Related papers: Global Regularity for the 2+1 Dimensional Equivari…
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 prove global regularity for the full water waves system in 3 dimensions for small data, under the influence of both gravity and surface tension. This problem presents essential difficulties which were absent in all of the…
The second Bianchi identity can be recast as an evolution equation for the Riemann curvatures. Here we will report on such a system for a vacuum static spherically symmetric spacetime. This is the first of two papers. In the following paper…
We argue that the presence of conformal anomalies in gravitational theories can lead to observable modifications to Einstein's equations via the induced anomalous effective actions, whose non-localities can overwhelm the smallness of the…
In this paper we consider finite energy, \ell-equivariant wave maps from 1+3-dimensional Minkowski space exterior to the unit ball at the origin into the 3-sphere. We impose a Dirichlet boundary condition at r=1, which in this context means…
In this paper, we study the coupled Einstein constraint equations on complete manifolds through the conformal method, focusing on non-compact manifolds with flexible asymptotics. This is physically well-motivated by standard cosmological…
The fundamental metrics, which describe any static three-dimensional Einstein-Maxwell spacetime (depending only on a unique spacelike coordinate), are found. In this case there are only three independent components of the electromagnetic…
The generalized harmonic representation of Einstein's equation is manifestly hyperbolic for a large class of gauge conditions. Unfortunately most of the useful gauges developed over the past several decades by the numerical relativity…
We present a method for generating exact solutions of Einstein equations in vacuum using harmonic maps, when the spacetime possesses two commutating Killing vectors. This method consists in writing the axisymmetric stationry Einstein…
A Lorenz-covariant system of wave equations is formulated for a quantum-mechanical two-body system in one space dimension, comprised of one electron and one photon. Manifest Lorentz covariance is achieved using Dirac's formalism of…
This article, written to appear as a chapter in "The Springer Handbook of Spacetime", is a review of the initial value problem for Einstein's gravitational field theory in general relativity. Designed to be accessible to graduate students…
Here we prove the linear stability of a family of `$n+1$'-dimensional Friedmann Lema\^{i}tre Robertson Walker (FLRW) cosmological models of general relativity. We show that the solutions to the linearized Einstein-Euler field equations…
The Euler-Poisson(EP) system describes the dynamic behavior of many important physical flows. In this work, a Riccati system that governs the flow's gradient is studied. The evolution of divergence is governed by the Riccati type equation…
In this paper we discuss the global symmetries and the renormalizibility of Lee-Wick scalar QED. In particular, in the "auxiliary-field" formalism we identify softly broken SO(1,1) global symmetries of the theory. We introduce SO(1,1)…
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…
Using the harmonic map heat flow and the function spaces of Tataru and the author, we establish a large data local well-posedness result in the energy class for wave maps from two-dimensional Minkowski space $\R^{1+2}$ to hyperbolic spaces…
This paper studies diagonal spacetime metrics. It is shown that the overdetermined Einstein vacuum equations are compatible if one Killing vector exists. The stability of plane gravitational waves of the Robinson type is studied. This…
We study the behavior of a general gravitational action, including quadratic terms in the curvature, supplemented by a compact scalar field in 4+1 dimensions. The generalized Einstein equation for this system admits solutions which are…
Towards the investigation of the full dynamics in higher-dimensional and/or stringy gravitational model, we present the basic equations of the Einstein-Gauss-Bonnet gravity theory. We show $(N+1)$-dimensional version of the ADM…
Pure (2+1)-dimensional Einstein gravity is analysed in the Ashtekar formulation, when the spatial manifold is a torus. We have found a set of globally defined observables, forming a closed algebra. This allowed us to solve the quantum…