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.Comment: Latex2e, 13 pages, no figures, no tables, 56 references. Accepted in The Open Astronomy Journal (TOAJ

Solar System planetary orbital motions and f(R) Theories of Gravity

In this paper we study the effects of $f(R)$ Theories of Gravity on Solar System gravitational tests. In particular, starting from an exact solution of the field equation in vacuum, in the Palatini formalism, we work out the effects that the modifications to the Newtonian potential would induce on the Keplerian orbital elements of the Solar System planets, and compare them with the latest results in planetary orbit determination from the EPM2004 ephemerides. It turns out that the longitudes of perihelia and the mean longitudes are affected by secular precessions. We obtain the resulting best estimate of the parameter $k$ which, being simply related to the scalar curvature, measures the non linearity of the gravitational theory. We use our results to constrain the cosmological constant and show how $f(R)$ functions can be constrained, in principle. What we obtain suggests that, in agreement with other recent papers, the Solar System experiments are not effective to set such constraints, if compared to the cosmologically relevant values.Comment: 6 Pages, RevTeX, minor revision, new references added, to appear in JCA

Constraining models of modified gravity with the double pulsar PSR J0737-3039A/B system

In this paper we use Delta P = -1.772341 +/- 13.153788 s between the phenomenologically determined orbital period P_b of the PSR J0737-3039 double pulsar system and the purely Keplerian period P^(0)=2\pi\sqrt{a^3/G(m_A+m_B)} calculated with the system's parameters, determined independently of the third Kepler law itself, in order to put constraints on some models of modified gravity (f(R), Yukawa-like fifth force, MOND). The major source of error affecting Delta P is not the one in the phenomenologically measured period (\delta P_b=4 10^-6 s), but the systematic uncertainty \delta P^(0) in the computed Keplerian one due to the relative semimajor axis a mainly caused, in turn, by the errors in the ratio R of the pulsars' masses and in sin i. We get |\kappa|< 0.8 10^-26 m^-2 for the parameter that in the f(R) framework is a measure of the non linearity of the theory, |\alpha|< 5.5 10^-4 for the fifth-force strength parameter (for \lambda\approx a=0.006 AU). The effects predicted by the strong-acceleration regime of MOND are far too small to be constrained with some effectiveness today and in the future as well. In view of the continuous timing of such an important system, it might happen that in the near future it will be possible to obtain somewhat tighter constraints.Comment: LaTex2e, World Scientific macros, 10 pages, no figures, 1 table, 27 references. To appear in International Journal of Modern Physics

Gravitomagnetic effects in Kerr-de Sitter space-time

We explicitly worked out the orbital effects induced on the trajectory of a test particle by the the weak-field approximation of the Kerr-de Sitter metric. It results that the node, the pericentre and the mean anomaly undergo secular precessions proportional to k, which is a measure of the non linearity of the theory. We used such theoretical predictions and the latest observational determinations of the non-standard precessions of the perihelia of the inner planets of the Solar System to put a bound on k getting k <= 10^-29 m^-2. The node rate of the LAGEOS Earth's satellite yields k <= 10^-26 m^-2. The periastron precession of the double pulsar PSR J0737-3039A/B allows to obtain k <= 3 10^-21 m^-2. Interpreting k as a cosmological constant \Lambda, it turns out that such constraints are weaker than those obtained from the Schwarzschild-de Sitter metric.Comment: Latex2e, 18 pages, 1 table, no figures. To appear in Journal of Cosmology and Astroparticle Physics (JCAP

Phenomenological constraints on the Kehagias-Sfetsos solution in the Horava-Lifshitz gravity from solar system orbital motions

We focus on Horava-Lifshitz (HL) theory of gravity, and, in particular, on the Kehagias and Sfetsos s solution that is the analog of Schwarzschild black hole of General Relativity. In the weak-field and slow-motion approximation we analytically work out the secular precession of the longitude of the pericentre of a test particle induced by this solution. Its analytical form is different from that of the general relativistic Einstein's pericentre precession. Then, we compare it to the latest determinations of the corrections to the standard Newtonian/ Einsteinian planetary perihelion precessions recently estimated by E.V. Pitjeva with the EPM2008 ephemerides. It turns out that the planets of the solar system, taken singularly one at a time, allow to put lower bounds on the adimensional HL parameter \psi_0 of the order of 10^-12 (Mercury) 10^-24 (Pluto). They are not able to account for the Pioneer anomalous acceleration for r > 20 AU.Comment: LaTex2e, 10 pages, no figures, 5 tables, 26 references. References updated. To appear in International Journal of Modern Physics A (IJMPA

Constraining f(T) gravity in the Solar System

In the framework of $f(T)$ theories of gravity, we solve the field equations for $f(T)=T+\alpha T^{n}$, in the weak-field approximation and for spherical symmetry spacetime. Since $f(T)=T$ corresponds to Teleparallel Gravity, which is equivalent to General Relativity, the non linearity of the Lagrangian are expected to produce perturbations of the general relativistic solutions, parameterized by $\alpha$. Hence, we use the $f(T)$ solutions to model the gravitational field of the Sun, and exploit data from accurate tracking of spacecrafts orbiting Mercury and Saturn to infer preliminary insights on what could be obtained about the model parameter $\alpha$ and the cosmological constant $\Lambda$. It turns out that improvements of about one-three orders with respect to the present-day constraints in the literature of magnitude seem possible.Comment: LaTex2e, 16 pages, 2 figures, no tables. Accepted for publication in Journal of Cosmology and Astroparticle Physics (JCAP). arXiv admin note: text overlap with arXiv:1501.0219

Perturbations of the orbital elements due to the magnetic-like part of the field of a plane gravitational wave

We focus on the secular changes of the orbital elements of a planet in the solar system, determined by the magnetic-like part of a gravitational wave field. Using Fermi coordinates we show that the total force acting on a test particle is made of two contributions: a gravito-electric one and a gravito-magnetic one. While the electric-like force has been thoroughly discussed in the past, the effect of the gravito-magnetic force, which depends on the velocity of the test particle, has not been considered yet. We obtain approximated results to some orders in the orbital eccentricity and show that these effects are much smaller than the corresponding gravito-electric ones.Comment: 10 pages, to appear in International Journal of Modern Physics

Gravitomagnetic time-varying effects on the motion of a test particle

We study the effects of a time-varying gravitomagnetic field on the motion of test particles. Starting from recent results, we consider the gravitomagnetic field of a source whose spin angular momentum has a linearly time-varying magnitude. The acceleration due to such a time-varying gravitomagnetic field is considered as a perturbation of the Newtonian motion, and we explicitly evaluate the effects of this perturbation on the Keplerian elements of a closed orbit. The theoretical predictions are compared with actual astronomical and astrophysical scenarios, both in the solar system and in binary pulsars systems, in order to evaluate the impact of these effects on real systems.Comment: 8 pages, RevTeX; revised to match the version accepted for publication in General Relativity and Gravitatio