General Relativity and Quantum Cosmology (gr-qc)

Abstract: The new geodetic satellite LARES 2, cousin of LAGEOS and sharing with it almost the same orbital parameters apart from the inclination, displaced by 180 deg, was launched last year. Its proponents suggest using the sum of the nodes of LAGEOS and of LARES 2 to measure the sum of the Lense-Thirring node precessions independently of the systematic bias caused by the even zonal harmonics of the geopotential, claiming a final $\simeq 0.2$ percent total accuracy. In fact, the actual orbital configurations of the two satellites do not allow one to attain the sought for mutual cancellation of their classical node precessions due to the Earth's quadrupole mass moment, as their sum is still $\simeq 5000$ times larger than the added general relativistic rates. This has important consequences. One is that the current uncertainties in the eccentricities and the inclinations of both satellites do not presently allow the stated accuracy goal to be met, needing improvements of 3-4 orders of magnitude. Furthermore, the imperfect knowledge of the Earth's angular momentum $S$ impacts the uncancelled sum of the node precessions, from 150 to 4900 percent of the relativistic signal depending on the uncertainty assumed in $S$. It is finally remarked that the real breakthrough in reliably testing the gravitomagnetic field of the Earth would consist in modeling it and simultaneously estimating one or more dedicated parameter(s) along with other ones characterising the geopotential, as is customarily performed for any other dynamical feature.

Abstract: We investigate the black hole (BH) solution of the Einstein's gravity coupled with non-linear electrodynamics (NED) source in the background of a cloud of strings. We analyze the horizon structure, regularity, and energy conditions of the obtained BH solution. The optical features of the BH are explored. The photon radius and shadows of the BH are obtained as a function of black hole parameters. We observe that the size of the shadow image is bigger than its horizon radius and photon sphere. We also study the Quasinormal modes (QNM) using WKB formula for this black hole. The dependence of shadow radius and QN modes on black hole parameters reflects that they are mimicker to each other.

Abstract: The cosmology of the $F(R)$ gravity rebuilding by the Cartan formalism is investigated. This is called Cartan $F(R)$ gravity. The well-known $F(R)$ gravity has been introduced to extend the standard cosmology, e.g. to explain the cosmological accelerated expansion as the inflation. Cartan $F(R)$ gravity is based on the Riemann-Cartan geometry. The curvature $R$ can separate to two parts, one is derived from the Levi-Civita connection and the other from the torsion. Assuming the matter-independent spin connection, we have successfully rewritten the action of Cartan $F(R)$ gravity into the Einstein-Hilbert action and a scalar field with canonical kinetic and potential terms without any conformal transformations. This feature simplifies building and analysis of new model of inflation. In this paper, we study two models, the power-law model and logarithmic model, and evaluate fluctuations in the cosmological microwave background (CMB) radiation. We found the robustness of CMB fluctuation by the analytical computation and confirm this feature by the numerical calculation.

Abstract: Certain well-known spacetimes of general relativity (GR) are generated from the collision of suitable null-sources coupled with gravitational waves. This is a classical process underlying the full nonlinearity of GR that may be considered alternative to the quantum creativity at a large scale. Schwarzschild, de Sitter, anti de Sitter and the $\gamma $-metrics are given as examples.

Abstract: The second postulate of special relativity states that the speed of light in vacuum is independent of the emitter's motion. Though this claim has been verified in various experiments and observations involving electromagnetic radiation with very high accuracy, such a test for gravitational radiation still needs to be explored. We analyzed data from the LIGO and Virgo detectors to test this postulate for gravitational radiation within the ambit of \textit{emission models}, where the speed of gravitational waves emitted by a source moving with a velocity $v$ relative to a stationary observer is given by ${c' = c + k\,v}$, where $k$ is a constant. We have estimated the upper bound on the 90\% credible interval over $k$ that parameterizes the deviation from the second postulate to be ${k \leq 8.3 \times {10}^{-18}}$ which is several orders of magnitude more stringent compared to previous bounds obtained from electromagnetic observations. The Bayes' factor supports the second postulate, with very strong evidence that the data is consistent with the null hypothesis $k = 0$. This confirms that the speed of gravity is independent of the motion of the emitter, upholding the principle of relativity for gravitational interactions.