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The Klein-Gordon equation in anti-de Sitter spacetime. (English) Zbl 1184.35109

Summary: We apply the fundamental solution constructed in a previous paper, and obtain the representation of the solution to the Cauchy problem for the Klein-Gordon equation \(\square _g\phi - m^2\phi = f\) in anti-de Sitter spacetime.

MSC:

35C15 Integral representations of solutions to PDEs
35L15 Initial value problems for second-order hyperbolic equations
35Q75 PDEs in connection with relativity and gravitational theory
85A40 Astrophysical cosmology
83C57 Black holes
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