29 research outputs found
Backreaction for Einstein-Rosen waves coupled to a massless scalar field
We present a one-parameter family of exact solutions to Einstein equations
that may be used to study the nature of the Green-Wald backreaction framework.
Our explicit example is a family of Einstein-Rosen waves coupled to a massless
scalar field. This solution may be reinterpreted as a generalized three-torus
polarized Gowdy cosmology with scalar and gravitational waves. We use it to
illustrate essential properties of the Green-Wald approach. Among other things
we show that within our model the Green-Wald framework uniquely determines
backreaction for finite size inhomogeneities on a predefined background. The
results agree with those calculated in the Charach-Malin approach. In the
vacuum limit, the Green-Wald, the Charach-Malin and the Isaacson method imply
identical backreaction as expected.Comment: 26 pages; minor changes to match published versio
Einstein clusters as models of inhomogeneous spacetimes
We study the effect of small-scale inhomogeneities for Einstein clusters. We
construct a spherically symmetric stationary spacetime with small-scale radial
inhomogeneities and propose the Gedankenexperiment. An hypothetical observer at
the center constructs, using limited observational knowledge, a simplified
homogeneous model of the configuration. An idealization introduces side
effects. The inhomogeneous spacetime and the effective homogeneous spacetime
are given by simple solutions to Einstein equations. They provide a basic
toy-model for studies of the effect of small-scale inhomogeneities in general
relativity. We show that within our highly inhomogeneous model the effect of
small-scale inhomogeneities remains small for a central observer. The
homogeneous model fits very well to all hypothetical observations as long as
their precision is not high enough to reveal a tension.Comment: 23 pages; minor changes to match published versio
On the Ernst electro-vacuum equations and ergosurfaces
The question of smoothness at the ergosurface of the space-time metric
constructed out of solutions (E,phi) of the Ernst electro-vacuum equations is
considered. We prove smoothness of those ergosurfaces at which Re(E) provides
the dominant contribution to f=-(Re(E)+|phi|^2) at the zero-level-set of f.
Some partial results are obtained in the remaining cases: in particular we give
examples of leading-order solutions with singular isolated "ergocircles".Comment: 15 pages, no figures, minor change
Black Hole Flyby
We calculate the minimum distance at which one may approach a black hole in a
free flyby. It corresponds to r=4m for the Schwarzschild black hole and a probe
which was non-relativistic at infinity. The problem is formulated in a way that
is useful for teaching introductory general relativity.Comment: 7 pages, 3 figures; changes to match published versio
Fractal Threshold Behavior in Vacuum Gravitational Collapse
We present the numerical evidence for fractal threshold behavior in the five
dimensional vacuum Einstein equations satisfying the cohomogeneity-two triaxial
Bianchi type-IX ansatz. In other words, we show that a flip of the wings of a
butterfly may influence the process of the black hole formation.Comment: 4 pages, 6 figures, minor change
Towards a classification of vacuum near-horizons geometries
We prove uniqueness of the near-horizon geometries arising from degenerate
Kerr black holes within the collection of nearby vacuum near-horizon
geometries.Comment: 16 pages, 3 figures; minor changes to match published versio
Standing waves in general relativity
We propose a covariant definition of standing gravitational waves in general
relativity.Comment: 9 page