We study a time-dependent five-dimensional (5D) metric which contains a static four-dimensional (4D) sub-metric whose three-dimensional (3D) part is spherically symmetric. An expansion in the metric coefficient allow us to obtain close-to Schwarzschild approximation to a class of spherically symmetric solutions. Using Campbell’s embedding theorem and the induced-matter formalism we obtain two 4D solutions. One describes a source with the stiff equation of state believed to be applicable to dense astrophysical objects, and the other describes a spherical source with a radial heat flow.

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