Abstract
The scalar field due to a point source at rest in the vicinity of a Schwarzschild space-time is studied. For the static scalar field ψ it is proved that as a solution of the Laplace equation it converges absolutely and uniformly and its limit is calculated explicitly on the horizonrs. It is proved also that ∇ψ = 0 atr = 0.5rs, ϑ = π/2 and that the function ψ satisfies certain symmetries which are independent of the source position. For the time-dependent scalar field we study the wave fronts of a perturbation due to a time-dependent point source and derive analytically the first correction to the field ψ(t, r, ϑ, ϕ) due to the Schwarzschild space-time.
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