Huygens' Principle for a Wave Equation and the Asymptotic Behavior of Solutions along Geodesies**This work was started by the author while being a fellow at the Weizmann Institute of Science, Rehovot, Israel.

1986 ◽  
pp. 257-271
Author(s):  
Kimimasa NISHIWADA
Keyword(s):  
Asymptotic Behavior ◽  
Wave Equation ◽  
Asymptotic Behavior Of Solutions ◽  
Weizmann Institute ◽  
Huygens Principle

scholarly journals THE SCALAR WAVE EQUATION IN A NON-COMMUTATIVE SPHERICALLY SYMMETRIC SPACE-TIME

2008 ◽  
Vol 05 (01) ◽  
pp. 33-47 ◽  
Author(s):  
ELISABETTA DI GREZIA ◽  
GIAMPIERO ESPOSITO ◽  
GENNARO MIELE
Keyword(s):  
Asymptotic Behavior ◽  
Wave Equation ◽  
Rest Mass ◽  
Physical Space ◽  
Scalar Fields ◽  
Space Time ◽  
Asymptotic Behavior Of Solutions ◽  
Scalar Wave ◽  
Null Infinity ◽  
Scalar Wave Equation

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 θ. The present paper studies the asymptotic behavior of solutions of the zero-rest-mass scalar wave equation in such a modified Schwarzschild space-time in a neighborhood of spatial infinity. The analysis is eventually reduced to finding solutions of an inhomogeneous Euler–Poisson–Darboux equation, where the parameter θ affects explicitly the functional form of the source term. Interestingly, for finite values of θ, 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 behavior with a fall-off going on rather more slowly than in flat space-time.

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