Conformally compact Lovelock metrics are polyhomogeneous near the boundary, and the leading obstruction to smoothness in even dimensions is the Einstein ambient obstruction tensor scaled by a coupling constant.
Poincaré-Lovelock metrics on conformally compact manifolds
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Conformally compact metrics and the Lovelock tensors
Conformally compact Lovelock metrics are polyhomogeneous near the boundary, and the leading obstruction to smoothness in even dimensions is the Einstein ambient obstruction tensor scaled by a coupling constant.