  We explore static spherically symmetric stars in the Gauss-Bonnet gravity
without cosmological constant, and present an exact internal solution which
attaches to the exterior vacuum solution outside stars. It turns out that the
presence of the Gauss-Bonnet term with a positive coupling constant completely
changes thermal and gravitational energies, and the upper bound of red shift of
spectral lines from the surface of stars. Unlike in general relativity, the
upper bound of red shift is dependent on the density of stars in our case.
Moreover, we have proven that two theorems for judging the stability of
equilibrium of stars in general relativity can be hold in Gauss-Bonnet gravity.
