info:eu-repo/semantics/doctoralThesis
Dynamic gravitational solutions with matter fields
Soluciones gravitacionales dinámicas con campos de materia
Autor
Avilés-Godoy, Luis Alberto Antonio
Institución
Resumen
In this thesis two related topics are studied. First, we analyze junction conditions at a null or non-null hypersurface Σ in a large class of scalar-tensor theories in arbitrary n(≥ 3) dimensions. After showing that the metric and a scalar field must be continuous at Σ as the first junction conditions, we derive the second junctions conditions from the Einstein equations and the equation of motion for the scalar field. Subsequently, we study C1 regular matching conditions as well as vacuum conditions at Σ both in the Jordan and Einstein frames. Our result suggests that the following configurations may be possible; (i) a vacuum thin-shell at null Σ in the Einstein frame, (ii) a vacuum thin-shell at null and non-null Σ in the Jordan frame, and (iii) a non-vacuum C1 regular matching at null Σ in the Jordan frame. Moreover, we clarify the relations between the conditions for C1 regularity and also
for vacuum Σ in the Jordan and Einstein frames.
As a second part of the thesis, we present exact dynamical and inhomogeneous solutions in three-dimensional AdS gravity with a conformally coupled scalar field. They contain stealth con gurations of the scalar field overflying the BTZ spacetime and also solutions with a non-vanishing energy momentum tensor. The latter non-stealth class consists of the solution obtained by Xu and its analytic extension. It is shown that this proper extension represents: (i) an eternally shrinking dynamical black hole, (ii) a curious spacetime which admits an event horizon without any trapped surface, or (iii) gravitational collapse of a scalar field in an asymptotically AdS spacetime. In the last case, by attaching the solution regularly to the past massless BTZ spacetime with a vanishing scalar field, the whole spacetime represents the black-hole formation from regular initial data in an asymptotically AdS spacetime. Depending on the parameters, the formed black hole can be asymptotically static in far future.