Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2007-05-02
Int.J.Geom.Meth.Mod.Phys.5:33-47,2008
Physics
High Energy Physics
High Energy Physics - Theory
19 pages, Revtex4, 7 figures
Scientific paper
10.1142/S0219887808002631
Recent 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.
Esposito Giampiero
Grezia Elisabetta Di
Miele Gennaro
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