相关论文: The reverse Burnett conjecture for null dusts
The vacuum cosmological model on the manifold $R \times M_1 \times \ldots \times M_n$ describing the evolution of $n$ Einstein spaces of non-zero curvatures is considered. For $n = 2$ the Einstein equations are reduced to the Abel (ordinary…
We give a sufficient condition, with no restrictions on the mean curvature, under which the conformal method can be used to generate solutions of the vacuum Einstein constraint equations on compact manifolds. The condition requires a…
Five tensor equations are obtained for a thin shell in Gauss-Bonnet gravity. There is the well known junction condition for the singular part of the stress tensor intrinsic to the shell, which we also prove to be well defined. There are…
The existence of stationary solutions to the Einstein-Vlasov system which are axially symmetric and have non-zero total angular momentum is shown. This provides mathematical models for rotating, general relativistic and asymptotically flat…
We derive evolution and constraint equations for second order perturbations of flat dust homogeneous and isotropic solutions to the Einstein field equations using all scalar, vector and tensor perturbation modes. We show that the…
We construct infinite-dimensional families of non-singular static space times, solutions of the vacuum Einstein-Maxwell equations with a negative cosmological constant. The families include an infinite-dimensional family of solutions with…
An idea which has been around in general relativity for more than forty years is that in the approach to a big bang singularity solutions of the Einstein equations can be approximated by the Kasner map, which describes a succession of…
Multi-parameter solutions to the Einstein equations in 2+1 dimensions are presented, with stress-energy given by a rotating dust with negative cosmological constant. The matter density is uniform in the corotating frame, and the ratio of…
We construct asymptotically Euclidean solutions of the vacuum Einstein constraint equations with an apparent horizon boundary condition. Specifically, we give sufficient conditions for the constant mean curvature conformal method to…
We consider the Einstein-Boltzmann system for massless particles in the Bianchi I space-time with scattering cross-sections in a certain range of soft potentials. We assume that the space-time has an initial conformal gauge singularity and…
We construct new vacuum solutions of the Einstein equations generated from electrovacuum configurations embedded in external electromagnetic backgrounds. Starting from accelerating Bertotti--Robinson black holes, we exploit two independent…
In this paper, vacuum and singularity formation are considered for compressible Euler equations with time-dependent damping. For $1<\gamma\leq 3$, by constructing some new control functions ingeniously, we obtain the lower bounds estimates…
We analyze the null geodesic equations in five dimensional spherically symmetric spacetime with collapsing inhomogeneous dust cloud. By using a new method, we prove the existence and non-existence of solutions to null geodesic equation…
We study Einstein's equations with matter in hydrostatic equilibrium in the nonstandard gauge which was recently investigated in the vacuum case. We obtain spherically symmetric solutions for any given rotation curve. These solutions can be…
We consider the Einstein equations coupled to an ultrastiff perfect fluid and prove the existence of a family of solutions with an initial singularity whose structure is that of explicit isotropic models. This family of solutions is…
The asymptotic behavior of Einstein-Rosen waves at null infinity in 4 dimensions is investigated in {\it all} directions by exploiting the relation between the 4-dimensional space-time and the 3-dimensional symmetry reduction thereof.…
We study the space-time geometry generated by coupling a free scalar field with a non-canonical kinetic term to General Relativity in $(2+1)$ dimensions. After identifying a family of scalar Lagrangians that yield exact analytical solutions…
We prove uniform finite-time existence of solutions to the vacuum Einstein equations in polarized U(1) symmetry which have uniformly positive incoming $H^1$ energy supported on an arbitrarily small set in the 2 + 1 spacetime obtained by…
A perfect fluid, spatially flat cosmology in a $f(T)$ model, derived from a recently proposed general Born-Infeld type theory of gravity is studied. Four dimensional cosmological solutions are obtained assuming the equation of state…
We establish results on the dynamics of interacting charged null fluids in general relativity, specifically in the context of the bouncing continuation proposed in [Ori91]. In this model - the setting for a number of prominent case studies…