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We show that small homogeneous solutions to the Einstein-Boltzmann-scalar field system exist globally towards the future and tend to the de Sitter solution in a suitable sense. More specifically, we assume that the spacetime is of Bianchi…

We consider one-dimensional, locally finite interacting particle systems with two conservation laws which under Eulerian hydrodynamic limit lead to two-by-two systems of conservation laws: \pt \rho +\px \Psi(\rho, u)=0 \pt u+\px…

We reformulate the Gross-Pitaevskii equation with an external parabolic potential as a discrete dynamical system, by using the basis of Hermite functions. We consider small amplitude stationary solutions with a single node, called dark…

Gravitational wave astronomy has tremendous potential for studying extreme astrophysical phenomena and exploring fundamental physics. The waves produced by binary black hole mergers will provide a pristine environment in which to study…

We introduce a general framework for the construction of well-balanced finite volume methods for hyperbolic balance laws. We use the phrase well-balancing in a broader sense, since our proposed method can be applied to exactly follow any…

We prove that any generalized hyperbolic operator on any Banach space is structurally stable. As a consequence, we obtain a generalization of the classical Grobman-Hartman theorem.

The spectrum of known black-hole solutions to the stationary Einstein equations has been steadily increasing, sometimes in unexpected ways. In particular, it has turned out that not all black-hole-equilibrium configurations are…

We prove local existence and uniqueness of the Cauchy problem for a large class of tensorial second order linear hyperbolic partial differential equations with coefficients of low regularity in a suitable class of generalized functions.

Contents: 1) Introduction and a few excursions [A word on the role of explicit solutions in other parts of physics and astrophysics. Einstein's field equations. "Just so" notes on the simplest solutions: The Minkowski, de Sitter and anti-de…

We review recent progress in taking the large dimension limit of Einstein's equations. Most of our analysis is classical in nature and concerns situations where there is a black hole horizon although we briefly discuss various extensions…

We review the experimental evidence for Einstein's special and general relativity. A variety of high precision null experiments verify the weak equivalence principle and local Lorentz invariance, while gravitational redshift and other clock…

In this paper, we propose a globally hyperbolic regularization to the general Grad's moment system in multi-dimensional spaces. Systems with moments up to an arbitrary order are studied. The characteristic speeds of the regularized moment…

Significant advances were made in recent years on the global evolution problem for self-gravitating massive matter in the small-perturbative regime close to Minkowski spacetime. To study the coupling between a Klein-Gordon equation and…

We show that, given any static spacetime whose spatial slices are asymptotically Euclidean (or, more generally, asymptotically conic) manifolds modeled on the large end of the Schwarzschild exterior, there exist stationary solutions to the…

Extending earlier work of Tian, we show that if a manifold admits a metric that is almost hyperbolic in a suitable sense, then there exists an Einstein metric that is close to the given metric in the $C^{2,\alpha}$-topology. In dimension…

We use an orthonormal frame approach to provide a general framework for the first order hyperbolic reduction of the Einstein equations coupled to a fairly generic class of matter models. Our analysis covers the special cases of dust and…

In this paper we discuss a method of generating supersymmetric solutions of the Einstein equations. The method involves the embedding of one supersymmetric spacetime into another. We present two examples with constituent spacetimes which…

We enunciate and prove here a generalization of Geroch's famous conjecture concerning analytic solutions of the elliptic Ernst equation. Our generalization is stated for solutions of the hyperbolic Ernst equation that are not necessarily…

We give a new proof for the local existence of a smooth isometric embedding of a smooth $3$-dimensional Riemannian manifold with nonzero Riemannian curvature tensor into $6$-dimensional Euclidean space. Our proof avoids the sophisticated…

We consider a characteristic initial value problem for a class of symmetric hyperbolic systems with initial data given on two smooth null intersecting characteristic surfaces. We prove existence of solutions on a future neighborhood of the…