Conformal Tensors via Lovelock Gravity

Constructs from conformal geometry are important in low dimensional gravity models, while in higher dimensions the higher curvature interactions of Lovelock gravity are similarly prominent. Considering conformal invariance in the context of Lovelock gravity leads to natural, higher-curvature generalizations of the Weyl, Schouten, Cotton and Bach tensors, with properties that straightforwardly extend those of their familiar counterparts. As a first application, we introduce a new set of conformally invariant gravity theories in D=4k dimensions, based on the squares of the higher curvature Weyl tensors.Comment: 16 pages; v2 - references adde

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

On black strings & branes in Lovelock gravity

It is well known that black strings and branes may be constructed in pure Einstein gravity simply by adding flat directions to a vacuum black hole solution. A similar construction holds in the presence of a cosmological constant. While these constructions fail in general Lovelock theories, we show that they carry over straightforwardly within a class of Lovelock gravity theories that have (locally) unique constant curvature vacua.Comment: 12 pages, Latex, references addde

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

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