  We study a time-dependent and spherically-symmetric solution with a star-like
source. We show that this solution can be interpreted as an exterior solution
of a contracting star which has a decreasing temperature and is immersed in a
homogenous and isotropic background radiation. Distribution of the temperature
in the fields and close-to Schwarzschild approximation of the solution are
studied. By identifying the radiation with the cosmic background one, we find
that the close-to-Schwarzschild approximate solution is valid in a wide range
in our solar system. Possible experimental tests of the solution are discussed
briefly.
