arXiv research

Characterizes Lorentzian manifolds embeddable in Minkowski spacetime.

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

Geodesic completeness and optimal Sobolev index proven for Minkowski spacetimes.

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 …

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.

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

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.

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…

New perspective on Ricci flow on spheres using Minkowski spacetime.

In this paper, we generalize a theorem {à} la Alexandrov of Wang, Wang and Zhang [WWZ] for closed codimension-two spacelike submanifolds in the Minkowski spacetime for an adapted CMC condition .

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.

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.

Sharp Minkowski inequality found for AdS-Melvin spacetime surfaces.

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 shows instability in Minkowski spacetime for a quantum system.

Solves Minkowski problem for affine invariant convex domains.

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…

A particular, yet relevant, particular case of the Penrose inequality involves null shells propagating in the Minkowski spacetime. Despite previous claims in the literature, the validity of this inequality remains open. In this paper we rewrite this inequality in terms of the geometry of the surface obtained by interse…

Paper proves isoperimetric inequality for Minkowski spacetime.

New spaces at infinity identified for Minkowski spacetime.

Assuming minimal regularity assumptions on the data, we revisit the classical problem of finding isometric immersions into the Minkowski spacetime for hypersurfaces of a Lorentzian manifold. Our approach encompasses metrics having Sobolev regularity and Riemann curvature defined in the distributional sense, only. It ap…

The paper establishes criteria for spacetime inextendibility using asymptotic volume-distance-ratio analysis.

New memory effect discovered in gravitational wave behavior.

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…

The study finds hypersurfaces with constant scalar curvature in Minkowski space.

Study gluing event horizons of Minkowski and Schwarzschild spacetimes.

In this paper we define a new type of 2-degenerate Cartan curves in Minkowski spacetime $R_{1}^{4}$. We prove that this type of curves contain only the polynomial functions as its components whose third derivative vanish completely. No curve with acceleration zero in $R_{1}^{4}$ is a 2-degenerate Cartan curve, therefor…

The study proves timelike Ricci bounds for low regularity spacetimes using optimal transport.

Initial data with zero mass must be in pp-wave spacetimes.

The paper classifies coverings and non-Hausdorff extensions of Misner spacetime.

Let $Ω$ be a compact and mean-convex domain with smooth boundary $Σ:=\partialΩ$, in an initial data set $(M^3,g,K)$, which has no apparent horizon in its interior. If $Σ$ is spacelike in a spacetime $(\E^4,g\_\E)$ with spacelike mean curvature vector $\mathcal{H}$ such that $Σ$ admits an isometric and isospin immersion…

Study of spacelike submanifolds in spherical RW spacetime, proving a Lorentzian Takahashi theorem.

New proof shows equality in spacetime mass theorem.

To cure the lack of predictive power of general relativity Geroch proposed to complete the theory with an additional postulate that only "hole-free" spacetimes are permitted. I argue that this postulate is too strong -- it prohibits even the Minkowski space.

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

The main topic of this paper is to show that in the 3-dimensional Minkowski spacetime, the torsion of a null curve is equal to the Schwarzian derivative of a certain function appearing in a description of the curve. As applications, we obtain descriptions of the slant helices, and null curves for which the torsion is o…

Optimizes transport in Finsler spacetimes with lower Ricci bounds.