26 research outputs found
Elliptic function solutions in Jackiw-Teitelboim dilaton gravity
We present a new family of solutions for the Jackiw-Teitelboim model of
two-dimensional gravity with a negative cosmological constant. Here, a metric
of constant Ricci scalar curvature is constructed, and explicit linearly
independent solutions of the corresponding dilaton field equations are
determined. The metric is transformed to a black hole metric, and the dilaton
solutions are expressed in terms of Jacobi elliptic functions. Using these
solutions we compute, for example, Killing vectors for the metric
Generalized EMP and nonlinear Schrodinger-type reformulations of some scalar field cosmological models
We show that Einstein's gravitational field equations for the
Friedmann-Robertson-Lema\^itre-Walker (FRLW) and for two conformal versions of
the Bianchi I and Bianchi V perfect fluid scalar field cosmological models, can
be equivalently reformulated in terms of a single equation of either
generalized Ermakov-Milne-Pinney (EMP) or (non)linear Schr\"odinger (NLS) type.
This work generalizes or presents an alternative to similar reformulations
published by the authors who inspired this thesis: R. Hawkins, J. Lidsey, T.
Christodoulakis, T. Grammenos, C. Helias, P. Kevrekidis, G. Papadopoulos and F.
Williams. In particular we cast much of these authors' works into a single
framework via straightforward derivations of the EMP and NLS equations from a
simple linear combination of the relevant Einstein equations. By rewriting the
resulting expression in terms of the volume expansion factor and performing a
change of variables, we obtain an uncoupled EMP or NLS equation that is
independent of the imposition of additional conservation equations. Since the
correspondences shown here present an alternative route for obtaining exact
solutions to Einstein's equations, we reconstruct many known exact solutions
via their EMP or NLS counterparts and show by numerical analysis the stability
properties of many solutions.Comment: author's PhD thesi