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 (EGB) 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.

众所周知，标准的Schwarzschild内部度量是保形平坦的，并且在爱因斯坦和爱因斯坦-高斯-贝内（EGB）引力的任何时空维度上都会生成恒定密度的球体。这激发了问题：在EGB中，保形平坦度准则是否产生Schwarzschild度量？恒定密度的假设会产生Schwarzschild内部时空吗？这两个问题的答案总的来说都是负面的。在恒定密度球体的情况下，出现了一个广义的Schwarzschild度量。当我们调用保形平坦度条件时，获得了Schwarschild内部解作为一个解，而找到了另一个在EGB理论中不产生恒定密度超球面的度量。对于后一种解决方案，显式地获得了一个重力度量，而另一个则在5维和6维上确定为正交。使用数值方法研究了这些新解决方案的物理特性，并为两个模型都显示出令人满意的物理行为的参数空间定位。