46 research outputs found
Cosmologies with Two-Dimensional Inhomogeneity
We present a new generating algorithm to construct exact non static solutions
of the Einstein field equations with two-dimensional inhomogeneity. Infinite
dimensional families of inhomogeneous solutions with a self interacting
scalar field, or alternatively with perfect fluid, can be constructed using
this algorithm. Some families of solutions and the applications of the
algorithm are discussed.Comment: 9 pages, one postscript figur
On asymptotically flat solutions of Einstein's equations periodic in time II. Spacetimes with scalar-field sources
We extend the work in our earlier article [4] to show that time-periodic,
asymptotically-flat solutions of the Einstein equations analytic at scri, whose
source is one of a range of scalar-field models, are necessarily stationary. We
also show that, for some of these scalar-field sources, in stationary,
asymptotically-flat solutions analytic at scri, the scalar field necessarily
inherits the symmetry. To prove these results we investigate miscellaneous
properties of massless and conformal scalar fields coupled to gravity, in
particular Bondi mass and its loss.Comment: 29 pages, published in Class. Quant. Grav. Replaced. Typos corrected,
version which appeared in Class. Quant.Gra
Exact Einstein-scalar field solutions for formation of black holes in a cosmological setting
We consider self-interacting scalar fields coupled to gravity. Two classes of
exact solutions to Einstein's equations are obtained: the first class
corresponds to the minimal coupling, the second one to the conformal coupling.
One of the solutions is shown to describe a formation of a black hole in a
cosmological setting. Some properties of this solution are described. There are
two kinds of event horizons: a black hole horizon and cosmological horizons.
The cosmological horizons are not smooth. There is a mild curvature
singularity, which affects extended bodies but allows geodesics to be extended.
It is also shown that there is a critical value for a parameter on which the
solution depends. Above the critical point, the black hole singularity is
hidden within a global black hole event horizon. Below the critical point, the
singularity appears to be naked. The relevance to cosmic censorship is
discussed.Comment: 25 pages, 2 figure
A New Non-Perturbative Approach to Quantum Theory in Curved Spacetime Using the Wigner Function
A new non-perturbative approach to quantum theory in curved spacetime and to
quantum gravity, based on a generalisation of the Wigner equation, is proposed.
Our definition for a Wigner equation differs from what have otherwise been
proposed, and does not imply any approximations. It is a completely exact
equation, fully equivalent to the Heisenberg equations of motion. The approach
makes different approximation schemes possible, e.g. it is possible to perform
a systematic calculation of the quantum effects order by order. An iterative
scheme for this is also proposed. The method is illustrated with some simple
examples and applications. A calculation of the trace of the renormalised
energy-momentum tensor is done, and the conformal anomaly is thereby related to
non-conservation of a current in d=2 dimensions and a relationship between a
vector and an axial-vector current in d=4 dimensions.
The corresponding ``hydrodynamic equations'' governing the evolution of
macroscopic quantities are derived by taking appropriate moments. The emphasis
is put on the spin-1/2 case, but it is shown how to extend to arbitrary spins.
Gravity is treated first in the Palatini formalism, which is not very
tractable, and then more successfully in the Ashtekar formalism, where the
constraints lead to infinite order differential equations for the Wigner
functions.Comment: LaTeX2e (uses amssymb), 36 page
Cosmology with exponential potentials
We examine in the context of general relativity the dynamics of a spatially
flat Robertson-Walker universe filled with a classical minimally coupled scalar
field \phi of exponential potential ~ e^{-\mu\phi} plus pressureless baryonic
matter. This system is reduced to a first-order ordinary differential equation,
providing direct evidence on the acceleration/deceleration properties of the
system. As a consequence, for positive potentials, passage into acceleration
not at late times is generically a feature of the system, even when the
late-times attractors are decelerating. Furthermore, the structure formation
bound, together with the constraints on the present values of \Omega_{m},
w_{\phi} provide, independently of initial conditions and other parameters,
necessary conditions on \mu. Special solutions are found to possess intervals
of acceleration. For the almost cosmological constant case w_{\phi} ~ -1, as
well as, for the generic late-times evolution, the general relation
\Omega_{\phi}(w_{\phi}) is obtained.Comment: RevTex4, 9 pages, 2 figures, References adde