Particle production from signature change

Dray, Tevian; Manogue, Corinne A.; Tucker, Robin

doi:10.1007/bf00756915

Cited by 73 publications

(103 citation statements)

References 4 publications

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“…In our proposal, the study of the change of signature becomes the simple geometrical analysis of imbedded submanifolds in the bulk: a well-posed mathematical problem without pathologies. It is remarkable that many of the traditional ad hoc assumptions concerning signature change [10] are shown to become pure necessary conditions in the brane case, which indirectly proves the plausibility of our idea and makes it worth exploring it, possibly sheding some light into the "signature-change controversy" [10].Whether a signature change occurred in our effective spacetime is debatable, and several independent works have considered this possibility [12,11]. From a classical viewpoint, a signature change may serve to avoid the singularities of general relativity [13], such as the big-bang, which might be replaced by a Euclidean region prior to the birth of time.…”

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confidence: 68%

Signature Change on the Brane

2001

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We explore the possibility of having a good description of classical signature change in the brane scenario.PACS Numbers: 04.50.+h, 98.80.Cq, 11.10.Kk, 04.20.Gz.The aim of this letter is to show, in simple terms, that a natural scenario for the change of signature in the physical spacetime is provided by the brane-world models [1][2][3] (see also [4][5][6] for an exhaustive list of references) or, in general, by every higher-dimensional theory [7] which may contain domain walls and/or branes.The main idea behind our proposal is that d-branes are nothing but timelike (d + 1)-surfaces in a higherdimensional spacetime (the bulk) [8]. However, nothing prevents the possibility of having perfectly regular branes which change its character from (say) spacelike to timelike, or which are partly null, or even more complicated possibilities. The first case corresponds to a signaturechanging brane. The interesting property is that both the bulk and the brane can be regular everywhere even though the change of signature may appear as a dramatical event when seen from within the brane. Notice that the signature in the bulk is left unchanged, so that our work differs significantly from other recent studies [9]. In our proposal, the study of the change of signature becomes the simple geometrical analysis of imbedded submanifolds in the bulk: a well-posed mathematical problem without pathologies. It is remarkable that many of the traditional ad hoc assumptions concerning signature change [10] are shown to become pure necessary conditions in the brane case, which indirectly proves the plausibility of our idea and makes it worth exploring it, possibly sheding some light into the "signature-change controversy" [10].Whether a signature change occurred in our effective spacetime is debatable, and several independent works have considered this possibility [12,11]. From a classical viewpoint, a signature change may serve to avoid the singularities of general relativity [13], such as the big-bang, which might be replaced by a Euclidean region prior to the birth of time. Signature change has also been vindicated as an effective classical description of both the no-boundary proposal [14] and the quantum tunneling [15] approach for the prescription of the Universe's wave function in quantum cosmology. In general, every process which can be studied by resorting to the "imaginary time", e.g. [14], can be also analyzed by means of change of the signature. All these possibilities could be naturally considered in our proposal.As a matter of concreteness we will focus on the recent models based on a single 3-brane embedded into a five-dimensional Lorentzian manifold with a noncompact fifth dimension [3] (a more geometrically focused review of this model can be found in [5]) and [16,17]. We can think of such a brane model as consisting of two Lorenztian regions joined together across corresponding smooth timelike boundaries. The matching between the two manifolds can be performed as long as the induced metrics on the two boundaries are isometric....

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confidence: 68%

Signature Change on the Brane

2001

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“…The problem of finding a generalization of general relativity which includes degenerate metrics has been studied in the past, motivated by the consideration of a class of metrics, the so called signature-changing metrics [21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,46,37,38,39] , which give a classical realization of the change of signature in quantum cosmology conjectured by Hartle and Hawking [40,41,42,43,44]. The classical change of signature for a homogeneous, isotropic and spatially flat universe is realized by a metric tensor defined by the following line element…”

Section: Isochronous Cosmologiesmentioning

confidence: 99%

Isochronous Spacetimes

Briscese

Calogero

2014

Acta Appl Math

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The possibility has been recently demonstrated to manufacture (nonrelativistic, Hamiltonian) many-body problems which feature an isochronous time evolution with an arbitrarily assigned period T yet mimic with good approximation, or even exactly, any given many-body problem (within a quite large class, encompassing most of nonrelativistic physics) over timesT which may also be arbitrarily large (but of course such thatT < T ). In this paper we review and further explore the possibility to extend this finding to a general relativity context, so that it becomes relevant for cosmology.

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“…We have proposed a formalism to deal with initial conditions formulated in Euclidean regimes, showing how they can be translated into initial conditions in the Lorentzian sector by means of the vacuum evolution and suitable continuity conditions in the process of signature change, making the framework compatible with the selection of a Fock quantization based on the uniqueness criterion that we have put forward. The continuity conditions that we have suggested are inspired by the works of Dray et al [36], in which particle production is proven to occur for a massless scalar field propagating in a signature changing spacetime, consisting of a Euclidean region between two Lorentzian parts of the spacetime. In addition, an extensive discussion about signature changing events and their consequences in Bose-Einstein condensates can be found in Ref.…”

Section: Discussionmentioning

confidence: 99%

“…At that point, it is necessary to provide matching conditions relating the considered solution for the field to another one in the Lorentzian region beyond the signature change. In order to do this, we adopt the ideas presented by Dray et al [36], which require continuity for the KG field and its time derivative on the hypersurface where the signature flips. An extended analysis can also be found in Ref.…”

Section: A Matching Conditionsmentioning

confidence: 99%

Uniqueness of the Fock quantization of scalar fields and processes with signature change in cosmology

Gomar

Marugán

2014

Phys. Rev. D

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We study scalar fields subject to an equation of the Klein-Gordon type in nonstationary spacetimes, such as those found in cosmology, assuming that all the relevant spatial dependence is contained in the Laplacian. We show that the field description -with a specific canonical pair-and the Fock representation for the quantization of the field are fixed indeed in a unique way (except for unitary transformations that do not affect the physical predictions) if we adopt the combined criterion of (a) imposing the invariance of the vacuum under the group of spatial symmetries of the field equations and (b) requiring a unitary implementation of the dynamics in the quantum theory. Besides, we provide a spacetime interpretation of the field equations as those corresponding to a scalar field in a cosmological spacetime that is conformally ultrastatic. In addition, in the privileged Fock quantization, we investigate the generalization of the evolution of physical states from the hyperbolic dynamical regime to an elliptic regime. In order to do this, we contemplate the possibility of processes with signature change in the spacetime where the field propagates and discuss the behavior of the background geometry when the change happens, proving that the spacetime metric degenerates. Finally, we argue that this kind of signature change leads naturally to a phenomenon of particle creation, with exponential production.

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Particle production from signature change

Cited by 73 publications

References 4 publications

Signature Change on the Brane

Signature Change on the Brane

Isochronous Spacetimes

Uniqueness of the Fock quantization of scalar fields and processes with signature change in cosmology

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