4 research outputs found
Intercommutation of Semilocal Strings and Skyrmions
We study the intercommuting of semilocal strings and Skyrmions, for a wide
range of internal parameters, velocities and intersection angles by numerically
evolving the equations of motion. We find that the collisions of strings and
strings, strings and Skyrmions, and Skyrmions and Skyrmions, all lead to
intercommuting for a wide range of parameters. Even the collisions of unstable
Skyrmions and strings leads to intercommuting, demonstrating that the
phenomenon of intercommuting is very robust, extending to dissimilar field
configurations that are not stationary solutions. Even more remarkably, at
least for the semilocal U(2) formulation considered here, all intercommutations
trigger a reversion to U(1) Nielsen-Olesen strings.Comment: 4 pages, 4 figures. Fixed typos, added reference
Area Invariance of Apparent Horizons under Arbitrary Boosts
It is a well known analytic result in general relativity that the
2-dimensional area of the apparent horizon of a black hole remains invariant
regardless of the motion of the observer, and in fact is independent of the slice, which can be quite arbitrary in general relativity.
Nonetheless the explicit computation of horizon area is often substantially
more difficult in some frames (complicated by the coordinate form of the
metric), than in other frames. Here we give an explicit demonstration for very
restricted metric forms of (Schwarzschild and Kerr) vacuum black holes. In the
Kerr-Schild coordinate expression for these spacetimes they have an explicit
Lorentz-invariant form. We consider {\it boosted} versions with the black hole
moving through the coordinate system. Since these are stationary black hole
spacetimes, the apparent horizons are two dimensional cross sections of their
event horizons, so we compute the areas of apparent horizons in the boosted
space with (boosted) , and obtain the same result as in the
unboosted case. Note that while the invariance of area is generic, we deal only
with black holes in the Kerr-Schild form, and consider only one particularly
simple change of slicing which amounts to a boost. Even with these restrictions
we find that the results illuminate the physics of the horizon as a null
surface and provide a useful pedagogical tool. As far as we can determine, this
is the first explicit calculation of this type demonstrating the area
invariance of horizons. Further, these calculations are directly relevant to
transformations that arise in computational representation of moving black
holes. We present an application of this result to initial data for boosted
black holes.Comment: 19 pages, 3 figures. Added a new section and 2 plots along with a
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