  It is known that the standard Schwarzschild interior metric is conformally
flat and generates a constant density sphere in any spacetime dimension in
Einstein and Einstein--Gauss--Bonnet gravity. This motivates the questions: In
EGB does the conformal flatness criterion yield the Schwarzschild metric? Does
the assumption of constant density generate the Schwarzschild interior
spacetime? The answer to both questions turn out in the negative in general. In
the case of the constant density sphere, a generalised Schwarzschild metric
emerges. When we invoke the conformal flatness condition the Schwarschild
interior solution is obtained as one solution and another metric which does not
yield a constant density hypersphere in EGB theory is found. For the latter
solution one of the gravitational metrics is obtained explicitly while the
other is determined up to quadratures in 5 and 6 dimensions. The physical
properties of these new solutions are studied with the use of numerical methods
and a parameter space is located for which both models display pleasing
physical behaviour.
