The mass of asymptotically hyperbolic Riemannian manifolds
Differential Geometry
2007-05-23 v2 Mathematical Physics
math.MP
Abstract
We present a set of global invariants, called "mass integrals", which can be defined for a large class of asymptotically hyperbolic Riemannian manifolds. When the "boundary at infinity" has spherical topology one single invariant is obtained, called the mass; we show positivity thereof. We apply the definition to conformally compactifiable manifolds, and show that the mass is completion-independent. We also prove the result, closely related to the problem at hand, that conformal completions of conformally compactifiable manifolds are unique.
Keywords
Cite
@article{arxiv.math/0110035,
title = {The mass of asymptotically hyperbolic Riemannian manifolds},
author = {Piotr T. Chrusciel and Marc Herzlich},
journal= {arXiv preprint arXiv:math/0110035},
year = {2007}
}
Comments
27 pages, Latex2e with several style files; various misprints corrected, positivity theorem for black holes considerably strengthened, to appear in Pacific Jour. of Mathematics