Spacetime Boundaries and Completions

In General
* Idea: Boundaries are attached to spacetime manifolds in certain directions in one of two contexts,
(i) The spacetime is non-compact and "infinite" (an affine parameter along a geodesic has an infinite range of values) along those directions, and is asymptotic to a spacetime of a highly symmetric, well-known form (mainly Minkowski or AdS); Compactifying spacetime along those directions by a conformal transformation allows one to define fields on the boundary that encode information on the rate of approach of various metric and curvature components to those of the asymptotic spacetime, and this information can be related to observable quantities;
(ii) The spacetime has a singularity a finite affine parameter distance from points in its interior, and compactifying it by defining a boundary there allows to study the structure of the singularity better.
@ Approaches: Rácz JMP(93), a0803; Marolf & Ross CQG(03)gq [future/past set pairs].
@ Conformal compactification: Penrose PRS(65) [at null infinity]; Herranz & Santander JPA(02); Dussan & Magid JGP(07); > s.a. asymptotic flatness.
@ With a cosmological constant: Ashtekar & Magnon CQG(84); Henneaux & Teitelboim CMP(85).

Specific Types of Boundaries
* b-boundary: A way of attaching endpoints to inextendible endless curves in a spacetime; The b-boundary of a manifold M with connection is constructed by forming the Cauchy completion of the frame bundle LM equipped with a certain Riemannian metric, the b-metric G.
@ Causal boundary and completion: Geroch et al PRS(72) [strongly causal spacetime]; Budic & Sachs JMP(74) [causally continuous spacetime]; Beem GRG(77) [metric topology]; Rácz GRG(88); Flores & Harris CQG(07)gq/06 [topology, static]; Flores CMP(07)gq/06; Alana & Flores a0704 [for product manifolds].
@ General references: Geroch et al JMP(82); Szabados CQG(88), CQG(89); Szekeres in(94); Harris gq/03-in [outline].
@ b-boundary: Schmidt GRG(71); Dodson GRG(79) [modification]; Ståhl CMP(99)gq, gq/00/JMP, gq/00/JMP.
@ Properties: Ashley GRG(02)gq [stability of essential singularities].
@ For Friedmann solution: Bosshard CMP(76); Johnson JMP(77); Amores & Gutiérrez JGP(99).
@ Abstract boundary: Scott & Szekeres JGP(94)gq; Ashley & Scott gq/03/CM [singularity theorems].
@ Other boundaries: Meyer JMP(86); Harris JMP(98)gq/97, CQG(00) [future chronological boundary]; Harada & Nakao PRD(04)gq ["border"].

Specific Types of Spacetimes > s.a. Kaluza-Klein theory; reissner-nordström; types of spacetimes.
@ Schwarzschild: Lynden-Bell & Katz MNRAS(90); Ho gq/93/PLA; Peeters et al CQG(95)gq/94; Heinzle & Steinbauer JMP(02)gq/01.
@ Other types: Flores & Sánchez JHEP(08)-a0712 [wave-type spacetimes].

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Send feedback and suggestions to bombelli at olemiss.edu – Modified 12 jun 2008