Flat synchronizations in spherically symmetric space-times

Herrero, Alicia; Morales-Lladosa, Juan Antonio

doi:10.1088/1742-6596/229/1/012043

Cited by 2 publications

(3 citation statements)

References 8 publications

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“…This is determined by a curve γ in the (r, t)-plane. Let ds be the metric restricted to γ then from (1) we have (5) ds 2 = −Q dt 2 + P dr 2 along γ . At each point of γ we have a 2-sphere of radius r and by the result just proved, the slice is flat iff ds 2 /dr 2 = 1.…”

Section: Flat Space Slicesmentioning

confidence: 99%

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Natural flat observer fields in spherically symmetric space-times

MacKay¹,

Rourke²

2015

J. Phys. A: Math. Theor.

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An observer field in a space-time is a time-like unit vector field. It is natural if the integral curves (field lines) are geodesic and the perpendicular 3-plane field is integrable (giving normal space slices). We prove that a natural observer field determines a coherent notion of time: a coordinate that is constant on the perpendicular space slices and whose difference between two space slices is the proper time along any field line. A natural observer field is flat if the normal space slices are metrically flat. For static spherically-symmetric space-times we find a necessary and sufficient condition for possession of a spherically-symmetric natural flat observer field. In this case, which includes the Schwarzschild and the Kottler space-times, there is in fact a dual pair of spherically-symmetric natural flat observer fields. One of these observer fields is expanding and the other contracting and it is natural to describe the expanding field as the "escape" field and the dual contracting field as the "capture" field. Observer fields are useful for understanding redshift and the fields described here are used in a possible explanation of redshift explored in [8].

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Section: Flat Space Slicesmentioning

confidence: 99%

“…Notes The existence of flat space slices for the Schwarzschild and de Sitter metrics is well known and this is also known for more general metrics (see eg [5,12,4,6] and their bibliographies). The normal geodesic field is also known in the special cases of the Schwarzschild and Reissner-Nordström metrics [10].…”

Section: Introductionmentioning

confidence: 99%

Natural flat observer fields in spherically symmetric space-times

MacKay¹,

Rourke²

2015

J. Phys. A: Math. Theor.

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“…Finally, in section 7 we discuss the role that our results can play for a better understanding of the geometry and physics in SSSTs. Some preliminary results of this work were presented at the Spanish Relativity meeting ERE-2009 [37].…”

Section: Introductionmentioning

confidence: 99%

Painlevé–Gullstrand synchronizations in spherical symmetry

Herrero

Morales-Lladosa

2010

Class. Quantum Grav.

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Abstract. A Painlevé-Gullstrand synchronization is a slicing of the space-time by a family of flat spacelike 3-surfaces. For spherically symmetric space-times, we show that a Painlevé-Gullstrand synchronization only exists in the region where (dr) 2 ≤ 1, r being the curvature radius of the isometry group orbits (2-spheres). This condition says that the Misner-Sharp gravitational energy of these 2-spheres is not negative and has an intrinsic meaning in terms of the norm of the mean extrinsic curvature vector. It also provides an algebraic inequality involving the Weyl curvature scalar and the Ricci eigenvalues. We prove that the energy and momentum densities associated with the Weinberg complex of a Painlevé-Gullstrand slice vanish in these curvature coordinates, and we give a new interpretation of these slices by using semi-metric Newtonian connections. It is also outlined that, by solving the vacuum Einstein's equations in a coordinate system adapted to a Painlevé-Gullstrand synchronization, the Schwarzschild solution is directly obtained in a whole coordinate domain that includes the horizon and both its interior and exterior regions.

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Flat synchronizations in spherically symmetric space-times

Cited by 2 publications

References 8 publications

Natural flat observer fields in spherically symmetric space-times

Natural flat observer fields in spherically symmetric space-times

Painlevé–Gullstrand synchronizations in spherical symmetry

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