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When gauging a $(d-1)$-form symmetry in $d$ spacetime dimensions, one formally expects the gauged theory to carry a dual $-1$-form symmetry. This work focuses on the study of such symmetries, in particular via the spacetime-filling…
Black hole solutions in higher dimensional Einstein and Einstein-Maxwell gravity have been discussed by Tangherlini as well as Myers and Perry a long time ago. These solutions are the generalizations of the familiar Schwarzschild,…
We present a general solution-generating result within the bidifferential calculus approach to integrable partial differential and difference equations, based on a binary Darboux-type transformation. This is then applied to the…
We revisit the Ricci-flat metrics in four dimensions that are stationary and algebraically special, together with the locally asymptotically flat conditions in the generalized Bondi-Sachs framework. We show that the Einstein equation is…
Generalised Complex Geometry provides a natural interpretation of the $\mathcal{N}=1$ supersymmetry conditions for warped solutions of type II supergravity as differential equations on polyforms on the internal manifold. Written in this…
Extending recent work in 5 dimensions, we prove the existence and uniqueness of solutions to the reduced Einstein equations for vacuum black holes in $(n+3)$-dimensional spacetimes admitting the isometry group $\mathbb{R}\times U(1)^{n}$,…
We give the general Kerr-de Sitter metric in arbitrary spacetime dimension D\ge 4, with the maximal number [(D-1)/2] of independent rotation parameters. We obtain the metric in Kerr-Schild form, where it is written as the sum of a de Sitter…
We reformulate eleven-dimensional supergravity, including fermions, in terms of generalised geometry, for spacetimes that are warped products of Minkowski space with a $d$-dimensional manifold $M$ with $d\leq7$. The reformation has a…
It is formulated a new 'anholonomic frame' method of constructing exact solutions of Einstein equations with off--diagonal metrics in 4D and 5D gravity. The previous approaches and results are summarized and generalized as three theorems…
Contents: 1) Introduction and a few excursions [A word on the role of explicit solutions in other parts of physics and astrophysics. Einstein's field equations. "Just so" notes on the simplest solutions: The Minkowski, de Sitter and anti-de…
We present a new formulation of Einstein's equations for an axisymmetric spacetime with vanishing twist in vacuum. We propose a fully constrained scheme and use spherical polar coordinates. A general problem for this choice is the…
We investigate static axially symmetric black hole solutions in a four-dimensional Einstein-Yang-Mills-SU(2) theory with a negative cosmological constant $\Lambda$. These solutions approach asymptotically the anti-de Sitter spacetime and…
The development of hyperbolic formulations of Einstein's equations has revolutionized our ability to perform long-time, stable, accurate numerical simulations of strong field gravitational phenomena. However, hyperbolic methods have seen…
Static axisymmetric Einstein-Maxwell-Dilaton and stationary axisymmetric Einstein-Maxwell-Dilaton-Axion (EMDA) theories in four space-time dimensions are shown to be integrable by means of the inverse scattering transform method. The proof…
We consider Maxwell-f(R) gravity and obtain an exact charged black hole solution with dynamic curvature in D-dimensions. Considering a spherically symmetric metric ansatz and without specifying the form of f(R) we fnd a general black hole…
We show that a class of Einstein-Maxwell-Dilaton (EMD) theories are related to higher dimensional AdS-Maxwell gravity via a dimensional reduction over compact Einstein spaces combined with continuation in the dimension of the compact space…
A new model of gravastar is obtained in $D$-dimensional Einstein gravity. This class of solutions includes the gravastar as an alternative to D-dimensional versions of the Schwarzschild-Tangherlini black hole. The configuration of this new…
The Einstein-Maxwell equations in D-dimensions admitting (D-3) commuting Killing vector fields have been investigated. The existence of the electric, magnetic and twist potentials have been proved. The system is formulated as the harmonic…
Here we construct new solution for the Einstein equations -- some analog of the Schwarzschild metric in anti--de Sitter--Beltrami space in the $c\to \infty$ limit ($R$-space). In this case we derive an adiabatic invariant for finite…
We study the effects of Snyder-de Sitter commutation relations on relativistic bosons by solving analytically in the momentum space representation the Klein-Gordon oscillator in arbitrary dimensions. The exact bound states spectrum and the…