Causally discontinuous space-times

Vyas, Utpal; Akolia, G. M.

doi:10.1007/bf00765889

Cited by 6 publications

(4 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Reflectivity was introduced by Kronheimer and Penrose (1967) through condition (iv). They actually imposed causality and our terminology of future and past is inverted with respect to theirs, but consistent with Vyas and Akolia (1986), Minguzzi and Sánchez (2008) and the subsequent literature (the terminological choice by Kronheimer and Penrose seems less natural in view of characterization (vi), but it is more natural in view of other results, cf. Remark 4.14).…”

Section: Reflectivity and Transverse Laddersupporting

confidence: 74%

See 1 more Smart Citation

Lorentzian causality theory

Minguzzi

2019

Living Rev Relativ

157

View full text Add to dashboard Cite

I review Lorentzian causality theory paying particular attention to the optimality and generality of the presented results. I include complete proofs of some foundational results that are otherwise difficult to find in the literature (e.g. equivalence of some Lorentzian length definitions, upper semi-continuity of the length functional, corner regularization, etc.). The paper is almost self-contained thanks to a systematic logical exposition of the many different topics that compose the theory. It contains new results on classical concepts such as maximizing curves, achronal sets, edges, horismos, domains of dependence, Lorentzian distance. The treatment of causally pathological spacetimes requires the development of some new versatile causality notions, among which I found particularly convenient to introduce: biviability, chronal equivalence, araying sets, and causal versions of horismos and trapped sets. Their usefulness becomes apparent in the treatment of the classical singularity theorems, which is here considerably expanded in the exploration of some variations and alternatives.

show abstract

Section: Reflectivity and Transverse Laddersupporting

confidence: 74%

“…through (v). Ishikawa (1979) and Vyas and Akolia (1986) studied the set where such a property fails.…”

Section: Reflectivity and Transverse Laddermentioning

confidence: 99%

Lorentzian causality theory

Minguzzi

2019

Living Rev Relativ

157

View full text Add to dashboard Cite

show abstract

“…There is a very rich literature on these topics on specialized books [1,3,10,12,14,[16][17][18] and on the original papers (see also [61][62][63][64][65][66][67][68][69][70][71][72][73][74][75][76][77][78]), but we thought it was important to analyze them in a single paper. This choice of arguments helps also nonexpert readers in gaining familiarity with concepts and techniques frequently used in classical gravity and which also find application in quantum gravity, as it happens for the theory of spinors and for Ashtekar's variables.…”

Section: Discussionmentioning

confidence: 99%

Mathematical Structures of Space-Time

Esposito

1992

Fortschr. Phys.

View full text Add to dashboard Cite

Abstract. At first we introduce the space-time manifold and we compare some aspects of Riemannian and Lorentzian geometry such as the distance function and the relations between topology and curvature. We then define spinor structures in general relativity, and the conditions for their existence are discussed. The causality conditions are studied through an analysis of strong causality, stable causality and global hyperbolicity. In looking at the asymptotic structure of space-time, we focus on the asymptotic symmetry group of Bondi, Metzner and Sachs, and the b-boundary construction of Schmidt. The Hamiltonian structure of space-time is also analyzed, with emphasis on Ashtekar's spinorial variables.Finally, the question of a rigorous theory of singularities in space-times with torsion is addressed, describing in detail recent work by the author. We define geodesics as curves 1 Mathematical Structures of Space-Time whose tangent vector moves by parallel transport. This is different from what other authors do, because their definition of geodesics only involves the Christoffel symbols, though studying theories with torsion. We then prove how to extend Hawking's singularity theorem without causality assumptions to the space-time of the ECSK theory. This is achieved studying the generalized Raychaudhuri equation in the ECSK theory, the conditions for the existence of conjugate points and properties of maximal timelike geodesics. Our result can also be interpreted as a no-singularity theorem if the torsion tensor does not obey some additional conditions. Namely, it seems that the occurrence of singularities in closed cosmological models based on the ECSK theory is less generic than in general relativity.Our work should be compared with important previous papers. There are some relevant differences, because we rely on a different definition of geodesics, we keep the field equations of the ECSK theory in their original form rather than casting them in a form similar to general relativity with a modified energy-momentum tensor, and we emphasize the role played by the full extrinsic curvature tensor and by the variation formulae. * Fortschritte der Physik, 40, 1-30 (1992). 2Mathematical Structures of Space-Time

show abstract

“…1.7]. Moreover, no point of R is isolated [55], and optimal bounds for its dimension are known [28,12]. From Lemma 3.46, obviously: (ii) The spacetime is past (resp.…”

Section: Proof (I) ⇒ (Ii) Let Imentioning

confidence: 99%