Memoirs of the American Mathematical Society 2013; 76 pp; softcover Volume: 226 ISBN10: 0821887750 ISBN13: 9780821887752 List Price: US$69 Individual Members: US$41.40 Institutional Members: US$55.20 Order Code: MEMO/226/1064
 Recently, the old notion of causal boundary for a spacetime \(V\) has been redefined consistently. The computation of this boundary \(\partial V\) on any standard conformally stationary spacetime \(V=\mathbb{R}\times M\), suggests a natural compactification \(M_B\) associated to any Riemannian metric on \(M\) or, more generally, to any Finslerian one. The corresponding boundary \(\partial_BM\) is constructed in terms of Busemanntype functions. Roughly, \(\partial_BM\) represents the set of all the directions in \(M\) including both, asymptotic and "finite" (or "incomplete") directions. This Busemann boundary \(\partial_BM\) is related to two classical boundaries: the Cauchy boundary \(\partial_{C}M\) and the Gromov boundary \(\partial_GM\). The authors' aims are: (1) to study the subtleties of both, the Cauchy boundary for any generalized (possibly nonsymmetric) distance and the Gromov compactification for any (possibly incomplete) Finsler manifold, (2) to introduce the new Busemann compactification \(M_B\), relating it with the previous two completions, and (3) to give a full description of the causal boundary \(\partial V\) of any standard conformally stationary spacetime. Table of Contents  Introduction
 Preliminaries
 Cauchy completion of a generalized metric space
 Riemannian Gromov and Busemann completions
 Finslerian completions
 Cboundary of standard stationary spacetimes
 Bibliography
