arXiv research

Anti-de Sitter spacetimes with convex boundaries are uniquely determined by their boundary metrics.

New theorem for spacetime mass in noncompact regions.

New research proves uniqueness of maximal spacetime boundaries under certain conditions.

Solves initial boundary value problem for vacuum Einstein equations and proves geometric uniqueness.

Study reveals how travel times on cylindrical boundaries can identify spacetime structure.

The paper studies the past inextendibility of FLRW spacetimes using the VDR asymptote.

Proves spacetime positive mass theorem for spin initial data sets with arbitrary ends.

Minimal TIP and TIF found in compact spacetimes, impacting spacetime splitting.

Study characterizes conformal boundaries of de Sitter spacetimes.

Study proves mean curvature flow in GRW spacetimes with perpendicular boundary condition.

The notion of a causal boundary for a spacetime has been a controversial topic during the last three decades. Moreover, recently the role of the boundary in the AdS/CFT correspondence for plane waves, have stimulated its redefinition with some possible alternatives. Our aim is threefold. First, to review the different …

Two different spacetimes can mimic each other's boundary measurements.

New boundary conditions solve Cauchy problem for Dirac operators on spacetimes.

The paper proves a conjecture about spacetimes and singularities.

Recently, a new viewpoint on the classical c-boundary in Mathematical Relativity has been developed, the relations of this boundary with the conformal one and other classical boundaries have been analyzed, and its computation in some classes of spacetimes, as the standard stationary ones, has been carried out. In the p…

New findings on lightconvex boundaries in Finslerian spacetimes.

Globally hyperbolic spacetimes with timelike boundary $(\overline{M} = M \cup \partial M, g)$ are the natural class of spacetimes where regular boundary conditions (eventually asymptotic, if $\overline{M}$ is obtained by means of a conformal embedding) can be posed. $\partial M$ represents the naked singularities and c…

We develop a general method of proving the ellipticity of boundary value problems for the stationary vacuum space time, by showing that the stationary vacuum field equations are elliptic subjected to a geometrically natural collection of boundary conditions in the projection formalism. Using this we prove the manifold …

We establish a moduli space $\mathbb E$ of stationary vacuum metrics in a spacetime, and set up a well-defined boundary map $Π$ in $\mathbb E$, assigning a metric class with its Bartnik boundary data. Furthermore, we prove the boundary map $Π$ is Fredholm by showing that the stationary vacuum equations (combined with p…

Motivated by recent proposals for a de Sitter version of the AdS/CFT correspondence, we give some topological restrictions on spacetimes of de Sitter type, i.e., spacetimes with $Λ>0$, which admit a regular past and/or future conformal boundary. For example we show that if $M^{n+1}$, $n \ge 2$, is a globally hyperbolic…

Study on unique spacetime extensions in 1+1 dimensions with applications to weak null singularities.

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

We construct an example which shows that two isocausal spacetimes, in the sense introduced by García-Parrado and Senovilla, may have c-boundaries which are not equal (more precisely, not equivalent, as no bijection between the completions can preserve all the binary relations induced by causality). This example also su…

Study proves behaviors of CMC surfaces near future null-infinity in Schwarzschild spacetime.

New proof of stability for expanding Kerr-de Sitter spacetimes with smoothness at the boundary.

It is shown that the space of null geodesics of a star-shaped causally simple subset of Minkowski space is contactomorphic to the canonical contact structure in the spherical cotangent bundle of $\mathbb{R}^n$. In the $3$-dimensional case we prove a similar result for a large class of causally simple contractible subse…

Recently, the old notion of causal boundary for a spacetime V has been redefined in a consistent way. The computation of this boundary $\partial V$ for a standard conformally stationary spacetime V = R x M, suggests a natural compactification $M_B$ associated to any Riemannian metric on M or, more generally, to any Fin…

The paper proves a rigidity theorem for null geodesic travel times in asymptotically AdS spacetimes.

Study proves rigidity results for analytic spacetimes without boundary or timelike boundary.

In the first part of this work we show a uniqueness result for globally hyperbolic spacetimes with a spacelike conformal boundary satisfying the vacuum Einstein equations with positive cosmological constant. Then we present applications of this result in the contexts of cosmic censorship and the initial value problem i…

Formula for index in Lorentzian spacetimes.

We derive necessary conditions for the spinorial Witten-Nester energy to be well-defined for asymptotically locally AdS spacetimes. We find that the conformal boundary should admit a spinor satisfying certain differential conditions and in odd dimensions the boundary metric should be conformally Einstein. We show that …

Study shows Fredholmness of a Lorentzian Dirac operator on spacetimes.

Proves properties of free boundary stable MOTS in spacetimes.

Proves density and mass theorems for specific initial data sets.

Higher-dimensional spacetimes have well-behaved boundaries.

Study stability of surfaces in spacetimes, proving new estimates and theorems.

Study reveals how boundary wave operator determines metric properties on anti-de Sitter spacetimes.

Research proves unique continuation for Einstein-vacuum equations on aAdS spacetimes.

Study shows Brakke flow's non-triviality for smooth boundaries in codimension 1.

In this global study of solutions to the linear wave equation on Schwarzschild de Sitter spacetimes we attend to the cosmological region of spacetime which is bounded in the past by cosmological horizons and to the future by a spacelike hypersurface at infinity. We prove an energy estimate capturing the expansion of th…

We show that Margulis spacetimes without parabolic holonomy are topologically tame. A Margulis spacetime is the quotient of the $3$-dimensional Minkowski space by a free proper isometric action of the free group of rank $\geq 2$. We will use our particular point of view that the Margulis spacetime is a manifold-with-bo…

We show that when a spacetime $\mathcal{M}(=M \cup \partial M)$ is globally hyperbolic with (possibly empty) smooth timelike boundary $\partial M$, a metrizable topology, the closed limit topology (CLT) introduced by F. Hausdorff himself in the 1950's in set theory, can be advantageously adopted on the Geroch-Kronheime…

When a spacetime has boundaries, the entangling surface does not have to be necessarily compact and it may have boundaries as well. Then there appear a new, boundary, contribution to the entanglement entropy due to the intersection of the entangling surface with the boundary of the spacetime. We study the boundary cont…

Warped-product black hole spacetimes are $C^0$-inextendible.

Milne-like spacetimes are a class of FLRW models which admit $C^0$ spacetime extensions through the big bang. The boundary of a Milne-like spacetime can be identified with a null cone in the extension. We find that the comoving observers all emanate from a single point in the extension. This suggests that something phy…

New CMC existence result for expanding cosmological spacetimes.

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…