Geodesics for impulsive gravitational waves and the multiplication of distributions

Balasin, Herbert

doi:10.1088/0264-9381/14/2/018

Cited by 48 publications

(79 citation statements)

References 14 publications

(18 reference statements)

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“…the coefficient of the right-hand side of (10) (2) in [9], resp. to (42) in [18], the only difference being that since we use an oriented atlas and our test objects are forms the determinants are automatically positive.…”

Section: )(Q)||=o(e −(N+l)mentioning

confidence: 99%

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A Global Theory of Algebras of Generalized Functions

Grosser

Kunzinger

Steinbauer

et al. 2002

Advances in Mathematics

188

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We present a geometric approach to defining an algebra Ĝ (M) (the Colombeau algebra) of generalized functions on a smooth manifold M containing the space DOE(M) of distributions on M. Based on differential calculus in convenient vector spaces we achieve an intrinsic construction of Ĝ (M). Ĝ (M) is a differential algebra, its elements possessing Lie derivatives with respect to arbitrary smooth vector fields. Moreover, we construct a canonical linear embedding of

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Section: )(Q)||=o(e −(N+l)mentioning

confidence: 99%

“…It treats the ''special'' version of the algebra in the sense of [22, p. 109f], whose elements (termed ultrafunctions by the authors) depend on a real regularization parameter. In both approaches, as well as in the construction envisaged in [2], the canonical embedding C .…”

Section: Introductionmentioning

confidence: 99%

A Global Theory of Algebras of Generalized Functions

Grosser

Kunzinger

Steinbauer

et al. 2002

Advances in Mathematics

188

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“…For a Lorentz boost in the z-directionx i → x i with 6) and A = 1, 2. The components R ijkl of the Riemann tensor in the unbarred coordinates are related to the barred components (B.1) by…”

Section: B Curvature Tensor Of the Weyl Space-timesmentioning

confidence: 99%

Aichelburg-Sexl boost of an isolated source in general relativity

Barrabès

Hogan

2001

Phys. Rev. D

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A study of the Aichelburg-Sexl boost of the Schwarzschild field is described in which the emphasis is placed on the field (curvature tensor) with the metric playing a secondary role. This is motivated by a description of the Coulomb field of a charged particle viewed by an observer whose speed relative to the charge approaches the speed of light. Our approach is exemplified by carrying out an AichelburgSexl type boost on the Weyl vacuum gravitational field due to an isolated axially symmetric source. Detailed calculations of the boosts transverse and parallel to the symmetry axis are given and the results, which differ significantly, are discussed. *

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“…The geodesics of (1), which actually are broken and refracted straight lines with a jump in the V-coordinate, have been derived in [FPV88], while in [Bal97,Ste98] the geodesic equations (which are non-linear ODEs with distributional right hand sides, hence mathematically delicate) have been treated rigorously. Finally in [KS99b] the geodesic equations of (1) have been proven to possess unique global solutions in a suitable space of (nonlinear) generalized functions ( [GKOS01,Col85]).…”

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confidence: 99%