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Sturm-Liouville and Carroll: at the heart of the Memory Effect

Autor: Peter A. Horvathy, M. Elbistan, Pengming Zhang, Gary W. Gibbons

Publikováno v: Gen.Rel.Grav.
Gen.Rel.Grav., 2018, 50 (9), pp.107. ⟨10.1007/s10714-018-2430-0⟩

For a plane gravitational wave whose profile is given, in Brinkmann coordinates, by a $2\times2$ symmetric traceless matrix $K(U)$, the matrix Sturm-Liouville equation $\ddot{P}=KP$ plays a multiple and central r\^ole: (i) it determines the isometrie

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::29a0eed5840e9ab313ec78b54f8b7185

Carroll symmetry of plane gravitational waves

Autor: Christian Duval, Gary W. Gibbons, Peter A. Horvathy, Pengming Zhang

Publikováno v: Classical and Quantum Gravity
Classical and Quantum Gravity, IOP Publishing, 2017, 34 (17), pp.175003
Classical and Quantum Gravity, 2017, 34 (17), pp.175003

The well-known 5-parameter isometry group of plane gravitational waves in $4$ dimensions is identified as Levy-Leblond's Carroll group in $2+1$ dimensions with no rotations. Our clue is that plane waves are Bargmann spaces into which Carroll manifold

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::898f97882078b19c2bc8c7b595e7f9d5
https://doi.org/10.1088/1361-6382/aa7f62

Carroll versus Newton and Galilei: two dual non-Einsteinian concepts of time

Autor: Christian Duval, Gary W. Gibbons, Peter A. Horvathy, Pengming Zhang

Publikováno v: Classical and Quantum Gravity
Classical and Quantum Gravity, 2014, 31 (085016), 24pp. ⟨10.1088/0264-9381/31/8/085016⟩
Classical and Quantum Gravity, IOP Publishing, 2014, 31 (085016), 24pp. ⟨10.1088/0264-9381/31/8/085016⟩

The Carroll group was originally introduced by Levy-Leblond [1] by considering the limit of the Poincar\'e group as $c\to0$. In this paper an alternative definition, based on the geometric properties of a non-Minkowskian, non-Galilean but nevertheles

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c14f00005ae209afd0a9c1ede51f0edb
http://arxiv.org/abs/1402.0657