Hořava-Lifshitz gravity, extrasolar planets and the double pulsar

We consider a spherically symmetric and asymptotically flat vacuum solution of the Hořava-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 periods of the transiting extrasolar planet HD209458b “Osiris” and of the double pulsar PSR J0737-3039A/B. The upper bounds on the HL adimensional parameter are ω0 ≤ 10 −15 from HD209458b and ω0 ≤ 10 −13 from PSR J07373039A/B. While the constrain from the pulsar is of the same order of magnitude of the most stringent one retrieved from the perihelion precessions of the inner planets of our solar system (10 − 10), the one by HD209458b is tighter by two orders of magnitude.