Related papers: Darboux Soft Hair in 3D Asymptotically Flat Spacet…
We study the Darboux equation, a fundamental PDE arising in the theory of isometric immersions of two-dimensional Riemannian manifolds into $\mathbb{R}^3$, in the low-regularity regime. We introduce a notion of weak solution for $u\in…
We study the problem of asymptotically flat bi-axially symmetric stationary solutions of the vacuum Einstein equations in $5$-dimensional spacetime. In this setting, the cross section of any connected component of the event horizon is a…
We present the complete family of higher dimensional spacetimes that admit a geodesic, shearfree, twistfree and expanding null congruence, thus extending the well-known D=4 class of Robinson-Trautman solutions. Einstein's equations are…
We consider 1 spacelike Killing vector field reductions of 4-d vacuum general relativity. We restrict attention to cases in which the manifold of orbits of the Killing field is $R^{3}$. The reduced Einstein equations are equivalent to those…
A finite action principle for Einstein-Gauss-Bonnet AdS gravity is presented. The boundary term, which is different for even and odd dimensions, is a functional of the boundary metric, intrinsic curvature and extrinsic curvature. For even…
We study the gravitational Dirichlet problem in AdS spacetimes with a view to understanding the boundary CFT interpretation. We define the problem as bulk Einstein's equations with Dirichlet boundary conditions on fixed timelike cut-off…
We construct solutions of higher-dimensional Einstein gravity coupled to nonlinear $\sigma$-model with cosmological constant. The $\sigma$-model can be perceived as exterior configuration of a spontaneously-broken $SO(D-1)$ global…
In this paper we present a new set of asymptotic boundary conditions for Einstein gravity in 2+1 dimensions with vanishing cosmological constant that are a generalization of the Barnich-Comp{\`e}re boundary conditions gr-qc/0610130. These…
We consider two BF formulations of the theory of gravity with a negative cosmological constant, of Plebanski and of MacDowell-Mansouri. Both give the standard Einstein equations in the bulk but differ in expressions of edge charges. We…
Four-dimensional spacetimes foliated by a two-parameter family of homologous two-surfaces are considered in Einstein's theory of gravity. By combining a 1+(1+2) decomposition, the canonical form of the spacetime metric and a suitable…
We present new second derivative, generally covariant theories of gravity for spherically symmetric spacetimes (general covariance is in the $t-r$ plane) belonging to the class where the spherically symmetric Einstein-Hilbert theory is…
In the context of Born-Infeld \emph{determinantal} gravity formulated in a n-dimensional spacetime with absolute parallelism, we found an exact 3-dimensional \emph{vacuum} circular symmetric solution without cosmological constant consisting…
Gowdy cosmologies are exact, spatially inhomogeneous solutions of the vacuum Einstein equations which describe nonlinear gravitational waves coalescing at the Big Bang singularity. With toroidal spatial sections they provenly have the…
We show that $3$-dimensional AdS spacetime can be semiclassically unstable due to strongly interacting quantum field effects. In our previous paper, we have pointed out the possibility of such an instability of AdS$_3$ by inspecting linear…
We show that the constructions of $C^{1,\alpha}$ asymptotically self-similar singularities for the 3D Euler equations by Elgindi, and for the 3D Euler equations with large swirl and 2D Boussinesq equations with boundary by Chen-Hou can be…
We study asymptotic symmetries and their associated charges for Maxwell theory on anti de Sitter (AdS) background in any dimension. This is obtained by constructing a conserved symplectic structure for the bulk and a theory on the boundary,…
In the realm of spacetimes governed by Einstein's general relativity and containing only Maxwell's electromagnetic field, stationary black holes are fully characterized by their mass, electric or magnetic charge, and angular momentum -- a…
Previous studies showed that, in the presence of a simple and well-motivated self-interaction scalar potential, asymptotically flat and spherical black holes can carry minimally coupled and charged scalar cloud/hair in Einstein-Maxwell…
This manuscript explores the Darboux transformation employed in the construction of exactly solvable models for pseudospin-one particles described by the Dirac-type equation. We focus on the settings where a flat band of zero energy is…
We present black hole solutions in $2+1-$dimensional Einstein's theory of gravity coupled with Born-Infeld nonlinear electrodynamic and a massless self-interacting scalar field. The model has five free parameters: mass $M$, cosmological…