Related papers: Elliptic-hyperbolic systems and the Einstein equat…
This is a short review of a series of papers which, in collaboration with Yue Ma, establish several novel existence results for systems of coupled wave-Klein-Gordon equation. Our method, the Hyperbolic Hyperboloidal Method, has allowed us…
Although the traditional form of the Einstein field equations is intrinsically four-dimensional, the field of numerical general relativity focuses on the reformulation of these equations as a 3 + 1-dimensional Cauchy problem, in which…
We have recently constructed a numerical code that evolves a spherically symmetric spacetime using a hyperbolic formulation of Einstein's equations. For the case of a Schwarzschild black hole, this code works well at early times, but…
We consider the initial boundary value problem for the Einstein vacuum equations in the maximal gauge, or more generally, in a gauge where the mean curvature of a timelike foliation is fixed near the boundary. We prove the existence of…
The issue of the physical equivalence between the different coordinate system in Einstein theory is revised. Gauge fixing influences results of measurements and physics are different in two different coordinate system. Spacetime metric…
We prove an asymptotic stability result for a linear coupled hyperbolic-elliptic system on a large class of singular background spacetimes in CMC gauge on the n-torus. At each spatial point these background spacetimes are perturbations of…
We numerically study spherical gravitational collapse in shift symmetric Einstein dilaton Gauss Bonnet (EdGB) gravity. We find evidence that there are open sets of initial data for which the character of the system of equations changes from…
The Einstein equations for a perfect fluid spatially homogeneous spacetime are studied in a unified manner by retaining the generality of certain parameters whose discrete values correspond to the various Bianchi types of spatial…
Spacetimes with collisionless matter evolving from data on a compact Cauchy surface with hyperbolic symmetry are shown to be timelike and null geodesically complete in the expanding direction, provided the data satisfy a certain size…
A broader perspective is suggested for the study of higher dimensional cosmological models. [1986: Considerations involving the Einstein constraints and the Ricci form of the evolution equations for spatially homogeneous spacetimes in 4 or…
The principle part of Einstein equations in the harmonic gauge consists of a constrained system of 10 curved space wave equations for the components of the space-time metric. A well-posed initial boundary value problem based upon a new…
This paper is the first part of a trilogy dedicated to the following problem: given spherically symmetric characteristic initial data for the Einstein-Maxwell-scalar field system with a cosmological constant $\Lambda$, with the data on the…
The dynamics for a thin, closed loop inextensible Euler's elastica moving in three dimensions are considered. The equations of motion for the elastica include a wave equation involving fourth order spatial derivatives and a second order…
We study the linearization stability of the Einstein constraint equations on an asymptotically hyperbolic manifold. In particular we prove that these equations are linearization stable in the neighborhood of vacuum solutions for a…
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…
Inflationary spatially homogeneous cosmological models within an Einstein-Aether gravitational framework are investigated. The matter source is assumed to be a scalar field which is coupled to the aether field expansion and shear scalars…
The main goal of this work consists in showing that the analytic solutions for a class of characteristic problems for the Einstein vacuum equations have an existence region larger than the one provided by the Cauchy-Kowalevski theorem due…
We study the constraint equations for the Einstein-scalar field system on compact manifolds. Using the conformal method we reformulate these equations as a determined system of nonlinear partial differential equations. By introducing a new…
We analyze existence and properties of solutions of two-dimensional general relativistic initial data sets with a negative cosmological constant, both on spacelike and characteristic surfaces. A new family of such vacuum, spacelike data…
We investigate spherically symmetric cosmological models in Einstein-aether theory with a tilted (non-comoving) perfect fluid source. We use a 1+3 frame formalism and adopt the comoving aether gauge to derive the evolution equations, which…