119 research outputs found
Magnetic Fields in an Expanding Universe
We find a solution to Einstein-Maxwell theory coupled to a massless
dilaton field describing a Melvin magnetic field in an expanding universe with
'stiff matter' equation of state parameter . As the universe expands,
magnetic flux becomes more concentrated around the symmetry axis for dilaton
coupling . An electric
field circulates around the symmetry axis in the direction determined by Lenz's
law. For the magnetic flux through a disk of fixed comoving radius is
proportional to the proper area of the disk. This result disagrees with the
usual expectation based on a test magnetic field that this flux should be
constant, and we show why this difference arises. We also find a Melvin
solution in an accelerating universe with for a dilaton field with a
certain exponential potential. Our main tools are simple manipulations in
Kaluza-Klein theory and related solution generating techniques. We also discuss
a number of directions for possible extensions of this work.Comment: 17 pages, 2 figures; v2 - references adde
The Dynamics of Collapsing Monopoles and Regular Black Holes
We study the formation and stability of regular black holes by employing a
thin shell approximation to the dynamics of collapsing magnetic monopoles. The
core deSitter region of the monopole is matched across the shell to a
Reissner-Nordstrom exterior. We find static configurations which are
nonsingular black holes and also oscillatory trajectories about these static
points that share the same causal structure. In these spacetimes the shell is
always hidden behind the black hole horizon. We also find shell trajectories
that pass through the asymptotically flat region and model collapse of a
monopole to form a regular black hole. In addition there are trajectories in
which the deSitter core encompasses a deSitter horizon and hence undergoes
topological inflation. However, these always yield singular black holes and
never have the shell passing through the aymptotically flat region. Although
the regular black hole spacetimes satisfy the strong energy condition, they
avoid the singularity theorems by failing to satisfy the genericity condition
on the Riemann tensor. The regular black holes undergo a change in spatial
topology in accordance with a theorem of Borde's.Comment: 22 pages, 19 figures, harvmac (b), references change
Dynamics of localized Kaluza-Klein black holes in a collapsing universe
The Clayton Antitrust Act of 1914 prohibits corporate mergers that would
result in certain highly undesired end states. We study an exact solution of
the Einstein equations describing localized, charged Kaluza-Klein black holes
in a collapsing deSitter universe and seek to demonstrate that a similar effect
holds, preventing a potentially catastrophic black hole merger. As the collapse
proceeds, it is natural to expect that the black hole undergoes a topological
transition, wrapping around the shrinking compact dimension to merge with
itself and form a black string. However, the putative uniform charged black
string end state is singular and such a transition would violate (a reasonable
notion of) cosmic censorship. We present analytic and numerical evidence that
strongly suggests the absence of such a transition. Based on this evidence, we
expect that the Kaluza-Klein black hole horizon stays localized, despite the
increasingly constraining size of the compact dimension. On the other hand, the
deSitter horizon does change between spherical and cylindrical topologies in a
simple way.Comment: 25 pages, 6 figure
Smarr Formula and an Extended First Law for Lovelock Gravity
We study properties of static, asymptotically AdS black holes in Lovelock
gravity. Our main result is a Smarr formula that gives the mass in terms of
geometrical quantities together with the parameters of the Lovelock theory. As
in Einstein gravity, the Smarr formula follows from applying the first law to
an infinitesimal change in the overall length scale. However, because the
Lovelock couplings are dimensionful, we must first prove an extension of the
first law that includes their variations. Key ingredients in this construction
are the Killing-Lovelock potentials associated with each of the the higher
curvature Lovelock interactions. Geometric expressions are obtained for the new
thermodynamic potentials conjugate to variation of the Lovelock couplings.Comment: 20 pages; v2 - references added; v3 - includes important corrections
to result
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