arXiv research

Study Minkowski formula for conformal Killing-Yano 2-forms in constant curvature spacetimes.

For a surface in 3-sphere, by identifying the conformal round 3-sphere as the projectivized positive light cone in Minkowski 5-spacetime, we use the conformal Gauss map and the conformal transform to construct the associate homogeneous 4-surface in Minkowski 5-spacetime. We then derive the local fundamental theorem for…

Characterizes Lorentzian manifolds embeddable in Minkowski spacetime.

In this article, we estimate the quasi-local energy with reference to the Minkowski spacetime [16,17], the anti-de Sitter spacetime [4], or the Schwarzschild spacetime [3]. In each case, the reference spacetime admits a conformal Killing-Yano 2-form which facilitates the application of the Minkowski formula in [15] to …

Study on spin-zero rest-mass fields using conformal geometric method.

The group of conformal diffeomorphisms and the group of causal automorphisms on two-dimensional globally hyperbolic spacetimes are clarified. It is shown that if spacetimes have non-compact Cauchy surfaces, then the groups are subgroups of that of two-dimensional Minkowski spacetime, and if spacetimes have compact Cauc…

New perspective on Ricci flow on spheres using Minkowski spacetime.

We give a geometrically intrinsic construction of a global time function for relatively compact diamond-shaped regions in arbitrary spacetimes. In the case of Minkowski spacetime, the flow of diffeomorphisms associated to a suitably normalized gradient of this time function becomes the conformal isotropy subgroup of th…

Maximal spacetimes have unique past/future sets.

Study submanifolds in null hypersurfaces of generalized Robertson-Walker spacetimes.

Proves a sharp inequality for toroidal surfaces in Horowitz-Myers geon.

New spaces at infinity identified for Minkowski spacetime.

We extend Eardley and Moncrief's $L^\infty$ estimates for the conformally invariant Yang-Mills-Higgs equations to the Einstein cylinder. Our method is to first work on Minkowski space and localise their estimates, and then carry them to the Einstein cylinder by a conformal transformation. By patching local estimates to…

Study spin-0 fields on n-dimensional Minkowski spacetimes, computing asymptotic charges.

Detect spacetime curvature without rulers and clocks in 3D.

A car's motion shows flat parabolic geometry.

The classical Minkowski formula is extended to spacelike codimension-two submanifolds in spacetimes which admit "hidden symmetry" from conformal Killing-Yano two-forms. As an application, we obtain an Alexandrov type theorem for spacelike codimension-two submanifolds in a static spherically symmetric spacetime: a codim…

We characterize those spacetimes which admit a isometric (or conformal) embedding in some Lorentz-Minkowski space L^N. In particular, any globally hyperbolic spacetime can be isometrically embedded in L^N. This is proven by a result of its own interest: the construction of a smooth time function whose gradient is bound…

The paper extends an Alexandrov theorem to Minkowski spacetime.

Geodesic completeness and optimal Sobolev index proven for Minkowski spacetimes.

New energy measure for isolated systems in general relativity.

Vortex solutions on flat surfaces map to harmonic spinors on Nappi-Witten space.

Crooked planes were defined by Drumm to bound fundamental polyhedra in Minkowski space for Margulis spacetimes. They were extended by Frances to closed polyhedral surfaces in the conformal compactification of Minkowski space (Einstein space) which we call crooked surfaces. The conformal model of anti-de Sitter space is…

New inequality shows all special submanifolds in light cone are totally umbilical spheres.

Extends Minkowski stability proof to minimal decay assumptions.

Researchers prove unique embedding of curved surfaces into Minkowski spacetime.

In the present paper a global conformal invariant $Y$ of a closed initial data set is constructed. A spacelike hypersurface $Σ$ in a Lorentzian spacetime naturally inherits from the spacetime metric a differentiation ${\cal D}_e$, the so-called real Sen connection, which turns out to be determined completely by the ini…

New method creates vacuum data at minimal and borderline decay thresholds.

Study shows contact structure on null geodesic space for specific spacetimes.

Lightlike manifolds studied via Cartan geometries in Lorentz-Minkowski spacetime.

In [1], we gave a method for constructing Bertrand curves from the spherical curves in 3 dimensional Minkowski space. In this work, we construct the Bertrand curves corresponding to a spacelike geodesic and a null helix in Minkowski 4 spacetime.

We prove that every $(3+1)$-dimensional flat GHMC Minkowski spacetime which is not a translation spacetime or a Misner spacetime carries a unique foliation by spacelike hypersurfaces of constant scalar curvature. In otherwords, we prove that every such spacetime carries a unique time function with isochrones of constan…

Survey on stability of Minkowski spacetime in relativity.

Spinor representations of surfaces immersed into 4-dimensional pseudo-riemannian manifolds are defined in terms of minimal left ideals and tensor decompositions of Clifford algebras. The classification of spinor fields and Dirac operators on the immersed surfaces is given. The Dirac-Hestenes spinor field on surfaces im…

Extends global stability of Minkowski spacetime to minimal decay assumptions.

New proof of Minkowski spacetime stability in exterior regions.

Any 2-dim Riemannian manifold with spherical topology can be embedded isometrically into a lightcone of the Minkowski spacetime. We apply this fact to give a proof of the Kazdan-Warner identity.

Sharp Minkowski inequality found for AdS-Melvin spacetime surfaces.

We consider the timelike minimal surface problem in Minkowski spacetimes and show local and global existence of such surfaces having arbitrary dimension $\geq 2$ and arbitrary co-dimension, provided they are initially close to a flat plane.

We study the existence of surfaces with constant or prescribed Gauss curvature in certain Lorentzian spacetimes. We prove in particular that every (non-elementary) 3-dimensional maximal globally hyperbolic spatially compact spacetime with constant non-negative curvature is foliated by compact spacelike surfaces with co…

Timelike curvature and Brunn-Minkowski inequality linked in non-smooth spacetimes.

A time-flat condition on spacelike 2-surfaces in spacetime is considered here. This condition is analogous to constant torsion condition for curves in three dimensional space and has been studied in [2, 4, 5, 12, 13]. In particular, any 2-surface in a static slice of a static spacetime is time-flat. In this article, we…

Given a regular curve in Minkowski spacetime, we describe necessary and sufficient conditions for this curve to admit a family of pairwise-disjoint crooked planes. Using this criterion, we describe crooked foliations along orbit curves of one-parameter groups of Lorentzian isometries.

Study complete space-like stationary surfaces with graphical Gauss image, estimating exceptional values and classifying degenerate surfaces.

The paper studies volumes of conformally flat manifolds in light-cone geometry.

We prove two theorems, announced in hep-th/0108170, for static spacetimes that solve Einstein's equation with negative cosmological constant. The first is a general structure theorem for spacetimes obeying a certain convexity condition near infinity, analogous to the structure theorems of Cheeger and Gromoll for manifo…

The paper shows instability in Minkowski spacetime for a quantum system.

Solves Minkowski problem for affine invariant convex domains.