TL;DR
This paper reviews the quasilinear reformulation of Lovelock gravity equations in harmonic gauge, focusing on well-posedness, causality, and stability analysis of black holes.
Contribution
It provides a detailed review of the reformulation, clarifies conditions for hyperbolicity, and discusses implications for black hole stability.
Findings
Conditions for Leray hyperbolicity are elucidated.
The reformulated system is not quasidiagonal, complicating causality analysis.
Relevance to black hole stability studies is highlighted.
Abstract
Here we give an extended review of the quasilinear reformulation of the Lovelock gravitational field equations in harmonic gauge presented in 1409.6656 [gr-qc]. This is important in order to establish rigorously well-posedness of the theory perturbed about certain backgrounds. The resulting system is not quasidiagonal, therefore analysis of causality is complicated in general. The conditions for the equations to be Leray hyperbolic are elucidated. The relevance to some recent results regarding the stability analysis of black holes is presented.
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