The Hawking effect
The holomorphic automorphism group of the complex disk.
The homological Kähler-de Rham differential mechanism. I: Application in general theory of relativity.
The hyperbolic triangle centroid
Some gyrocommutative gyrogroups, also known as Bruck loops or K-loops, admit scalar multiplication, turning themselves into gyrovector spaces. The latter, in turn, form the setting for hyperbolic geometry just as vector spaces form the setting for Euclidean geometry. In classical mechanics the centroid of a triangle in velocity space is the velocity of the center of momentum of three massive objects with equal masses located at the triangle vertices. Employing gyrovector space techniques we find...
The instability of naked singularities in the gravitational collapse of a scalar field.
The laser interferometer gravitational wave observatory project LIGO
The Laser Interferometer Gravitational Wave Observatory (LIGO) will search for direct evidence of gravitational waves emitted by astrophysical sources in accord with Einstein’s General Theory of Relativity. State of the art laser interferometers located in Hanford, Washington and Livingston Parish, Louisiana will unambiguously measure the infinitesimal displacements of isolated test masses which convey the signature of these gravitational waves. The initial implementation of LIGO will consist of...
The motion of point particles in curved spacetime.
The nonlinear future stability of the FLRW family of solutions to the irrotational Euler-Einstein system with a positive cosmological constant
In this article, we study small perturbations of the family of Friedmann-Lemaître-Robertson-Walker cosmological background solutions to the coupled Euler-Einstein system with a positive cosmological constant in spacetime dimensions. The background solutions model an initially uniform quiet fluid of positive energy density evolving in a spacetime undergoing exponentially accelerated expansion. Our nonlinear analysis shows that under the equation of state , the background metric + fluid solutions...
The null condition and global existence for nonlinear wave equations on slowly rotating Kerr spacetimes
We study a semilinear equation with derivatives satisfying a null condition on slowly rotating Kerr spacetimes. We prove that given sufficiently small initial data, the solution exists globally in time and decays with a quantitative rate to the trivial solution. The proof uses the robust vector field method. It makes use of the decay properties of the linear wave equation on Kerr spacetime, in particular the improved decay rates in the region .
The Pioneer anomaly.
The Plane-Time in Which Paths of Inertional Motions Are Conics
The positive mass theorem for ALE manifolds
We show what extra condition is necessary to be able to use the positive mass argument of Witten [12] on an asymptotically locally euclidean manifold. Specifically we show that the 'generalized positive action conjecture' holds if one assumes that the signature of the manifold has the correct value.
The quantum spheres and their embedding into quantum Minkowski space-time.
The resolution of the bounded curvature conjecture in general relativity
This paper reports on the recent proof of the bounded curvature conjecture. More precisely we show that the time of existence of a classical solution to the Einstein-vacuum equations depends only on the -norm of the curvature and a lower bound of the volume radius of the corresponding initial data set.
The spacetime positive mass theorem in dimensions less than eight
We prove the spacetime positive mass theorem in dimensions less than eight. This theorem asserts that for any asymptotically flat initial data set that satisfies the dominant energy condition, the inequality holds, where is the ADM energy-momentum vector. Previously, this theorem was only known for spin manifolds [38]. Our approach is a modification of the minimal hypersurface technique that was used by the last named author and S.-T. Yau to establish the time-symmetric case of this theorem...
The stability of tachyonic field system by factorization method.
The structure of the space of solutions of Einstein's equations. I. One Killing field
The theory of Kaluza-Klein-Jordan-Thiry revisited
The thermodynamics of black holes.
The variational principle for the uniform acceleration and quasi-spin in two dimensional space-time.