Related papers: An angular momentum bound at null infinity
We prove the existence and uniqueness of the Dirichlet problem for spacelike, spherically symmetric, constant mean curvature equation with symmetric boundary data in the extended Schwarzschild spacetime. As an application, we completely…
In this short paper, we review recent progress on the positive mass theorem for spacelike hypersurfaces which approach to null infinity in asymptotically flat spacetimes. We use it to prove, if the functions $c(u, \theta, \psi)$, $d(u,…
We exam the validity of the definition of the ADM angular momentum without the parity assumption. Explicit examples of asymptotically flat hypersurfaces in the Minkowski spacetime with zero ADM energy-momentum vector and finite non-zero…
We prove a continuation condition in the context of 3+1 dimensional vacuum Einstein gravity in Constant Mean extrinsic Curvature (CMC) gauge. More precisely, we obtain quantitative criteria under which the physical spacetime can be extended…
A universal inequality that bounds the angular momentum of a body by the square of its size is presented and heuristic physical arguments are given to support it. We prove a version of this inequality, as consequence of Einstein equations,…
We establish a new CMC (constant mean curvature) existence result for cosmological spacetimes, i.e., globally hyperbolic spacetimes with compact Cauchy surfaces satisfying the strong energy condition. If the spacetime contains an expanding…
We prove an upper bound for angular-momentum and charge in terms of the mass for electro-vacuum asymptotically flat axisymmetric initial data sets with simply connected orbit space.
We find new classes of exact solutions of the initial momentum constraint for vacuum Einstein's equations. Considered data are either invariant under a continuous symmetry or they are assumed to have the exterior curvature tensor of a…
We present a definition of angular momentum for radiative spacetimes which does not suffer from any ambiguity of supertranslations. We succeed in providing an appropriate notion of {\it intrinsic} angular momentum; and at the same time a…
We extend the validity of Dain's angular-momentum inequality to maximal, asymptotically flat, initial data sets on a simply connected manifold with several asymptotically flat ends which are invariant under a U(1) action and which admit a…
A method for interpreting discontinuities of the twist potential of vacuum stationary axisymmetric solutions of Einstein's equations is introduced. Surface densities for the angular momentum of the source can be constructed after solving a…
The Einstein initial-value equations in the extrinsic curvature (Hamiltonian) representation and conformal thin sandwich (Lagrangian) representation are brought into complete conformity by the use of a decomposition of symmetric tensors…
Bekenstein bounds for the entropy of a body imply an universal inequality between size, energy, angular momentum and charge. We prove this inequality in Electromagnetism. We also prove it, for the particular case of zero angular momentum,…
I describe the construction of a large class of asymptotically flat initial data with non-vanishing mass and angular momentum for which the metric and the extrinsic curvature have asymptotic expansions at space-like infinity in terms of…
The main result of this paper is a proof that there are examples of spatially compact solutions of the Einstein-dust equations which only exist for an arbitrarily small amount of CMC time. While this fact is plausible, it is not trivial to…
In this article, we consider the limit of quasi-local conserved quantities [31,9] at the infinity of an asymptotically hyperbolic initial data set in general relativity. These give notions of total energy-momentum, angular momentum, and…
We find complete hypersurfaces of constant curvature in hyperbolic space with a prescribed asymptotic boundary at infinity for a general class of (elliptic) curvature functions which includes the higher order mean curvatures and their…
We prove that a spacelike spherical symmetric constant mean curvature (SSCMC) surface and a general spacelike constant mean curvature (CMC) surface with certain boundary condition at the future null-infinity in Schwarzschild spacetime are…
We show that extreme Myers-Perry initial data realize the unique absolute minimum of the total mass in a physically relevant (Brill) class of maximal, asymptotically flat, bi-axisymmetric initial data for the Einstein equations with fixed…
We study the difficulties associated with the evaluation of the total Bondi momentum at finite distances around the central source of a general (asymptotically flat) spacetime. Since the total momentum is only rigorously defined at future…