Constraining the Kehagias-Sfetsos Solution of the Ho!ava-Lifshitz Modi- fied Gravity with Extrasolar Planets

We consider the Kehagias-Sfetsos (KS) solution in the Ho!ava-Lifshitz gravity that is the analog of the general relativistic Schwarzschild black hole. In the weak-field and slow-motion approximation, we, first, work out the correction to the third Kepler law of a test particle induced by such a solution. Then, we compare it to the phenomenologically determined orbital period of the transiting extrasolar planet HD209458b “Osiris” to preliminarily obtain an order-ofmagnitude lower bound on the KS dimensionless parameter !0 > 1.4 " 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.