Modos quase-normais e a correspondência AdS/CFT

Abstract

The electromagnetic and gravitational quasinormal mode spectra of plane-symmetric anti-de Sitter black holes are investigated in the present work. According to the AdS/CFT correspondence, the black hole quasinormal frequencies correspond to the poles of R-current and stress-energy tensor correlation functions in the holographically dual field theory: the N = 8 super-Yang-Mills in 2 + 1 dimensions. In the present study, this duality is explored in order to choose the quasinormal mode boundary conditions and the gauge invariant variables governing the black hole perturbations. Among the main results, it is shown that zero wavenumber axial perturbations yield only small rotations on the system, while the polar perturbations lead to a change in the mass of the black hole and may also produce cylindrical gravitational waves. In relation to the quasinormal spectra, the long-distance and low-frequency limit of the dispersion relations present the hydrodynamical behavior that is characteristic of a conformally invariant theory, with diffusion, shear and sound-wave modes. In the electromagnetic perturbation sector, it also appears purely damped modes that tend to the bosonic Matsubara frequencies in the long-wavelength regime.