6 research outputs found
Wigner function and quantum kinetic theory in curved space-time and external fields
A new definition of the Wigner function for quantum fields coupled to curved
space--time and an external Yang--Mills field is studied on the example of a
scalar and a Dirac fields. The definition uses the formalism of the tangent
bundles and is explicitly covariant and gauge invariant. Derivation of
collisionless quantum kinetic equations is carried out for both quantum fields
by using the first order formalism of Duffin and Kemmer. The evolution of the
Wigner function is governed by the quantum corrected Liouville--Vlasov equation
supplemented by the generalized mass--shell constraint. The structure of the
quantum corrections is perturbatively found in all adiabatic orders. The lowest
order quantum--curvature corrections coincide with the ones found by Winter.Comment: 41 page
Quantum Kinetic Equations and Cosmology
We analyse quantum--kinetic effects in the early Universe. We show that
quantum corrections to the Vlasov equation give rise to a dynamical variation
of the gravitational constant. The value of the gravitational constant at the
Grand Unification epoch is shown to differ from its present value to about
.Comment: 10 page
Conformal Transformations of the Wigner Function and Solutions of the Quantum Corrected Vlasov Equation
We study conformal properties of the quantum kinetic equations in curved
spacetime. A transformation law for the covariant Wigner function under
conformal transformations of a spacetime is derived by using the formalism of
tangent bundles. The conformal invariance of the quantum corrected Vlasov
equation is proven. This provides a basis for generating new solutions of the
quantum kinetic equations in the presence of gravitational and other external
fields. We use our method to find explicit quantum corrections to the class of
locally isotropic distributions, to which equilibrium distributions belong. We
show that the quantum corrected stress--energy tensor for such distributions
has, in general, a non--equilibrium structure. Local thermal equilibrium is
possible in quantum systems only if an underlying spacetime is conformally
static (not stationary). Possible applications of our results are discussed.Comment: 30 page
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