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In this work we give a complete picture of how to in a direct simple way define the mass at null infinity in harmonic coordinates in three different ways that we show satisfy the Bondi mass loss law. The first and second way involve only the limit of metric (Trautman mass) respectively the null second fundamental forms along asymptotically characteristic surfaces (asymptotic Hawking mass) that only depend on the ADM mass. The last in an original way involves construction of special characteristic coordinates at null infinity (Bondi mass). The results here rely on asymptotics of the metric derived in [24].
The main objective of this work, is to show two inequivalent methods to obtain new spherical symmetric solutions of Einsteins Equations with anisotropy in the pressures in isotropic coordinates. This was done inspired by the MGD method, which is know
We prove an inequality relating the trace of the extrinsic curvature, the total angular momentum, the centre of mass, and the Trautman-Bondi mass for a class of gravitational initial data sets with constant mean curvature extending to null infinity.
We show that the spherically symmetric Einstein-scalar-field equations for wave-like decaying initial data at null infinity have unique global solutions in (0, infty) and unique generalized solutions on [0, infty) in the sense of Christodoulou. We emphasize that this decaying condition is sharp.
We present two methods to include the asymptotic domain of a background spacetime in null directions for numerical solutions of evolution equations so that both the radiation extraction problem and the outer boundary problem are solved. The first met
We present a symmetric hyperbolic formulation of the Einstein equations in affine-null coordinates. Giannakopoulos et. al. (arXiv:2007.06419) recently showed that the most commonly numerically implemented formulations of the Einstein equations in aff