相关论文: The Hyperboloidal and Spacetime Positive Mass Theo…

We prove a local in time existence and uniqueness theorem of classical solutions of the coupled Einstein--Euler system, and therefore establish the well posedness of this system. We use the condition that the energy density might vanish or…

We establish versions of the Positive Mass and Penrose inequalities for a class of asymptotically hyperbolic hypersurfaces. In particular, under the usual dominant energy condition, we prove in all dimensions $n\geq 3$ an optimal Penrose…

We define the (total) center of mass for suitably asymptotically hyperbolic time-slices of asymptotically anti-de Sitter spacetimes in general relativity. We do so in analogy to the picture that has been consolidated for the (total) center…

A generalized version of Bertrand's theorem on spherically symmetric curved spaces is presented. This result is based on the classification of (3+1)-dimensional (Lorentzian) Bertrand spacetimes, that gives rise to two families of…

We prove the mean ergodic theorem of von Neumann in a Hilbert-Kaplansky space. We also prove a multiparameter, modulated, subsequential and a weighted mean ergodic theorems in a Hilbert-Kaplansky space

An extension of the finite and infinite Lie groups properties of complex numbers and functions of complex variable is proposed. This extension is performed exploiting hypercomplex number systems that follow the elementary algebra rules. In…

The general model of an arbitrary spin massive particle in any dimensional space-time is derived on the basis of Kirillov - Kostant - Souriau approach. It is shown that the model allows consistent coupling to an arbitrary background of…

We analyze asymptotic properties of higher-dimensional vacuum spacetimes admitting a "non-degenerate" geodetic multiple WAND. After imposing a fall-off condition necessary for asymptotic flatness, we determine the behaviour of the Weyl…

We show that the positive mass theorem holds for continuous Riemannian metrics that lie in the Sobolev space $W^{2, n/2}_{loc}$ for manifolds of dimension less than or equal to $7$ or spin-manifolds of any dimension. More generally, we give…

Away from the central axis, we prove the stability of the Positive Mass Theorem in the $W^{1,p}$ sense for asymptotically flat axisymmetric manifolds with nonnegative scalar curvature satisfying some additional technical assumptions. We…

In this paper, the following two propositions are proven under the dominant energy condition for the matter field in the higher-dimensional spherically symmetric spacetime in Einstein-Gauss-Bonnet gravity in the presence of a cosmological…

It is shown that various pathological properties of spacetimes can be explained by the presence of negative mass, including the cases when the total mass of the solution is a positive quantity. As an illustration, we consider several…

This talk reports on recent progress toward the semiglobal study of asymptotically flat spacetimes within numerical relativity. The development of a 3D solver for asymptotically Minkowski-like hyperboloidal initial data has rendered…

We use a transformation due to Bekenstein to relate the ADM and Bondi masses of asymptotically-flat solutions of the Einstein equations with, respectively, scalar sources and conformal-scalar sources. Although the conformal-scalar…

A major issue in general relativity, from its earliest days to the present, is how to extract physical information from any solution or class of solutions to the Einstein equations. Though certain information can be obtained for arbitrary…

We show that ultra-massive spacetimes exist also in 2 + 1 dimensions with a positive cosmological constant {\Lambda} > 0. They can be created through the collapse of a spherical null dust shell. The exterior of the shell is then a Mess…

In \cite{ly, ly2}, Liu and the second author propose a definition of the quasi-local mass and prove its positivity. This is demonstrated through an inequality which in turn can be interpreted as a total mean curvature comparison theorem for…

A new local, covariant ``counter-term'' is used to construct a variational principle for asymptotically flat spacetimes in any spacetime dimension $ d \ge 4$. The new counter-term makes direct contact with more familiar background…

We begin by emphasizing that we are dealing with standard Einstein or Einstein-Maxwell theory - absolutely no new physics has been inserted. The fresh item is that the well-known asymptotically flat solutions of the Einstein-Maxwell theory…

Penrose et al. investigated the physical incoherence of the spacetime with negative mass via the bending of light. Precise estimates of time-delay of null geodesics were needed and played a pivotal role in their proof. In this paper, we…