American Institute of Physics;New York: American Institute of Physics
摘要:
摘要： Motivated by the desire to understand the causal structure of physical signals produced in curved spacetimes – particularly around black holes – we show how, for certain classes of geometries, one might obtain its retarded or advanced minimally coupled massless scalar Green's function by using the corresponding Green's functions in the higher dimensional Minkowski spacetime where it is embedded. Analogous statements hold for certain classes of curved Riemannian spaces, with positive definite metrics, which may be embedded in higher dimensional Euclidean spaces. The general formula is applied to (d ≥ 2)-dimensional de Sitter spacetime, and the scalar Green's function is demonstrated to be sourced by a line emanating infinitesimally close to the origin of the ambient (d + 1)-dimensional Minkowski spacetime and piercing orthogonally through the de Sitter hyperboloids of all finite sizes. This method does not require solving the de Sitter wave equation directly. Only the zero mode solution to an ordinary differential equation, the “wave equation” perpendicular to the hyperboloid – followed by a one-dimensional integral – needs to be evaluated. A topological obstruction to the general construction is also discussed by utilizing it to derive a generalized Green's function of the Laplacian on the (d ≥ 2)-dimensional sphere. 出版者： New York: American Institute of Physics 出版日期： 2014-09-01 出處： Journal of mathematical physics, 2014-09, Vol.55 (9), p.1 資源來源： AIP Journals (American Institute of Physics) 版權： Copyright American Institute of Physics Sep 2014 版權： 2014 AIP Publishing LLC. 識別號： ISSN: 0022-2488 識別號： EISSN: 1089-7658 識別號： DOI: 10.1063/1.4895506
