Electronic ISBN:  9781470410643 
Product Code:  MEMO/226/1064.E 
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 226; 2013; 76 ppMSC: Primary 53; 83;
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

Chapters

1. Introduction

2. Preliminaries

3. Cauchy completion of a generalized metric space

4. Riemannian Gromov and Busemann completions

5. Finslerian completions

6. Cboundary of standard stationary spacetimes


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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.

Chapters

1. Introduction

2. Preliminaries

3. Cauchy completion of a generalized metric space

4. Riemannian Gromov and Busemann completions

5. Finslerian completions

6. Cboundary of standard stationary spacetimes