Showing papers by "José Natário published in 2009"
TL;DR: In this article, a coordinate system for the Kerr solution was proposed based on the zero angular momentum observers dropped from infinity, which generalizes the Painleve-Gullstrand coordinate systems for the Schwarzschild solution.
Abstract: We construct a coordinate system for the Kerr solution, based on the zero angular momentum observers dropped from infinity, which generalizes the Painleve–Gullstrand coordinate system for the Schwarzschild solution. The Kerr metric can then be interpreted as describing space flowing on a (curved) Riemannian 3-manifold. The stationary limit arises as the set of points on this manifold where the speed of the flow equals the speed of light, and the horizons as the set of points where the radial speed equals the speed of light. A deeper analysis of what is meant by the flow of space reveals that the acceleration of free-falling objects is generally not in the direction of this flow. Finally, we compare the new coordinate system with the closely related Doran coordinate system.
35 citations
TL;DR: In this paper, the necessary and sufficient conditions for the matching of two stationary spacetimes along a stationary time-like hypersurface, expressed in terms of the gravitational and gravitomagnetic fields and the 2-dimensional matching surface on the space manifold, were derived.
6 citations
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TL;DR: In this article, an elementary derivation of the Montgomery phase formula for the motion of an Euler top was given, using only basic facts about the Euler equation and parallel transport on the 2-sphere.
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.
2 citations
TL;DR: In this paper, the authors study higher dimensional gravitational collapse to topological black holes in two steps, and investigate the global properties of the matched solutions which, besides black holes, may include the existence of naked singularities and wormholes.
Abstract: We study higher dimensional gravitational collapse to topological black holes in two steps. Firstly, 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 $\Lambda$-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. Secondly, 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.
05 May 2009
TL;DR: In this paper, an idealised model of gravitational collapse is presented, describing a collapsing rotating cylindrical shell of null dust in flat space, with the metric of a spinning cosmic string as the exterior.
Abstract: We present an idealised model of gravitational collapse, describing a collapsing rotating cylindrical shell of null dust in flat space, with the metric of a spinning cosmic string as the exterior. We find that the shell bounces before closed timelike curves can be formed. Our results also suggest slightly different definitions for the mass and angular momentum of the string.
05 May 2009
TL;DR: In this article, the necessary and sufficient conditions for the matching of two stationary spacetimes along a stationary timelike hypersurface, using a 2+1 splitting of the matching conditions in terms of the gravitational and gravitomagnetic fields, were derived.
Abstract: We derive the necessary and sufficient conditions for the matching of two stationary spacetimes along a stationary timelike hypersurface, using a 2+1 splitting of the matching conditions in terms of the gravitational and gravitomagnetic fields. We prove existence and uniqueness results to the matching problem for stationary perfect fluid spacetimes with cylindrical symmetry.