Title: Introduction to Lovelock metrics
Abstract: Lovelock metrics serve as one possible extension of Einstein's gravitational theory into higher dimensions. An essential feature of Lovelock metrics lies in their ability to incorporate non-linear dependencies on second-order derivatives of the metric.
Several properties associated with Einstein metrics find their extensions within the realm of Lovelock metrics. For instance, these metrics are critical to the generalized Einstein-Hilbert action, providing a way to derive the Lovelock tensors. Furthermore, a generalization of DeTurck's trick enables us to apply of elliptic regularities within a modified harmonic gauge. Thus, it is demonstrated that asymptotically hyperbolic Lovelock metrics exhibit a comparable behavior within the collar neighborhood of the boundary.
