382 research outputs found
Stresses and Strains in the First Law for Kaluza-Klein Black Holes
We consider how variations in the moduli of the compactification manifold
contribute pdV type work terms to the first law for Kaluza-Klein black holes.
We give a new proof for the circle case, based on Hamiltonian methods, which
demonstrates that the result holds for arbitrary perturbations around a static
black hole background. We further apply these methods to derive the first law
for black holes in 2-torus compactifications, where there are three real
moduli. We find that the result can be simply stated in terms of constructs
familiar from the physics of elastic materials, the stress and strain tensors.
The strain tensor encodes the change in size and shape of the 2-torus as the
moduli are varied. The role of the stress tensor is played by a tension tensor,
which generalizes the spacetime tension that enters the first law in the circle
case.Comment: 18 pages, 1 figure, Dedicated to Rafael Sorkin in honor of his 60th
Birthda
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
Boost Mass and the Mechanics of Accelerated Black Holes
In this paper we study the concept of the boost mass of a spacetime and
investigate how variations in the boost mass enter into the laws of black hole
mechanics. We define the boost mass as the gravitational charge associated with
an asymptotic boost symmetry, similiar to how the ADM mass is associated with
an asymptotic time translation symmetry. In distinction to the ADM mass, the
boost mass is a relevant concept when the spacetime has stress energy at
infinity, and so the spacetime is not asymptotically flat. We prove a version
of the first law which relates the variation in the boost mass to the change in
the area of the black hole horizon, plus the change in the area of an
acceleration horizon, which is necessarily present with the boost Killing
field, as we discuss. The C-metric and Ernst metric are two known analytical
solutions to Einstein-Maxwell theory describing accelerating black holes which
illustrate these concepts.Comment: 23 pages, A few modifications and clarifications at the referee's
suggestions; References added and correcte
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
- âŠ