Gravitational Cherenkov Radiation from Extended Theories of Gravity

We linearize the field equations for higher order theories of gravity that contain scalar invariants other than the Ricci scalar. We find that besides a massless spin-2 field (the standard graviton), the theory contains also spin-0 and spin-2 massive modes with the latter being, in general, ghost modes. The rate at which such particles would emit gravitational Cherenkov radiation is calculated for some interesting physical cases.

💡 Research Summary

The paper investigates the linearized dynamics of a broad class of higher‑order gravity theories whose Lagrangians contain scalar invariants beyond the Ricci scalar, such as (R^{2}), (R_{\mu\nu}R^{\mu\nu}) and (R_{\mu\nu\rho\sigma}R^{\mu\nu\rho\sigma}). By expanding the metric around flat spacetime, (g_{\mu\nu}= \eta_{\mu\nu}+h_{\mu\nu}), the authors obtain fourth‑order field equations that can be decomposed into two independent sectors. The first sector reproduces the familiar massless spin‑2 graviton of General Relativity, obeying the wave equation (\Box h_{\mu\nu}=0) and propagating at the speed of light. The second sector contains additional degrees of freedom: a massive scalar (spin‑0) mode and a massive spin‑2 mode. The scalar mass (m_{0}) is set by the coefficient of the (R^{2}) term, while the massive spin‑2 mass (m_{2}) is linked to the coefficient of the Ricci‑tensor‑square term. In most higher‑order models the spin‑2 mode appears with the wrong sign in the kinetic term, i.e., as a ghost, which raises concerns about quantum stability but does not prevent a classical analysis.

Having identified these modes, the authors turn to the phenomenon of gravitational Cherenkov radiation. When a particle travels faster than the phase velocity (c_{i}) of a given mode (with (c_{i}<c) because the mode is massive), it can emit radiation analogous to electromagnetic Cherenkov radiation. By applying energy‑momentum conservation to the linearized field equations, they derive a universal expression for the power emitted per unit time, \