arXiv subjects

Edward T. Bryden

Publications and source records attributed to Edward T. Bryden.

3 recordsLinked to original sources

arXiv2021

The Positive Mass Theorem with Angular Momentum and Charge for Manifolds with Boundary

Motivated by the cosmic censorship conjecture in mathematical relativity, we establish the precise mass lower bound for an asymptotically flat Riemannian 3-manifold with nonnegative scalar curvature and minimal surface boundary, in terms of angular momentum and charge. In particular this result does not require the restrictive assumptions of simple connectivity and completeness, which are undesirable from both a mathematical and physical perspective.

gr-qc↗

arXiv2018

Stability of the Positive Mass Theorem for Axisymmetric Manifolds

Away from the central axis, we prove the stability of the Positive Mass Theorem in the $W^{1,p}$ sense for asymptotically flat axisymmetric manifolds with nonnegative scalar curvature satisfying some additional technical assumptions. We also derive estimates for the volumes of regions, the areas of axisymmetric surfaces, and the distances between points within the manifolds.

math.DG↗

arXiv2016

The Area-Angular Momentum-Charge Inequality for Black Holes With Positive Cosmological Constant

We establish the conjectured area-angular momentum-charge inequality for stable apparent horizons in the presence of a positive cosmological constant, and show that it is saturated precisely for extreme Kerr-Newman-de Sitter horizons. As with previous inequalities of this type, the proof is reduced to minimizing an `area functional' related to a harmonic map energy; in this case maps are from the 2-sphere to the complex hyperbolic plane. The proof here is simplified compared to previous results for less embellished inequalities, due to the observation that the functional is convex along geodesic deformations in the target.

gr-qc↗