Related papers: Smoothness at null infinity and the structure of i…
We investigate the dynamics of spatially homogeneous solutions of the Einstein-Vlasov equations with Bianchi type I symmetry by using dynamical systems methods. All models are forever expanding and isotropize toward the future; toward the…
For the Cauchy problem of nonlinear elastic wave equations of three dimensional isotropic, homogeneous and hyperelastic materials satisfying the null condition, global existence of classical solutions with small initial data was proved in…
We extend the work in our earlier article [4] to show that time-periodic, asymptotically-flat solutions of the Einstein equations analytic at scri, whose source is one of a range of scalar-field models, are necessarily stationary. We also…
Asymptotically flat spacetimes have been studied in five separate regions: future/past timelike infinity $i^\pm$, future/past null infinity $\mathcal{I}^\pm$, and spatial infinity $i^0$. We formulate assumptions and definitions such that…
This article is focused on the asymptotic expansions, as time tends to infinity, of solutions of a system of ordinary differential equations with non-smooth nonlinear terms. The forcing function decays to zero in a very complicated but…
We consider the Cauchy problem for an evolution equation modeling bidirectional surface waves in a convecting fluid. Under small condition on the initial value, the existence and asymptotic behavior of global solutions in some time weighted…
Self-similar, spherically symmetric cosmological models with a perfect fluid and a scalar field with an exponential potential are investigated. New variables are defined which lead to a compact state space, and dynamical systems methods are…
We prove global stability of Minkowski space for the Einstein vacuum equations in harmonic (wave) coordinate gauge for the set of restricted data coinciding with Schwartzschild solution in the neighborhood of space-like infinity. The result…
Shear-free or asymptotically shear-free null geodesic congruences possess a large number of fascinating geometric properties and to be closely related, in the context of general relativity, to a variety of physically significant affects. It…
In this paper we investigate spectral flow symmetry in asymptotically flat spacetimes both from a gravity as well as a putative dual quantum field theory perspective. On the gravity side we consider models in Einstein gravity and…
We study locally spatially homogeneous solutions of the Einstein-Vlasov system with a positive cosmological constant. First the global existence of solutions of this system and the casual geodesic completeness are shown. Then the asymptotic…
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…
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…
In some cosmological theories with varying constants there are anthropic reasons why the expansion of the universe must not be too {\it close} to flatness or the cosmological constant too close to zero. Using exact theories which…
Recent work in the literature has studied a version of non-commutative Schwarzschild black holes where the effects of non-commutativity are described by a mass function depending on both the radial variable r and a non-commutativity…
In this work we investigate the asymptotic behaviour of solutions to the Einstein equations with a minimally coupled scalar field. The primary focus of the present paper here establishing under what conditions a solution becomes…
This paper concerns the large time asymptotic behavior of solutions to the free boundary problem of the compressible primitive equations in atmospheric dynamics with physical vacuum. Up to second order of the perturbations of an…
I discuss a formulation of M-theory at null infinity, which is based on general principles of holographic space-time, and is manifestly covariant. The construction utilizes a certain Type II Von Neumann algebra, which provides a kinematic…
We are considering the asimptotic behavior as $t\to\infty$ of solutions of the Cauchy problem for parabolic second order equations with time periodic coefficients. The problem is reduced to considering degenerate time-homogeneous diffusion…
We prove a harmonic asymptotics density theorem for asymptotically flat initial data sets with compact boundary that satisfy the dominant energy condition. We use this to settle the spacetime positive mass theorem, with rigidity, for…