Higher-derivative gravitational effective field theories are generically weakly hyperbolic
arXiv:2607.11879
The paper studies the initial‑value problem for metric higher‑derivative gravitational effective field theories and demonstrates that any such theory with characteristic speeds independent of metric derivatives is intrinsically weakly hyperbolic, a property that cannot be removed by gauge choices or constraints.
Abstract
We analyse the initial-value problem of metric higher-derivative effective theories of gravity. We show that any such theory whose characteristic velocities are independent of derivatives of the metric is intrinsically weakly hyperbolic, independently of the gauge fixing. To show this, we identify the spin- physical sector directly from the characteristic equation; this can be done without introducing an order-reduced formulation, which greatly simplifies the computation. In this sector, every metric theory with more than two derivatives in the equations of motion contains a weakly hyperbolic block. Since this obstruction is physical, no choice of gauge or constraint addition can remove it, providing a structural explanation for the failure of strong hyperbolicity in this broad class of theories.