Related papers: Null hypersurface data and ambient vector fields: …
We present a general formalism for describing singular hypersurfaces in the Einstein theory of gravitation with a Gauss--Bonnet term. The junction conditions are given in a form which is valid for the most general embedding and matter…
We establish a uniform estimate for the injectivity radius of the past null cone of a point in a general Lorentzian manifold foliated by spacelike hypersurfaces and satisfying an upper curvature bound. Precisely, our main assumptions are,…
We introduce a new elliptic operator on null hypersurfaces of four-dimensional Lorentzian manifolds. This operator depends on the first and second fundamental forms of the sections of a foliation of the null hypersurface and its novelty…
We present a ten-dimensional theory, named \beta-supergravity, that contains non-geometric fluxes and could uplift some four-dimensional gauged supergravities. Building on earlier work, we study here its NSNS sector, where Q- and R-fluxes…
The stress-energy tensor of a matter shell whose history coincides with a null hypersurface in the Einstein-Cartan gravity is revisited. It is demonstrated that with a proper choice for the torsion discontinuity taken to be orthogonal to…
We give a spinorial characterization of isometrically immersed hypersurfaces into 4-dimensional space forms and product spaces $\M^3(\kappa)\times\R$, in terms of the existence of particular spinor fields, called generalized Killing spinors…
We discuss various properties of rotating Killing horizons in generic $F(R)$ theories of gravity in dimension four for spacetimes endowed with two commuting Killing vector fields. Assuming there is no curvature singularity anywhere on or…
It is well-known that unlike space-like and time-like hypersurfaces, null hypersurfaces in Lorentzian manifolds do not naturally inherit an affine connection from the spacetime in which they are embedded. On the other hand, recent…
I present a model of discrete gravity, which is formulated in terms of a topological gauge theory with defects. The theory has no local degrees of freedom and the gravitational field is trivial everywhere except at a number of colliding…
In this paper, we prove Bernstein type theorems for entire convex graphical hypersurfaces with zero Gaussian curvature in both Euclidean and Minkowski context. A supplementary example illustrates that zero Gaussian convex spacelike…
We consider elliptic surfaces $\mathcal{E}$ over a field $k$ equipped with zero section $O$ and another section $P$ of infinite order. If $k$ has characteristic zero, we show there are only finitely many points where $O$ is tangent to a…
The purpose of this article is to investigate the holomorphic vector fields tangent to a real hypersurface in $\mathbb C^2$ vanishing at an infinite type point.
In this paper, we introduce two notions on a surface in a contact manifold. The first one is called degree of transversality (DOT) which measures the transversality between the tangent spaces of a surface and the contact planes. The second…
Using the principle of least action, the motion equations for a singular hypersurface of arbitrary type in quadratic gravity are derived. Equations containing the "external pressure" and the "external flow" components of the surface…
We consider the problem of how to construct the curvature perturbation $\zeta$ to nonlinear levels, which is expected to evolve time independently on super-horizon scales; in particular we concentrate on the situation where the universe is…
Following Geroch, Traschen, Mars and Senovilla, we consider Lorentzian manifolds with distributional curvature tensor. Such manifolds represent spacetimes of general relativity that possibly contain gravitational waves, shock waves, and…
The holomorphy conjecture for suspensions of plane curve singularities and the holomorphy and monodromy conjectures for L\^e-Yomdin singularities of surfaces are proved. The first part of this paper provides formul{\ae} for the motivic and…
We study the principal configurations around an isolated $\eta$-umbilical point on a generic spacelike surface $S$ immersed in a null hypersurface $M$ of Minkowski space $\mathbb{R}_1^4$ relative to a well-defined null vector field $\eta$…
Given a complete non-compact surface embedded in R^3, we consider the Dirichlet Laplacian in a layer of constant width about the surface. Using an intrinsic approach to the layer geometry, we generalise the spectral results of an original…
We construct a covariant phase space for rotating weakly isolated horizons in Einstein-Maxwell-Chern-Simons theory in all (odd) $D\geq5$ dimensions. In particular, we show that horizons on the corresponding phase space satisfy the zeroth…