53 research outputs found
Cosmological Solutions in Multiscalar Field Theory
We consider a cosmological model with two scalar fields minimally coupled to
gravity which have a mixed kinetic term. Hence, Chiral cosmology is included in
our analysis. The coupling function and the potential function, which depend on
one of the fields, characterize the model we study. We prove the existence of
exact solutions that are of special interest for the cosmological evolution.
Furthermore, we provide with a methodology that relates the scale factor
behaviour to the free functions characterizing the scalar field kinetic term
coupling and potential. We derive the necessary conditions that connect these
two functions so that the relative cosmological solutions can be admitted. We
find that unified dark matter and dark energy solutions are allowed by the
theory in various scenarios involving the aforementioned functions.Comment: 15 pages, 3 figures, Latex2e source file, revised to agree with the
accepted EPJC versio
Canonical Quantization of the BTZ Black Hole using Noether Symmetries
The well-known BTZ black hole solution of (2+1) Einstein's gravity, in the
presence of a cosmological constant, is treated both at the classical and
quantum level. Classically, the imposition of the two manifest local Killing
fields of the BTZ geometry at the level of the full action results in a
mini-superspace constraint action with the radial coordinate playing the role
of the independent dynamical variable. The Noether symmetries of this reduced
action are then shown to completely determine the classical solution space,
without any further need to solve the dynamical equations of motion. At a
quantum mechanical level, all the admissible sets of the quantum counterparts
of the generators of the above mentioned symmetries are utilized as
supplementary conditions acting on the wave-function. These additional
restrictions, in conjunction with the Wheeler-DeWitt equation, help to
determine (up to constants) the wave-function which is then treated
semiclassically, in the sense of Bohm. The ensuing space-times are, either
identical to the classical geometry, thus exhibiting a good correlation of the
corresponding quantization to the classical theory, or are less symmetric but
exhibit no Killing or event horizon and no curvature singularity, thus
indicating a softening of the classical conical singularity of the BTZ
geometry.Comment: 24 pages, no figures, LaTeX 2e source fil
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