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arXiv · 0705.0242

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

Elisabetta Di Grezia·Giampiero Esposito·Gennaro Miele
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Abstract

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.

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Elisabetta Di Grezia, Giampiero Esposito, Gennaro Miele. 2007-05-02. The scalar wave equation in a non-commutative spherically symmetric space-time. https://doi.org/10.1142/s0219887808002631

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