Circularly symmetric solutions of Minimal Massive Gravity at its merger point

I find all the static circularly symmetric solutions of Minimal Massive 3D Gravity at its merger point, construct stationary versions of these and discuss some of their geometric and physical properties. It turns out that apart from a static hairy black hole, there is also a static gravitational soliton, that has been overlooked in the literature.Comment: latex, 23 pages, 1 table, no figures; ver 2: corrected a marginal mistake that does not affect the main result

A note on cosmological Levi-Civita spacetimes in higher dimensions

We find a class of solutions to cosmological Einstein equations that generalizes the four dimensional cylindrically symmetric spacetimes to higher dimensions. The AdS soliton is a special member of this class with a unique singularity structure.Comment: 3 pages; version to appear in Phys. Rev.

Stationary Lifshitz black holes ofR2-corrected gravity theory

In this short note, I present a generalization of a set of static D-dimensional (D >= 3) Lifshitz black holes, which are solutions of the gravitational model obtained by amending the cosmological Einstein theory with the addition of only the curvature-scalar-squared term and that are described by two parameters, to a more general class of exact, analytic solutions that involves an additional parameter which now renders them stationary. In the special D = 3 and the dynamical exponent z = 1 cases, the parameters can be adjusted so that the solution becomes identical to the celebrated BTZ black hole metric

New currents with Killing-Yano tensors

New relations involving the Riemann, Ricci and Einstein tensors that have to hold for a given geometry to admit Killing-Yano tensors are described. These relations are then used to introduce novel conserved "currents" involving such Killing-Yano tensors. For a particular current based on the Einstein tensor, we discuss the issue of conserved charges and consider implications for matter coupled to gravity. The condition on the background geometry to allow asymptotic conserved charges for a current introduced by Kastor and Traschen is found and a number of other new aspects of this current are commented on. In particular we show that it vanishes for rank $(D-1)$ Killing-Yano tensors in $D$ dimensions.Comment: 1+21 pages, 1 table, no figures; version 2: clarifications added version 3: The d index raised in the middle formulae in (6.2) and (6.10). Makes the comments on (6.10) correc

Geometry, conformal Killing-Yano tensors and conserved "currents"

In this paper we discuss the construction of conserved tensors (currents) involving conformal Killing-Yano tensors (CKYTs), generalising the corresponding constructions for Killing-Yano tensors (KYTs). As a useful preparation for this, but also of intrinsic interest, we derive identities relating CKYTs and geometric quantities. The behaviour of CKYTs under conformal transformations is also given, correcting formulae in the literature. We then use the identities derived to construct covariantly conserved ``currents''. We find several new CKYT currents and also include a known one by Penrose which shows that ``trivial'' currents are also useful. We further find that rank-$n$ currents based on rank-$n$ CKYTs $k$ must have a simple form in terms of $dk$. By construction, these currents are covariant under a general conformal rescaling of the metric. How currents lead to conserved charges is then illustrated using the Kerr-Newman and the C-metric in four dimensions. Separately, we study a rank-1 current, construct its charge and discuss its relation to the recently constructed Cotton current for the Kerr-Newman black hole.Comment: 15 pages; This version considerably reworked relative to previous ones, prompted by a number of comments from various researcher

Comment on the new AdS universe

We show that Bonnor's new Anti-de Sitter (AdS) universe and its D-dimensional generalization is the previously studied AdS soliton.Comment: 2 pages; version 2: major changes including the titl

AN INTEGRABLE FAMILY OF MONGE-AMPERE EQUATIONS AND THEIR MULTI-HAMILTONIAN STRUCTURE

We have identified a completely integrable family of Monge-Ampère equations through an examination of their Hamiltonian structure. Starting with a variational formulation of the Monge-Ampère equations we have constructed the first Hamiltonian operator through an application of Dirac's theory of constraints. The completely integrable class of Monge-Ampère equations are then obtained by solving the Jacobi identities for a sufficiently general form of the second Hamiltonian operator that is compatible with the first

Shock-free wave propagation in gauge theories

We present the shock-free wave propagation requirements for massless fields. First, we briefly argue how the "completely exceptional" approach, originally developed to study the characteristics of hyperbolic systems in 1 + 1 dimensions, can be generalized to higher dimensions and used to describe propagation without emerging shocks, with characteristic flow remaining parallel along the waves. We then study the resulting requirements for scalar, vector, vector-scalar, and gravity models and characterize physically acceptable actions in each case