Vilson T. Zanchin

Geodesic stability, Lyapunov exponents, and quasinormal modes

Geodesic motion determines important features of spacetimes. Null unstable geodesics are closely related to the appearance of compact objects to external observers and have been associated with the characteristic modes of black holes. By computing the Lyapunov exponent, which is the inverse of the instability time scale associated with this geodesic motion, we show that, in the eikonal limit, quasinormal modes of black holes in any dimensions are determined by the parameters of the circular null geodesics. This result is independent of the field equations and only assumes a stationary, spherically symmetric and asymptotically flat line element, but it does not seem to be easily extendable to anti-de Sitter spacetimes. We further show that (i) in spacetime dimensions greater than four, equatorial circular timelike geodesics in a Myers-Perry black-hole background are unstable, and (ii) the instability time scale of equatorial null geodesics in Myers-Perry spacetimes has a local minimum for spacetimes of dimension d ≥ 6.

Quasinormal modes of plane-symmetric black holes according to the AdS/CFT correspondence

The electromagnetic and gravitational quasinormal spectra of (3+1)-dimensional plane-symmetric anti-de Sitter black holes are analyzed in the context of the AdS/CFT correspondence. According to such a correspondence, the electromagnetic and gravitational quasinormal frequencies of these black holes are associated respectively to the poles of retarded correlation functions of R-symmetry currents and stress-energy tensor in the holographically dual conformal field theory: the (2+1)-dimensional = 8 super-Yang-Mills theory. The connection between AdS black holes and the corresponding field theory is used to unambiguously fix the boundary conditions that enter the proper definition of quasinormal modes. Such a procedure also helps one to decide, among the various different possibilities, what are the appropriate gauge-invariant quantities one should use in order to correctly describe the electromagnetic and gravitational blackhole perturbations. These choices imply in different dispersion relations for the quasinormal modes when compared to some of the results in the literature. In particular, the long-distance, low-frequency limit of dispersion relations presents the characteristic hydrodynamic behavior of a conformal field theory with the presence of diffusion, shear, and sound wave modes. There is also a family of purely damped electromagnetic modes which tend to the bosonic Matsubara frequencies in the long-wavelength regime.

Quasinormal modes of black holes in anti-de Sitter space: A numerical study of the eikonal limit

Using series solutions and time-domain evolutions, we probe the eikonal limit of the gravitational and scalar-field quasinormal modes of large black holes and black branes in anti-de Sitter backgrounds. These results are particularly relevant for the AdS/CFT correspondence, since the eikonal regime is characterized by the existence of long-lived modes which (presumably) dominate the decay time scale of the perturbations. We confirm all the main qualitative features of these slowly damped modes as predicted by Festuccia and Liu [G. Festuccia and H. Liu, arXiv:0811.1033.] for the scalar-field (tensor-type gravitational) fluctuations. However, quantitatively we find dimensional-dependent correction factors. We also investigate the dependence of the quasinormal mode frequencies on the horizon radius of the black hole (brane) and the angular momentum (wave number) of vector- and scalar-type gravitational perturbations.

Gravitational quasinormal modes of AdS black branes in d spacetime dimensions

The AdS/CFT duality has established a mapping between quantities in the bulk AdS black-hole physics and observables in a boundary finite-temperature field theory. Such a relationship appears to be valid for an arbitrary number of spacetime dimensions, extrapolating the original formulations of Maldacenas correspondence. In the same sense properties like the hydrodynamic behavior of AdS black-hole fluctuations have been proved to be universal. We investigate in this work the complete quasinormal spectra of gravitational perturbations of d-dimensional plane-symmetric AdS black holes (black branes). Holographically the frequencies of the quasinormal modes correspond to the poles of two-point correlation functions of the field-theory stress-energy tensor. The important issue of the correct boundary condition to be imposed on the gauge-invariant perturbation fields at the AdS boundary is studied and elucidated in a fully d-dimensional context. We obtain the dispersion relations of the first few modes in the low-, intermediate- and high-wavenumber regimes. The sound-wave (shear-mode) behavior of scalar (vector)-type low-frequency quasinormal mode is analytically and numerically confirmed. These results are found employing both a power series method and a direct numerical integration scheme.

Regular black holes in f (R) gravity coupled to nonlinear electrodynamics

We obtain a class of regular black hole solutions in four-dimensional

Compact stars with a small electric charge: the limiting radius to mass relation and the maximum mass for incompressible matter

f(R)

Electromagnetic quasinormal modes of rotating black strings and the AdS/CFT correspondence

gravity,

Separable wave equations for gravitoelectromagnetic perturbations of rotating charged black strings

R

New regular black hole solutions

being the curvature scalar, coupled to a nonlinear electromagnetic source. The metric formalism is used and static spherically symmetric spacetimes are assumed. The resulting

New Regular Black Hole Solutions and Other Electrically Charged Compact Objects with A De Sitter Core and A Matter Layer

f(R)