The magnetic part of the Weyl tensor, and the expansion of discrete universes

Clifton, Timothy; Gregoris, Daniele; Rosquist, Kjell

doi:10.1007/s10714-017-2192-0

Cited by 21 publications

(38 citation statements)

References 20 publications

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“…It seems worthwhile to use these results to illustrate the (1+1+2) decomposition of the Weyl tensor discussed in detail in Ref. [18] and Appendix A of Ref. [2].…”

Section: B W-metricmentioning

confidence: 92%

Twisted gravitational waves of Petrov type D

2018

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Twisted gravitational waves (TGWs) are nonplanar unidirectional Ricci-flat solutions of general relativity. Thus far only TGWs of Petrov type II are implicitly known that depend on a solution of a partial differential equation and have wave fronts with negative Gaussian curvature. A special Petrov type D class of such solutions that depends on an arbitrary function is explicitly studied in this paper and its Killing vectors are worked out. Moreover, we concentrate on two solutions of this class, namely, the Harrison solution and a simpler solution we call the w-metric and determine their Penrose plane-wave limits. The corresponding transition from a nonplanar TGW to a plane gravitational wave is elucidated.

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“…It seems worthwhile to use these results to illustrate the (1+1+2) decomposition of the Weyl tensor discussed in detail in Ref. [18] and Appendix A of Ref. [2].…”

Section: B W-metricmentioning

confidence: 92%

Twisted gravitational waves of Petrov type D

2018

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“…, n − 1. For n ≥ 3 it can be shown that curves associated with such a discrete symmetry group have the LRS property [6] while for n = 2 this does not follow (see discussion in [5] and [7]). Vectors and tensors satisfying (9) have the following properties when evaluated along LRS curves:…”

Section: Locally Rotationally Symmetric Curvesmentioning

confidence: 99%

“…We restrict attention to the LRS curve for which the evolution can be studied by analytical methods. The evolution is governed by the system of ordinary differential equations [6,7] …”

Section: Equations Governing Dynamicsmentioning

confidence: 99%

“…(22) can be evaluated recursively in a truncated Taylor series over time. The first and second order terms are zero, permitting us to stick with the third order term only, given by [7] Fig. 18 The red curve depicts the ODE (22), while the blue curve corresponds to the curlH term (34).…”

Section: Calculating the Curlh-termmentioning

confidence: 99%

“…[3]). A new avenue to address this issue was recently opened by considering a universe filled with Schwarzschild black holes as sources [4][5][6][7][8][9]. The idea is to first specify the sources as initial data on a time-symmetric spatial hypersurface with spherical topology.…”

Section: Introductionmentioning

confidence: 99%

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Analytic analysis of irregular discrete universes

Jolin

Rosquist

2018

Gen Relativ Gravit

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In this work we investigate the dynamics of cosmological models with spherical topology containing up to 600 Schwarzschild black holes arranged in an irregular manner. We solve the field equations by tessellating the 3-sphere into eight identical cells, each having a single edge which is shared by all cells. The shared edge is enforced to be locally rotationally symmetric, thereby allowing for solving the dynamics to high accuracy along this edge. Each cell will then carry an identical (up to parity) configuration which can however have an arbitrarily random distribution. The dynamics of such models is compared to that of previous works on regularly distributed black holes as well as with the standard isotropic dust models of the FLRW type. The irregular models are shown to have richer dynamics than that of the regular models. The randomization of the distribution of the black holes is done both without bias and also with a certain clustering bias. The geometry of the initial configuration of our models is shown to be qualitatively different from the regular case in the way it approaches the isotropic model.

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Cosmological solutions with charged black holes

2017

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We consider the problem of constructing cosmological solutions of the Einstein-Maxwell equations that contain multiple charged black holes. By considering the field equations as a set of constraint and evolution equations, we construct exact initial data for N charged black holes on a hypersphere. This corresponds to the maximum of expansion of a cosmological solution, and provides sufficient information for a unique evolution. We then consider the specific example of a universe that contains eight charged black holes, and show that the existence of non-zero electric charge reduces the scale of the cosmological region of the space. These solutions generalize the Majumdar-Papapetrou solutions away from the extremal limit of charged black holes, and provide what we believe to be some of the first relativistic calculations of the effects of electric charge on cosmological backreaction.

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The magnetic part of the Weyl tensor, and the expansion of discrete universes

Cited by 21 publications

References 20 publications

Twisted gravitational waves of Petrov type D

Twisted gravitational waves of Petrov type D

Analytic analysis of irregular discrete universes

Cosmological solutions with charged black holes

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