Causal continuity in degenerate spacetimes

Borde, Arvind; Dowker, Fay; Garcia, Raquel S.; Sorkin, Rafael D.; Surya, Sumati

doi:10.1088/0264-9381/16/11/303

Cited by 38 publications

(66 citation statements)

References 26 publications

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“…We then show that the above conjecture implies the k-causal continuity in the spacetime with the degeneracies is equivalent to the causal continuity of the spacetime with the degeneracies excised. We also show that, independently of whether the conjecture holds, index 1 and n − 1 Morse spacetimes are k-causally discontinuous, as expected [7,8].…”

Section: Introductionsupporting

confidence: 58%

“…In particular, one can construct a rather general class of such spacetimes which contain only isolated degeneracies. These "Morse spacetimes" were studied in detail in [6,16,7] within the Sum-Over-Histories approach to quantum gravity, and can be defined in any topological cobordism, as follows.…”

Section: Causal Continuity In Morse Spacetimesmentioning

confidence: 99%

“…Traditionally, such degeneracies are excised from the spacetime, so that what remains is a globally Lorentzian spacetime. This was the procedure followed in [7,8], to examine the causal continuity of Morse spacetimes. One way to incorporate the degeneracies in the overall causal structure would be to treat them as the boundaries of the spacetime, in the sense of [9].…”

Section: Introductionmentioning

confidence: 99%

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K -causality and degenerate spacetimes

Dowker¹,

Garcia²,

Surya³

2000

Class. Quantum Grav.

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The causal relation K + was introduced by Sorkin and Woolgar to extend the standard causal analysis of C 2 spacetimes to those that are only C 0 . Most of their results also hold true in the case of spacetimes with degeneracies. In this paper we seek to examine K + explicitly in the case of Lorentzian topology changing Morse spacetimes containing isolated degeneracies. We first demonstrate some interesting features of this relation in globally Lorentzian spacetimes. In particular, we show that K + is robust and that it coincides with the Seifert relation when the spacetime is stably causal. Moreover, the Hawking and Sachs characterisation of causal continuity translates into a natural expression in terms of K + for general spacetimes. We then examine K + in topology changing Morse spacetimes both with and without the degeneracies and find further characterisations of causal continuity. a f.dowker@qmw.ac.uk,

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Section: Introductionsupporting

confidence: 58%

Section: Causal Continuity In Morse Spacetimesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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K -causality and degenerate spacetimes

Dowker¹,

Garcia²,

Surya³

2000

Class. Quantum Grav.

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“…In a series of papers Sorkin, Dowker et.al. [7,8,9] analyzed possible topology changes. In particular they showed that causal discontinuity occurs if and only if the Morse index is 1 or n − 1, i.e.…”

Section: Introductionmentioning

confidence: 99%

How to obtain a cosmological constant from small exotic R4

Asselmeyer-Maluga

Król

2018

Physics of the Dark Universe

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In this paper we determine the cosmological constant as a topological invariant by applying certain techniques from low dimensional differential topology. We work with a small exotic R 4 which is embedded into the standard R 4 . Any exotic R 4 is a Riemannian smooth manifold with necessary non-vanishing curvature tensor. To determine the invariant part of such curvature we deal with a canonical construction of R 4 where it appears as a part of the complex surface K3#CP (2). Such R 4 's admit hyperbolic geometry. This fact simplifies significantly the calculations and enforces the rigidity of the expressions. In particular, we explain the smallness of the cosmological constant with a value consisting of a combination of (natural) topological invariant. Finally, the cosmological constant appears to be a topologically supported quantity.

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“…Firstly, there is no barrier to sprinkling into manifolds with spatial topology change, as long as it is degeneracy of the metric at a set of isolated points that enables topology change, and not the existence of closed timelike curves (one of these conditions must exist for topology change to occur, see e.g. [48] and references therein) -and in this discrete theory there is no problem with characterising the set of histories. For those who believe that topology change will be necessary in quantum gravity [11,49], this is important.…”

Section: Reconstructing the Continuummentioning

confidence: 99%

The causal set approach to Quantum Gravity

Henson¹

2009

Approaches to Quantum Gravity

128

193

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The ideas of spacetime discreteness and causality are important in several of the popular approaches to quantum gravity. But if discreteness is accepted as an initial assumption, conflict with Lorentz invariance can be a consequence. The causal set is a discrete structure which avoids this problem and provides a possible history space on which to build a "path integral" type quantum gravity theory. Motivation, results and open problems are discussed and some comparisons to other approaches are made. Some recent progress on recovering locality in causal sets is recounted. On the occasion of his 60th birthday, this article is dedicated to Rafael Sorkin, without whom the causal set idea would not have survived its infancy.How can we reach a theory of quantum gravity? Many answers to this question have been proposed, motivated by different experiences and views of current theories [1]. A more specific set of questions might be: what demands should we put on our framework, so that it is best able to meet all the challenges involved in creating a theory of quantum gravity? What choices are most likely to give the correct theory, according to the clues we have from known physics? Are there any problems with our initial assumptions that may lead to trouble further down the road? The latter seems to be one of the most important strategic questions when beginning to formulate a candidate theory. For example, can a canonical approach overcome the multifaceted problem of time? And how far can a theory based on a fixed background spacetime be pushed? On the one hand, these questions may only be answered in the very attempt to formulate the theory. On the other, many such attempts have been made, and now that quantum gravity research has built up some history, perhaps it is time to plough some of the experience gained back into a new approach, laying the groundwork for our theory in such a way as to avoid well-known problems. The causal set program [2,3,4,5,6] represents such an attempt.In this review, some answers to the above questions, as embodied by the causal set program, are set out and explained, and some of their consequences are given. As part of this, the results and open problems in the program are discussed. In section 1, reasons for hypothesising spacetime discreteness are reviewed. The definition of a causal set is given, along with the proposed correspondence principle between this structure and the effective continuum description of spacetime. Then some of the unique features of this discretisation scheme are discussed. In section 2, ideas for causal set dynamics are given. Next, a review is made of some phenomenological models based on this quantum gravity program, and successes and challenges in this line of work are summarised. The final section deals with the issue of recovering locality for causal sets, something which touches

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Causal continuity in degenerate spacetimes

Cited by 38 publications

References 26 publications

K -causality and degenerate spacetimes

K -causality and degenerate spacetimes

How to obtain a cosmological constant from small exotic R4

The causal set approach to Quantum Gravity

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