The extended conformal Einstein field equations with matter: The Einstein–Maxwell field

Abstract. The conformal structure of the Schwarzschild-de Sitter spacetime is analysed using the extended conformal Einstein field equations. To this end, initial data for an asymptotic initial value problem for the Schwarzschild-de Sitter spacetime are obtained. This initial data allow to understand the singular behaviour of the conformal structure at the asymptotic points where the horizons of the Schwarzschild-de Sitter spacetime meet the conformal boundary. Using the insights gained from the analysis of the Schwarzschild-de Sitter spacetime in a conformal Gaussian gauge, we consider nonlinear perturbations close to the Schwarzschild-de Sitter spacetime in the asymptotic region. We show that small enough perturbations of asymptotic initial data for the Schwarzschild-de Sitter spacetime give rise to a solution to the Einstein field equations which exists to the future and has an asymptotic structure similar to that of the Schwarzschild-de Sitter spacetime.

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“…The proof of Lemma 5 can be found in [20,21,53] -see also [41] for a discussion of these equations in the presence of an electromagnetic field.…”

Section: Conformal Gauss Gauge In Spinorial Form and Evolution Equationsmentioning

confidence: 99%

“…The Schwarzschild-de Sitter spacetime is the spherically symmetric solution to the Einstein field equationsR ab = λg ab (41) with, in the signature conventions of this article, a negative Cosmological constant given in static coordinates (t, r, θ, ϕ) byg…”

Section: The Schwarzschild-de Sitter Spacetimementioning

confidence: 99%

Perturbations of the Asymptotic Region of the Schwarzschild–de Sitter Spacetime

Gasperin

Kroon

2017

Ann. Henri Poincaré

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“…Using the spinorial Ricci identities to replace DE Γ E D AB in equation (16) and exploiting the symmetry…”

Section: Wave Equation For the Connection Coefficientsmentioning

confidence: 99%

“…The CEFE have been extended to include matter sources consisting of suitable trace-free matter -see e.g. [11,16,17]. The CEFE can be expressed in terms of a Weyl connection (i.e.…”

Section: Introductionmentioning

confidence: 99%

Spinorial wave equations and stability of the Milne spacetime

Gasperin

Kroon

2015

Class. Quantum Grav.

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The spinorial version of the conformal vacuum Einstein field equations are used to construct a system of quasilinear wave equations for the various conformal fields. As a part of analysis we also show how to construct a subsidiary system of wave equations for the zero quantities associated to the various conformal field equations. This subsidiary system is used, in turn, to show that under suitable assumptions on the initial data a solution to the wave equations for the conformal fields implies a solution to the actual conformal Einstein field equations. The use of spinors allows for a more unified deduction of the required wave equations and the analysis of the subsidiary equations than similar approaches based on the metric conformal field equations. As an application of our construction we study the non-linear stability of the Milne Universe. It is shown that sufficiently small perturbations of initial hyperboloidal data for the Milne Universe gives rise to a solution to the Einstein field equations which exist towards the future and has an asymptotic structure similar to that of the Milne Universe.

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“…A hyperbolic formulation as described in the previous paragraph has been developed by Friedrich [13,14] resulting in the so-called conformal field equations and they have been sucessfully used to prove a number of remarkable global existence results: first proof [9,10] of the non-linear stability of some of the simplest solutions of Einstein's equation (Minkowski and de Sitter) and similar results for the Einstein-Yang-Mills system [11] (see also [23]), purely radiative spacetimes [25], cosmological solutions [24] and the asymptotic region of the Schwarzschild-de Sitter black hole [19]. In any case, the rough idea is that the hyperbolic character of the conformal equations makes it possible to use classical local existence results of the partial differential equations theory to prove a local existence result for the former.…”

Section: Introductionmentioning

confidence: 99%

Type D conformal initial data

Gómez-Lobo

2020

Gen Relativ Gravit

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For a vacuum initial data set of the Einstein field equations it is possible to carry out a conformal rescaling or conformal compactification of the data. This gives rise to a conformal hyperboloidal initial data set for the vacuum conformal equations. When will the data development with respect to the conformal equations of this set be a conformal extension of a type D solution? In this work we provide an answer to this question. As an application of our construction we find a set of conditions for the data for the conformal equations which guarantee that the development is conformal to the Kerr

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The extended conformal Einstein field equations with matter: The Einstein–Maxwell field

Cited by 19 publications

References 20 publications

Perturbations of the Asymptotic Region of the Schwarzschild–de Sitter Spacetime

Perturbations of the Asymptotic Region of the Schwarzschild–de Sitter Spacetime

Spinorial wave equations and stability of the Milne spacetime

Type D conformal initial data

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