相关论文: A rigidity property of asymptotically simple space…

We determine the exact solution of the Einstein field equations for the case of a spherically symmetric shell of liquid matter, characterized by an energy density which is constant with the Schwarzschild radial coordinate $r$ between two…

It is proved that any static system that is spacetime-geodesically complete at infinity, and whose spacelike-topology outside a compact set is that of R^3 minus a ball, is asymptotically flat. The matter is assumed compactly supported and…

The field equations of the recent nonlocal generalization of Einstein's theory of gravitation are presented in a form that is reminiscent of general relativity. The implications of the nonlocal field equations are studied in the case of…

According to Birkhoff's theorem the only spherically symmetric solution of the vacuum Einstein field equations is the Schwarzschild solution. Inspite of imposing asymptotically flatness and staticness as initial conditions we obtain that…

We obtain necessary and sufficient conditions for an initial data set for the vacuum conformal Einstein field equations to give rise to a spacetime development in possession of a Killing spinor. The fact that the conformal Einstein field…

In a recent work, Ringstr\"om proposed a geometric notion of initial data on big bang singularities. Moreover, he conjectured that initial data on the singularity could be used to parameterize quiescent solutions to Einstein's equations;…

We hereby show that the Kasner spacetime turns out to be singularity-free in Einstein's conformal gravity in vacuum or in presence of matter. Such a statement is based on the regularity of the curvature invariants and on the geodesic…

Solutions to the wave equation on de Sitter-Schwarzschild space with smooth initial data on a Cauchy surface are shown to decay exponentially to a constant at temporal infinity, with corresponding uniform decay on the appropriately…

The existence of symmetries in asymptotically flat space-times are studied from the point of view of initial value problems. General necessary and sufficient (implicit) conditions are given for the existence of Killing vector fields in the…

In Einstein's theory of general relativity the vacuum solution yields a blackhole with a curvature singularity, where there exists a point-like source with a Dirac delta distribution which is introduced as a boundary condition in the static…

We apply a new method with explicit solution operators to construct asymptotically flat initial data sets of the vacuum Einstein equation with new localization properties. Applications include an improvement of the decay rate in…

We show that in the conformally flat case the Penrose inequality is satisfied for the Schwarzschild initial data with a small addition of the axially symmetric traceless exterior curvature. In this class the inequality is saturated only for…

Using asymptotic characterization results of spacetimes at conformal infinity, we prove that Kerr-Schild-de Sitter spacetimes are in one-to-one correspondence with spacetimes in the Kerr-de Sitter-like class with conformally flat…

In case of a spherically symmetric non-linear scalar field (SF) in flat space, besides singularity at the center, spherical singularities can occur for non-zero values of radial variable $r>0$. We show that in the General Relativity the…

We construct perturbations of Minkowski spacetime in general relativity, when given initial data that decays inverse polynomially to initial data of a Kerr spacetime towards spacelike infinity. We show that the perturbations admit a regular…

It is shown how the gauge of the ``regular finite initial value problem at spacelike infinity'' can be used to construct a certain type of estimates for the Maxwell field propagating on a Schwarzschild background. These estimates are…

We present the exact solution of Einstein's equation corresponding to a static and plane symmetric distribution of matter with constant positive density located below $z=0$. This solution depends essentially on two constants: the density…

We study spherically symmetric spacetimes in Einstein-aether theory in three different coordinate systems, the isotropic, Painlev\`e-Gullstrand, and Schwarzschild coordinates, in which the aether is always comoving, and present both…

It is shown that solutions to Einstein's field equations with positive cosmological constant can include non-zero rest-mass fields which coexist with and travel unimpeded across a smooth conformal boundary. This is exemplified by the…

We make use of Friedrich's construction of the cylinder at spatial infinity to relate the logarithmic terms appearing in asymptotic expansions of components of the Weyl tensor to the freely specifiable parts of time symmetric initial data…