Scalar field as a time variable during gravitational evolution

2016

J. High Energ. Phys.

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Investigating the dynamics of gravitational systems, especially in the regime of quantum gravity, poses a problem of measuring time during the evolution. One of the approaches to this issue is using one of the internal degrees of freedom as a time variable. The objective of our research was to check whether a scalar field or any other dynamical quantity being a part of a coupled multi-component matter-geometry system can be treated as a 'clock' during its evolution. We investigated a collapse of a self-gravitating electrically charged scalar field in the Einstein and Brans-Dicke theories using the 2+2 formalism. Our findings concentrated on the spacetime region of high curvature existing in the vicinity of the emerging singularity, which is essential for the quantum gravity applications. We investigated several values of the Brans-Dicke coupling constant and the coupling between the Brans-Dicke and the electrically charged scalar fields. It turned out that both evolving scalar fields and a function which measures the amount of electric charge within a sphere of a given radius can be used to quantify time nearby the singularity in the dynamical spacetime part, in which the apparent horizon surrounding the singularity is spacelike. Using them in this respect in the asymptotic spacetime region is possible only when both fields are present in the system and, moreover, they are coupled to each other. The only nonzero component of the Maxwell field four-potential cannot be used to quantify time during the considered process in the neighborhood of the whole central singularity. None of the investigated dynamical quantities is a good candidate for measuring time nearby the Cauchy horizon, which is also singular due to the mass inflation phenomenon.

Section: Dynamical Quantities In the Evolving Spacetimesupporting

confidence: 90%

Section: Discussionmentioning

confidence: 62%

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Scalar field as an intrinsic time measure in coupled dynamical matter-geometry systems. II. Electrically charged gravitational collapse

2016

J. High Energ. Phys.

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“…11. 44 Overall, using scalar fields as time variables within whole spacetimes during dynamical gravitational evolutions of coupled matter-geometry systems is limited. First, the two above conditions which are necessary for treating the field as a time measurer are not fulfilled in the whole spacetimes.…”

Section: Applications To (Loop) Quantum Gravitymentioning

confidence: 99%

Black hole factory: A review of double-null formalism

Nakonieczny

2019

Int. J. Mod. Phys. D

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In this review paper, we comprehensively summarize numerical applications of doublenull formalism for studying dynamics within the theory of gravity. By using the doublenull coordinates, we can investigate dynamical black holes and gravitational phenomena within spherical symmetry, including gravitational collapse, formation of horizons and singularities, as well as evaporations. This formalism can be extended to generic situations, where we can change dimensions, topologies, the gravity sector, as well as the matter sector. We also discuss its possible implications for black hole physics and particle astrophysics. This strong numerical tool will have lots of future applications for various research areas including general relativity, string theory, and various approaches to quantum gravity.

“…Hence, there exists a need for research on dynamical processes, which will justify or contradict the above-mentioned assumptions. An introductory attempt in respect of validating these premises was made using the simplest matter-geometry model, which involved a gravitationally self-interacting scalar field minimally coupled to gravity [62]. It turned out that the sole scalar field evolving in the spacetime under the influence of gravitational selfinteraction possesses properties, which predestine it for being a time measurer, especially in the area of high curvature nearby the singularity.…”

Section: Introductionmentioning

confidence: 99%

Scalar field as an intrinsic time measure in coupled dynamical matter-geometry systems. I. Neutral gravitational collapse

2016

J. High Energ. Phys.

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There does not exist a notion of time which could be transferred straightforwardly from classical to quantum gravity. For this reason, a method of time quantification which would be appropriate for gravity quantization is being sought. One of the existing proposals is using the evolving matter as an intrinsic 'clock' while investigating the dynamics of gravitational systems. The objective of our research was to check whether scalar fields can serve as time variables during a dynamical evolution of a coupled multicomponent matter-geometry system. We concentrated on a neutral case, which means that the elaborated system was not charged electrically nor magnetically. For this purpose, we investigated a gravitational collapse of a self-interacting complex and real scalar fields in the Brans-Dicke theory using the 2+2 spacetime foliation. We focused mainly on the region of high curvature appearing nearby the emerging singularity, which is essential from the perspective of quantum gravity. We investigated several formulations of the theory for various values of the Brans-Dicke coupling constant and the coupling between the Brans-Dicke field and the matter sector of the theory. The obtained results indicated that the evolving scalar fields can be treated as time variables in close proximity of the singularity due to the following reasons. The constancy hypersurfaces of the Brans-Dicke field are spacelike in the vicinity of the singularity apart from the case, in which the equation of motion of the field reduces to the wave equation due to a specific choice of free evolution parameters. The hypersurfaces of constant complex and real scalar fields are spacelike in the regions nearby the singularities formed during the examined process. The values of the field functions change monotonically in the areas, in which the constancy hypersurfaces are spacelike.