluctuations with wavenumber and frequency much smaller than the Hawking temperature of the string (or the temperature of the CFT in the dual description). We obtain these dispersion relations both by studying the gravitational perturbations of rotating black strings and by investigating relativistic wave vectors in a moving fluid living on the boundary of the AdS spacetime. Relativistic effects like the Doppler shift of the frequencies, wavelength contraction, and dilation of the thermalization time are shown explicitly in such a regime. The numerical solutions for the fundamental QNMs show a crossover (a transition) from a hydrodynamic-like behavior to a linear relativistic scaling for large wavenumbers. Additionally, we find a new family of QNMs which are purely damped in the zero wavenumber limit and that does not follow as a continuation of QNMs of the static black string, but that appears to be closely related to the algebraically special perturbation modes. I. INTRODUCTIONSince its advent in the late 1990's, the celebrated antide Sitter/conformal field theory (AdS/CFT) correspondence [1-4] has been extended and applied to different areas of physics. Such developments have lead to what is now known as the AdS/QCD [5][6][7][8], the AdS/condensed matter [9][10][11], and the fluid/gravity [12][13][14] correspondences. Over the last two decades, the AdS/CFT duality has allowed the study of properties of strongly coupled systems in a n-dimensional flat spacetime by mapping them to a weakly coupled gravitational theory in an asymptotically AdS n+1 spacetime. In applications to particle physics, top-down and bottom-up models were used to study, among other things, the mass spectrum, the correlation functions, and the deep inelastic scattering of glueballs, vector and scalar mesons [15][16][17][18][19][20][21][22][23]. Some phenomena in condensed matter, such as the hightemperature superconductivity [24][25][26], the classical and quantum Hall effects [27][28][29][30][31][32] and the (non-)Fermi liquid behavior of certain materials [33][34][35], were also object of study in the literature. In relation to plasma physics, the fluid/gravity correspondence establishes a one-to-one

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Section: Fundamental Equations For the Gravitational Perturbationsmentioning

confidence: 60%

“…We may follow the study on gravitoelectromagnetic perturbations of rotating charged black strings of Ref. [80] for this purpose.…”

Section: Final Comments and Conclusionmentioning

confidence: 99%

From quasinormal modes of rotating black strings to hydrodynamics of a moving CFT plasma

et al. 2018

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“…Additionally, the SUSY quantum mechanics of perturbations also occurs in the presence of a (positive or negative) cosmological constant. In particular, it has been shown to hold in four-dimensional asymptotically AdS spacetimes [26,27].…”

Section: Jhep05(2020)019mentioning

confidence: 99%

Third-order relativistic hydrodynamics: dispersion relations and transport coefficients of a dual plasma

Diles¹,

Mamani²,

Miranda³

et al. 2020

J. High Energ. Phys.

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Hydrodynamics is nowadays understood as an effective field theory that describes the dynamics of the long-wavelength and slow-time fluctuations of an underlying microscopic theory. In this work we extend the relativistic hydrodynamics to third order in the gradient expansion for neutral fluids in a general curved spacetime of d dimensions. We find 58 new transport coefficients, 19 due to third-order scalar corrections and 39 due to tensorial corrections. In the particular case of a conformal fluid, the number of new transport coefficients is reduced to 19, all of them due to third-order tensorial corrections. The dispersion relations of linear fluctuations in the third-order relativistic hydrodynamics is obtained, both in the rest frame of the fluid and in a general moving frame. As an application we obtain some of the transport coefficients of a relativistic conformal fluid in three dimensions by using the AdS/CFT correspondence. These transport coefficients are extracted from the dispersion relations of the linear fluctuations. The gravity dual of the fluctuations in this conformal fluid is described by the gravitational perturbations of fourdimensional anti-de Sitter black branes, which are solutions of the Einstein equations with a negative cosmological constant. To find the hydrodynamic quasinormal modes (QNMs) of the scalar sector we use the SUSY quantum mechanics of the gravitational perturbations of four-dimensional black branes. Such a symmetry allows us to find the wavefunction of the scalar (or sound) sector in the hydrodynamic limit directly from the wavefunction of the vector (or shear) sector, which is usually easier to be found because the perturbation wave equations for the vector sector are much simpler than the ones for the scalar sector.

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“…Eqs. (16), (15), (31)], and then by taking the limit of vanishing wave numbers. This approach for polar perturbations of planar black holes with k = 0 is quite different from the approach for spherically symmetric black holes, since it is not possible to investigate the special modes l = 0 and l = 1 from the general equations of perturbations with l ≥ 2 in the spherically symmetric case.…”

Section: Discussionmentioning

confidence: 99%

New results on the physical interpretation of black-brane gravitational perturbations

2019

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The linear perturbation theory applied to the study of black holes is a traditional and powerful tool to investigate some of the basic properties of these objects, such as the stability of the event horizon, the spectra of quasinormal modes, the scattering and the production of waves in a process of gravitational collapse. Since long ago, the physical interpretation of the linear fluctuations in the metric of spherically symmetric black holes has been established. In a multipolar expansion, it is known that polar perturbations of a monopole type (l = 0) can only increase the black-hole mass, axial perturbations of a dipole type (l = 1) induce a slow rotation in the system, and perturbations with l ≥ 2 always lead to the production of gravitational waves. However, in relation to the planar Schwarzschild anti-de Sitter black holes (or black branes, for short), there is still no conclusive study on some aspects of the physical meaning of these perturbations. In particular, there is some controversy concerning the polar sector of fluctuations with zero wave numbers (k = 0). Some authors claim that this kind of perturbation causes only a small variation in the black-brane mass parameter, while others obtained also evidence for the existence of gravitational waves associated to such modes. The present study aims to contribute to the resolution of this controversy by revealing the physical meaning of the gravitational perturbations of anti-de Sitter black branes. In this work we use the Chandrasekhar's gauge formalism to evaluate the linear variations in the complex Weyl scalars in terms of the Regge-Wheeler-Zerilli gauge-invariant quantities. Then we use the Szekeres' proposal for the meaning of the Weyl scalars and the Pirani's criterion for the existence of gravitational radiation in order to give a physical interpretation of the black-brane perturbations with arbitrary wave number values.

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Separable wave equations for gravitoelectromagnetic perturbations of rotating charged black strings

Cited by 11 publications

References 97 publications

From quasinormal modes of rotating black strings to hydrodynamics of a moving CFT plasma

From quasinormal modes of rotating black strings to hydrodynamics of a moving CFT plasma

Third-order relativistic hydrodynamics: dispersion relations and transport coefficients of a dual plasma

New results on the physical interpretation of black-brane gravitational perturbations

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