Magnetic Fields in an Expanding Universe

We find a solution to $4D$ 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 $w=+1$. As the universe expands, magnetic flux becomes more concentrated around the symmetry axis for dilaton coupling $a1/\sqrt{3}$. An electric field circulates around the symmetry axis in the direction determined by Lenz's law. For $a=0$ 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 $w=-7/9$ for a dilaton field with a certain exponential potential. Our main tools are simple manipulations in $5D$ 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

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

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