Rigidity of geodesic completeness in the Brinkmann class of gravitational wave spacetimes

Silva, Ivan P. Costa e; Flores, José Luis Martínez; Herrera, J.

doi:10.48550/arxiv.1605.03619

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Solvable Indecomposable Lorentzian Symmetric Spaces1

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2019

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“…It is called a Cahen-Wallach space. In dimension 4, it is an example of pp-waves in the Brinkmann class which are idealized gravitational wave models in general relativity [3,7,24].…”

Section: Solvable Indecomposable Lorentzian Symmetric Spacesmentioning

confidence: 99%

Orbital integrals on Lorentzian symmetric spaces

Grouy

2019

Journal of Geometry and Physics

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In this paper, we address the problem of determining a function in terms of its orbital integrals on Lorentzian symmetric spaces. It has been solved by S. Helgason [13] for even-dimensional isotropic Lorentzian symmetric spaces via a limit formula involving the Laplace-Beltrami operator. The result has been extended by J. Orloff [21] for rank-one semisimple pseudo-Riemannian symmetric spaces giving the keys to treat the odd-dimensional isotropic Lorentzian symmetric spaces. Indecomposable Lorentzian symmetric spaces are either isotropic or have solvable transvection group. We study orbital integrals including an inversion formula on the solvable ones which have been explicitly described by M. Cahen and N. Wallach [5].

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“…It is called a Cahen-Wallach space. In dimension 4, it is an example of pp-waves in the Brinkmann class which are idealized gravitational wave models in general relativity [3,7,24].…”

Section: Solvable Indecomposable Lorentzian Symmetric Spacesmentioning

confidence: 99%

Orbital integrals on Lorentzian symmetric spaces

Grouy

2019

Journal of Geometry and Physics

View full text Add to dashboard Cite

show abstract

Rigidity of geodesic completeness in the Brinkmann class of gravitational wave spacetimes

Cited by 1 publication

References 0 publications

Orbital integrals on Lorentzian symmetric spaces

Orbital integrals on Lorentzian symmetric spaces

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