Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Line Source In Minkowski For The de Sitter Spacetime Scalar Green's
  Function: Massless Minimally Coupled Case   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 $(d \geq
2)$-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 $(d \geq 2)$-dimensional sphere.

22
The categories of this paper are: chao-dyn
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
23
The categories of this paper are: solv-int
33
The categories of this paper are: plasm-ph
26
The categories of this paper are: bayes-an
25
The categories of this paper are: patt-sol
20
The categories of this paper are: acc-phys
9
The categories of this paper are: nlin
18
The categories of this paper are: econ
34
The categories of this paper are: chem-ph
32
The categories of this paper are: atom-ph
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
21
The categories of this paper are: adap-org