Scalar quasinormal modes of rotating black holes in low-energy Horava gravity

We investigate the quasinormal modes (QNMs) of a massless scalar field perturbing a rotating black hole solution in the low-energy sector of Horava–Lifshitz gravity. In this background, the radial and angular parts of the perturbation equation generally can not separate, preventing a direct reduction to a one-dimensional Schrödinger-like equation. To overcome this problem, we adopt two distinct approximation schemes. The first one expands the equations in powers of the rotation parameter a up to cubic order, which restores separability and yields standard QNM frequencies. The second one treats the Lorentz-violating parameter l as a small quantity and uses the biorthogonality of spheroidal harmonics to expand the angular dependence, thereby obtaining an effective radial potential from which the QNM spectrum can be computed. We compare the QNM frequencies derived from both methods and find excellent agreement in the regime where both a and l are small. However, because current astrophysical observations place stringent upper bounds on l, while black hole spins can be appreciably large, the second approach—valid for small l but arbitrary a—is more suitable for confronting realistic astrophysical data. Our analysis thus provides a practical framework for testing Horava gravity through black-hole spectroscopy in the era of gravitational-wave astronomy.