This article introduces the notions of asymptotic dust and asymptotic radiation equations of state. With these non-linear generalizations of the well known dust or (incoherent) radiation equations of state the perfect-fluid equations lose any conformal covariance or privilege. We analyse the conformal field equations induced with these equations of state. It is shown that the Einstein-\(\lambda \)-perfect-fluid equations with an asymptotic radiation equation of state allow for large sets of Cauchy data that develop into solutions which admit smooth conformal boundaries in the future and smooth extensions beyond. In the case of asymptotic dust equations of state sharp results on the future asymptotic behaviour are not available yet.

本文介绍了渐近尘埃和渐近辐射状态方程的概念。通过这些众所周知的尘埃或（非相干）辐射状态方程的非线性推广，完美流体方程失去了任何共形协方差或特权。我们分析由这些状态方程导出的共形场方程。结果表明，具有渐近辐射状态方程的爱因斯坦- \(\lambda\)完美流体方程允许大量柯西数据，这些数据发展成允许未来平滑共形边界和平滑扩展的解。在渐近尘埃状态方程的情况下，关于未来渐近行为的清晰结果尚不可用。