2018
DOI: 10.1142/s0217751x18500525
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Quantum no-singularity theorem from geometric flows

Abstract: In this paper, we analyze the classical geometric flow as a dynamical system. We obtain an action for this system, such that its equation of motion is the Raychaudhuri equation. This action will be used to quantize this system. As the Raychaudhuri equation is the basis for deriving the singularity theorems, we will be able to understand the effects such a quantization will have on the classical singularity theorems. Thus, quantizing the geometric flow, we can demonstrate that a quantum space-time is complete (… Show more

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Cited by 14 publications
(24 citation statements)
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“…It would be interesting to examine quantum effects (which depend on the wavefunction of the fluid) over and above the above classical terms. However, since these effects are always repulsive in nature, and prevents the quantal trajectories (quantum counterparts of geodesics) from crossing, such effects should reinforce the above conclusion [46,47].…”
Section: Discussionmentioning
confidence: 83%
“…It would be interesting to examine quantum effects (which depend on the wavefunction of the fluid) over and above the above classical terms. However, since these effects are always repulsive in nature, and prevents the quantal trajectories (quantum counterparts of geodesics) from crossing, such effects should reinforce the above conclusion [46,47].…”
Section: Discussionmentioning
confidence: 83%
“…The motivation of the present work is to find a "correct" quantum version of the Raychaudhuri equation following the approach as that of Alsaleh et al [36]. We arrive at an equation which is valid for an arbitrary dimension.…”
Section: Introductionmentioning
confidence: 97%
“…The idea of presenting a geodesic congruence as a dynamical system was suggested by Alsaleh et al [36]. Their method is an attempt to reveal what a back to basics endeavour can do.…”
Section: Introductionmentioning
confidence: 99%
“…Saurya Das has proposed in the quantum theory a Raychaudhuri equation where the usual classical trajectories are replaced by Bohmian trajectories [7]. Bohmian trajectories do not converge and thus the issue of geodesic incompleteness, singularities such as big bang or big crunch can be avoided [8,9]. In this paper we treat the classical geometrical flow as a dynamical system in such a way that the Raychaudhuri equation becomes the equation of motion and that the action can be used to quantize the dynamical system.…”
Section: Introductionmentioning
confidence: 99%
“…The study is expected to show the effect such a quantization will have on the geometrical flow, and as part of the process it can be shown that a quantum space-time is non-singular. The existence of a conjugate point is a necessary condition for the occurrence of singularities [9]. However it is possible to demonstrate that conjugate points cannot arise because of the quantum effects.…”
Section: Introductionmentioning
confidence: 99%