Solar System tests of Hořava–Lifshitz gravity

Abstract

In the present paper, we consider the possibility of observationally constraining Hořava gravity at the scale of the Solar System, by considering the classical tests of general relativity (perihelion precession of the planet Mercury, deflection of light by the Sun and the radar echo delay) for the spherically symmetric black hole KehagiasSfetsos solution of Hořava-Lifshitz gravity. All these gravitational effects can be fully explained in the framework of the vacuum solution of Hořava gravity. Moreover, the study of the classical general relativistic tests also constrains the free parameter of the solution. From the analysis of the perihelion precession of the planet Mercury, we obtain for the free parameter u of the Kehagias-Sfetsos solution the constraint u ≥ 3.212 × 10 −26 cm −2 , the deflection of light by the Sun gives u ≥ 4.589 × 10 −26 cm −2 , while the radar echo delay observations can be explained if the value of u satisfies the constraint u ≥ 9.179 × 10 −26 cm −2 .

Weyl conformastatic perihelion advance

“…For inner planets, it is clear that the planets with low eccentricity generates a low value for β0 and essentially reproduce the same results as PPN approximation does, except for Mercury which presents a larger eccentricity among the planets and the correction for perihelion advance appears in good agrement with observations and other works in literature Anderson J.D. et al (1992); Shapiro, Counselman III and King (1976); Nambuya (2010); Harko et al (2011). Moreover, we find a very small β0, i.e, β0 << 1 for the cases of Venus, Earth and Mars, and we do not observe any difference in δφ + and δφ − solutions.…”

“…(19), we stress that in the first approximation we have c0 = 0 and the coefficient σ(r, z)|z=0 is simply reduced to σ(r, z)|z=0 = k0 2 ln r . In order to obtain the resulting perihelion advance, first of all, in the same way as in Harko et al (2011), we evaluate the first approximation of Weyl's conformastatic metric and find…”

“…In order to test this assumption, we study the gravitational field produced by geodesic equation alone which can induce to an intermediate gravitational regime between Einstein's strong field and the newtonian field, known as nearly-newtonian regime (Wheeler et al 1973;Infeld and Plebanski 1960).…”

“…In recent years there has been a renewed interest in the perihelion advance and several proposals have been worked using it as one of the fundamental solar system tests, such as, e.g, the modification of Newtonian Dynamics (MOND)(Schmidt 2008), azimuthally symmetric theory of gravitation based on the study of Poisson equation (Nambuya 2010), Kaluza-Klein five-dimensional gravity (Lim and Wesson 1992), Yukawa-like Modified Gravity (Iorio 2008a), Horava-Lifshitz gravity (Harko et al 2011), brane-world models and variants (Mak and Harko 2004;Cheung and Xu 2013;Chakraborty and Sengupta 2014;Jalalzadeh et al 2009;Iorio 2009a,b) and also in the PPN framework and outside it giving rise to extra-perihelion precessions and approaches in the weak field/slow motion limits (Avalos-Vargas and Ares de Parga 2012; Arakida 2013; Adkins and McDonnell 2007;D'Eliseo 2012;Deng and Xie 2014;Feldman 2013;Kalinowski 2013;Liang and Xie 2014;Li et al 2014;Iorio 2005Iorio , 2006Iorio , 2008bIorio , 2011Iorio , 2012aIorio ,b,c, 2013aIorio ,b, 2014aRuggiero 2014;Xie and Deng 2014;Wilhelm and Dwivedi 2014).…”

Gravitációs lencsézés alternatív gravitációelméletekben

“…A (3.5) Kehagias-Sfetsos téridőnek görbületi szingularitása van az origóban. Az ω 0 = m 2 ω dimenziótlan mennyiség hasznosnak bizonyult a (3.5) téridő naprendszerbeli tesztjeiben [89]. Az…”