We propose an underground experiment to detect the general relativistic effects due to the curvature of space-time around the Earth (de~Sitter effect) and to the rotation of the planet (dragging of the inertial frames or Lense-Thirring effect). It is based on the comparison between the IERS value of the Earth rotation vector and corresponding measurements obtained by a triaxial laser detector of rotation. The proposed detector consists of six large ring lasers arranged along three orthogonal axes. In about two years of data taking, the 1% sensitivity required for the measurement of the Lense-Thirring drag can be reached with square rings of 6~m side, assuming a shot noise limited sensitivity (20\,\,prad/s/Hz). The multigyros system, composed of rings whose planes are perpendicular to one or the other of three orthogonal axes, can be built in several ways. Here, we consider cubic and octahedral structures. It is shown that the symmetries of the proposed configurations provide mathematical relations that can be used to ensure the long term stability of the apparatus.

We study weak-field solutions having spherical symmetry in $f(T)$ gravity; to this end, we solve the field equations for a nondiagonal tetrad, starting from Lagrangian in the form $f(T)=T+\alpha T^n$, where $\alpha$ is a small constant, parametrizing the departure of the theory from general relativity. We show that the classical spherically symmetric solutions of general relativity, i.e., the Schwarzschild and Schwarzschild–de Sitter solutions, are perturbed by terms in the form $\propto r^{2-2n}$ and discuss the impact of these perturbations in observational tests.

We investigate the four solar system tests of gravity—perihelion precession, light bending, Shapiro time delay, gravitational redshift—in $f(T)$ gravity. In particular, we investigate the solution derived by Ruggiero and Radicella, Phys. Rev. D 91, 104014 (2015). for a nondiagonal vierbein field for a polynomial $f(T)=T+\alpha T^n$, where $\alpha$ is a constant and $|n|\ne 1$. In this paper, we derive the solutions for each test, in which Weinberg’s, Bodenner and Will’s, Cattani et al., and Rindler and Ishak’s methods are applied, Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity (Wiley, New York, 1972); Am. J. Phys. 71 (2003); Phys. Rev. D 87, 047503 (2013); Phys. Rev. D 76, 043006 (2007). We set a constraint on $\alpha$ for $n=2$, 3 by using data available from literature.