Constraining theories of gravity by GINGER experiment

The debate on gravity theories to extend or modify general relativity is very active today because of the issues related to ultraviolet and infrared behavior of Einstein’s theory. In the first case, we have to address the quantum gravity problem. In the latter, dark matter and dark energy, governing the large-scale structure and the cosmological evolution, seem to escape from any final fundamental theory and detection. The state of the art is that, up to now, no final theory, capable of explaining gravitational interaction at any scale, has been formulated. In this perspective, many research efforts are devoted to test theories of gravity by space-based experiments. Here, we propose straightforward tests by the GINGER experiment, which, being Earth based, requires little modeling of external perturbation, allowing a thorough analysis of the systematics, crucial for experiments where sensitivity breakthrough is required. Specifically, we want to show that it is possible to constrain parameters of gravity theories, like scalar–tensor or Horava–Lifshitz gravity, by considering their post-Newtonian limits matched with experimental data. In particular, we use the Lense–Thirring measurements provided by GINGER to find out relations among the parameters of theories and finally compare the results with those provided by LARES and Gravity Probe B satellites.

An improved approach for testing gravitational redshift via spacecraft based three frequency links combination

<p>We propose a new approach for testing the gravitational redshift based on frequency signals transmission between a spacecraft and a ground station. By a combination of one uplink signal and two downlink signals, the gravitational redshift can be tested at about 6.5×10<sup>-6</sup> level for a GNSS satellite (the signals’ frequencies are about 1.2~1.6 GHz), and about 2.2×10<sup>-6</sup> level for the International Space Station (the signals’ frequencies are up to 14.7 GHz), under the assumption that the clock accuracy is about 10<sup>-17</sup> level. For better desinged cases the accuracy of gravitational redshift test can be improved to several parts in 10<sup>-8</sup> level (the signals’ frequencies are about 8~12 GHz). Compared to the scheme of Gravity Probe-A (GP-A) experiment conducted in1976, the new approach does not require any onboard signal transponders, and the frequency values of the three links can be quite arbitrarily given. As the hardware requirement is reduced, a number of spacecrafts could be chosen as candidates for a gravitational redshift experiment. This approach could also be used in gravitational potential determination, which has prospective applications in geodesy. This study is supported by National Natural Science Foundation of China (NSFC) (grant Nos. 42030105, 41721003, 41631072, 41874023, 41804012), Space Station Project (2020)228, and Natural Science Foundation of Hubei Province(grant No. 2019CFB611).</p>

Results of space experiments and effect of torsion

The results of two space experiments, around the world clocks and gravity probe B, are analyzed theoretically using a field theory. The field equations of this theory are reduced to those of general relativity outside material distribution, while its equations of motion are not a geodesic one. This equation violates the weak equivalence principle because of the non-vanishing torsion in the geometry used. The predictions of the theory give rise to the time dilation measured by the first experiment and to the geodetic and frame drag effects measured by the second experiment. Furthermore, we show that these predictions are affected by the torsion of space-time. The torsion term, in the equation of motion, is connected to other effects through a coupling parameter. This parameter is called the “spin-torsion” coupling if the moving test particle is elementary one with non-vanishing quantum spin. We call this parameter “rotation-torsion” coupling if the moving test particle is a gyroscope. In the first case, the coupling parameter is well defined and confirmed by terrestrial experiment, while in the second case the parameter still needs further investigation and discussion.

Post-Newtonian limit: second-order Jefimenko equations

The purpose of this paper is to get second-order gravitational equations, a correction made to Jefimenko’s linear gravitational equations. These linear equations were first proposed by Oliver Heaviside in [1], making an analogy between the laws of electromagnetism and gravitation. To achieve our goal, we will use perturbation methods on Einstein field equations. It should be emphasized that the resulting system of equations can also be derived from Logunov’s non-linear gravitational equations, but with different physical interpretation, for while in the former gravitation is considered as a deformation of space-time as we can see in [2–5], in the latter gravitation is considered as a physical tensor field in the Minkowski space-time (as in [6–8]). In Jefimenko’s theory of gravitation, exposed in [9, 10], there are two kinds of gravitational fields, the ordinary gravitational field, due to the presence of masses, at rest, or in motion and other field called Heaviside field due to and acts only on moving masses. The Heaviside field is known in general relativity as Lense-Thirring effect or gravitomagnetism (The Heaviside field is the gravitational analogous of the magnetic field in the electromagnetic theory, its existence was proved employing the Gravity Probe B launched by NASA (See, for example, [11, 12]). It is a type of gravitational induction), interpreted as a distortion of space-time due to the motion of mass distributions, (see, for example [13, 14]). Here, we will present our second-order Jefimenko equations for gravitation and its solutions.

Is There Still Something Left That Gravity Probe B Can Measure?

We perform a full analytical and numerical treatment, to the first post-Newtonian (1pN) order, of the general relativistic long-term spin precession of an orbiting gyroscope due to the mass quadrupole moment J 2 of its primary without any restriction on either the gyro’s orbital configuration and the orientation in space of the symmetry axis k ^ of the central body. We apply our results to the past spaceborne Gravity Probe B (GP-B) mission by finding a secular rate of its spin’s declination δ which may be as large as ≲30–40 milliarcseconds per year mas yr − 1 , depending on the initial orbital phase f 0 . Both our analytical calculation and our simultaneous integration of the equations for the parallel transport of the spin 4-vector S and of the geodesic equations of motion of the gyroscope confirm such a finding. For GP-B, the reported mean error in measuring the spin’s declination rate amounts to σ δ ˙ GP − B = 18.3 mas yr − 1 . We also calculate the general analytical expressions of the gravitomagnetic spin precession induced by the primary’s angular momentum J . In view of their generality, our results can be extended also to other astronomical and astrophysical scenarios of interest like, e.g., stars orbiting galactic supermassive black holes, exoplanets close to their parent stars, tight binaries hosting compact stellar corpses.

Gravitomagnetism in modified theory of gravity

We study the gravitomagnetism in the Scalar-Vector-Tensor theory or Moffat’s Modified theory of Gravity (MOG). We compute the gravitomagnetic field that a slow-moving mass distribution produces in its Newtonian regime. We report that the consistency between the MOG gravitomagnetic field and that predicted by the Einstein’s gravitational theory and measured by Gravity Probe B, LAGEOS and LAGEOS 2, and with a number of GRACE and Laser Lunar ranging measurements requires [Formula: see text].