On the existence ofn-geodesically complete or future complete solutions of Einstein's field equations with smooth asymptotic structure

Friedrich, Helmut

doi:10.1007/bf01205488

Cited by 475 publications

(626 citation statements)

References 9 publications

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“…Up to questions of extensibility, all such solutions which are smooth have been characterized here by initial data on a space-like hypersurface and boundary data on 2-. As has been recognized before in the case of a negative cosmological constant [5,7], it is seen now that the concept of asymptotic simplicity is natural for Einstein's field equations also in the case of a positive cosmological constant.…”

Section: With Positive Cosmological Constant )~ Which Has Conformal Ementioning

confidence: 71%

“…In a suitable representation the equations for the rescaled metric retain their hyperbolicity even under conformal rescalings with conformal factors which vanish on subsets of space-time. The consequences of this property for the longtime behaviour of gravitational fields have been worked out in detail for de Sitter-type space-times [5,7], i.e. for solutions to Einstein's field equations…”

Section: Introductionmentioning

confidence: 99%

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Einstein equations and conformal structure: Existence of anti-de Sitter-type space-times

Friedrich

1995

Journal of Geometry and Physics

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185

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We discuss Einstein's equations in the context of normal conformal Caftan connections, derive a new conformal representation of the equations, and express the equations in a conformally invariant gauge. The resulting formulation of the equations is used to show the existence of asymptotically simple solutions to Einstein's equations with a positive cosmological constant. The solutions are characterized by Cauchy data on a space-like slice and by the intrinsic conformal structure on the conformal boundary at space-like and null infinity.

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Section: With Positive Cosmological Constant )~ Which Has Conformal Ementioning

confidence: 71%

Section: Introductionmentioning

confidence: 99%

Einstein equations and conformal structure: Existence of anti-de Sitter-type space-times

Friedrich

1995

Journal of Geometry and Physics

Self Cite

185

409

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“…Hence, the respective cone is Minkowski. This implies in particular that the solution g ij = δ ij in (3.20) is also Minkowski and the direct transformation of coordinates is given by: 25) such that:…”

Section: Ricci-flat Asymptoticsmentioning

confidence: 99%

“…26 The holographic Ward identities for the 24 Here and in equation (4.28) we have performed the intermedium step: δS/δq AB = (z/β) 2 δS/δq AB , where:qAB := (z/β) 2 qAB, and performed the decomposition of δ/δq AB in the same way as in (4.23)-(4.25). 25 Notice that the term QAB as well as: ∂Cn/∂q AB and: (4.21) are purely spatial and therefore vanish when contracted with n A . The expression for E follows from an explicit computation of (4.28) for each value of d and has been verified up to d = 6.…”

Section: Holographic Stress Tensorsmentioning

confidence: 99%

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Holographic reconstruction and renormalization in asymptotically Ricci-flat spacetimes

Costa

2012

J. High Energ. Phys.

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In this work we elaborate on an extension of the AdS/CFT framework to a subclass of gravitational theories with vanishing cosmological constant. By building on earlier ideas, we construct a correspondence between Ricci-flat spacetimes admitting asymptotically hyperbolic hypersurfaces and a family of conformal field theories on a codimension two manifold at null infinity. By truncating the gravity theory to the pure gravitational sector, we find the most general spacetime asymptotics, renormalize the gravitational action, reproduce the holographic stress tensors and Ward identities of the family of CFTs and show how the asymptotics is mapped to and reconstructed from conformal field theory data. In even dimensions, the holographic Weyl anomalies identify the bulk time coordinate with the spectrum of central charges with characteristic length the bulk Planck length. Consistency with locality in the bulk time direction requires a notion of locality in this spectrum.

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Is general relativity ‘essentially understood’?

Friedrich¹

2006

Ann. Phys.

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The content of Einstein's theory of gravitation is encoded in the properties of the solutions to his field equations. There has been obtained a wealth of information about these solutions in the ninety years the theory has been around. It led to the prediction and the observation of physical phenomena which confirm the important role of general relativity in physics. The understanding of the domain of highly dynamical, strong field configurations is, however, still quite limited. The gravitational wave experiments are likely to provide soon observational data on phenomena which are not accessible by other means. Further theoretical progress will require, however, new methods for the analysis and the numerical calculation of the solutions to Einstein's field equations on large scales and under general assumptions. We discuss some of the problems involved, describe the status of the field and recent results, and point out some open problems.

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On the existence ofn-geodesically complete or future complete solutions of Einstein's field equations with smooth asymptotic structure

Cited by 475 publications

References 9 publications

Einstein equations and conformal structure: Existence of anti-de Sitter-type space-times

Einstein equations and conformal structure: Existence of anti-de Sitter-type space-times

Holographic reconstruction and renormalization in asymptotically Ricci-flat spacetimes

Is general relativity ‘essentially understood’?

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