The scalar wave equation in a non-commutative spherically symmetric space-time

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dc.creatorDi Grezia, Elisabetta
dc.creatorEsposito, Giampiero
dc.creatorMiele, Gennaro
dc.date2007-05-02
dc.date.accessioned2026-07-07T11:20:26Z
dc.date.available2026-07-07T11:20:26Z
dc.descriptionRecent work in the literature has studied a version of non-commutative Schwarzschild black holes where the effects of non-commutativity are described by a mass function depending on both the radial variable r and a non-commutativity parameter theta. The present paper studies the asymptotic behaviour of solutions of the zero-rest-mass scalar wave equation in such a modified Schwarzschild space-time in a neighbourhood of spatial infinity. The analysis is eventually reduced to finding solutions of an inhomogeneous Euler--Poisson--Darboux equation, where the parameter theta affects explicitly the functional form of the source term. Interestingly, for finite values of theta, there is full qualitative agreement with general relativity: the conformal singularity at spacelike infinity reduces in a considerable way the differentiability class of scalar fields at future null infinity. In the physical space-time, this means that the scalar field has an asymptotic behaviour with a fall-off going on rather more slowly than in flat space-time.
dc.description19 pages, Revtex4, 7 figures
dc.identifierhttps://arxiv.org/abs/0705.0242
dc.identifierhttp://arxiv.org/abs/0705.0242
dc.identifierInt.J.Geom.Meth.Mod.Phys.5:33-47,2008
dc.identifierdoi:10.1142/S0219887808002631
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/193964
dc.subjectHigh Energy Physics - Theory
dc.titleThe scalar wave equation in a non-commutative spherically symmetric space-time
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