Constraining the Kehagias-Sfetsos solution in the Horava-Lifshitz gravity with extrasolar planets

We consider a spherically symmetric and asymptotically flat vacuum solution of the Horava-Lifshitz (HL) gravity that is the analog of the general relativistic Schwarzschild black hole. In the weak-field and slow-motion approximation, we work out the correction to the third Kepler law of a test particle induced by such a solution and compare it to the phenomenologically determined orbital period of the transiting extrasolar planet HD209458b Osiris to preliminarily obtain an order-of-magnitude lower bound on the KS dimensionless parameter \omega_0 >= 1.4\times 10^-18. As suggestions for further analyses, the entire data set of HD209458b should be re-processed by explicitly modeling KS gravity as well, and one or more dedicated solve-for parameter(s) should be estimated.

💡 Research Summary

The paper investigates whether the Kehagias‑Sfetsos (KS) solution of Hořava‑Lifshitz (HL) gravity can be constrained using the orbital dynamics of an extrasolar planet. HL gravity is a candidate quantum‑gravity theory that breaks Lorentz invariance at high energies by introducing anistropic scaling between space and time (z = 3). In the low‑energy, weak‑field limit the theory must reproduce General Relativity (GR), but it also predicts small deviations that can, in principle, be detected with precise astronomical measurements.

The KS metric is the HL analogue of the Schwarzschild solution. It differs from Schwarzschild by a single dimensionless parameter ω₀ = ω M², where M is the mass of the central object and ω is a constant appearing in the HL action. When ω₀ → 0 the KS metric reduces exactly to Schwarzschild, so any non‑zero ω₀ quantifies the departure from GR.

The authors first work out the orbital consequences of the KS metric in the Newtonian‑like regime (weak field, slow motion). By expanding the geodesic equation they obtain an effective potential that modifies Kepler’s third law. For a circular orbit of radius a around a mass M the orbital period becomes

T ≈ 2π √(a³/GM)