Showing papers by "José Natário published in 2010"

Greybody Factors for d-Dimensional Black Holes

Abstract: Gravitational greybody factors are analytically computed for static, spherically symmetric black holes in d-dimensions, including black holes with charge and in the presence of a cosmological constant (where a proper definition of greybody factors for both asymptotically de Sitter and Anti-de Sitter spacetimes is provided). This calculation includes both the low-energy case—where the frequency of the scattered wave is small and real—and the asymptotic case—where the frequency of the scattered wave is very large along the imaginary axis—addressing gravitational perturbations as described by the Ishibashi-Kodama master equations, and yielding full transmission and reflection scattering coefficients for all considered spacetime geometries. At low frequencies a general method is developed, which can be employed for all three types of spacetime asymptotics, and which is independent of the details of the black hole. For asymptotically de Sitter black holes the greybody factor is different for even or odd spacetime dimension, and proportional to the ratio of the areas of the event and cosmological horizons. For asymptotically Anti-de Sitter black holes the greybody factor has a rich structure in which there are several critical frequencies where it equals either one (pure transmission) or zero (pure reflection, with these frequencies corresponding to the normal modes of pure Anti-de Sitter spacetime). At asymptotic frequencies the computation of the greybody factor uses a technique inspired by monodromy matching, and some universality is hidden in the transmission and reflection coefficients. For either charged or asymptotically de Sitter black holes the greybody factors are given by non-trivial functions, while for asymptotically Anti-de Sitter black holes the greybody factor precisely equals one (corresponding to pure blackbody emission).

An elementary derivation of the Montgomery phase formula for the Euler top

Abstract: We give an elementary derivation of the Montgomery phase formula for the motion of an Euler top, using only basic facts about the Euler equation and parallel transport on the $2$-sphere (whose holonomy is seen to be responsible for the geometric phase). We also give an approximate geometric interpretation of the geometric phase for motions starting close to an unstable equilibrium point.

Formation of Higher-dimensional Topological Black Holes

Abstract: We study higher-dimensional gravitational collapse to topological black holes in two steps. First, we construct some (n + 2)-dimensional collapsing space–times, which include generalised Lemaitre–Tolman–Bondi-like solutions, and we prove that these can be matched to static Λ-vacuum exterior space–times. We then investigate the global properties of the matched solutions which, besides black holes, may include the existence of naked singularities and wormholes. Second, we consider as interiors classes of 5-dimensional collapsing solutions built on Riemannian Bianchi IX spatial metrics matched to radiating exteriors given by the Bizon–Chmaj–Schmidt metric. In some cases, the data at the boundary for the exterior can be chosen to be close to the data for the Schwarzschild solution.