Regression analysis of LIGO-Virgo observations WG200115 using curvature tensors from Einstein’s equations and Dirac’s gravitational waves

Abstract

This research presents the mathematical derivation of curvature tensors from the Schwarzschild solution of the gravitational field, along with the derivation of gravitational waves as the second derivative of the field. The elimination of the event horizon is the core contribution of this paper, building on Paul Dirac’s approach in his 1975 book, General Theory of Relativity. This paper introduceslinear and non-linear models for the spacetime distortion function. The fit of the tensor equation for gravitational waves is tested using geometrical information from the LIGO-Virgo observation of WG200115, employing econometric techniques with indicators such as R-squared for the robustness of the given data and the fit of the model to the data distribution, as well as the Durbin–Watson statistic for time-series predictability. The results show a good fit of the derived mathematical model to the observed geometry. Different models for simulating spacetime distortion exhibit varying degrees of fit to the observed geometry, with a less distorted model providing a better explanation for the observed gravitational waves. The model’s fit decreases when considering the rotation of the source object, whether it be a neutron star or a black hole. Further modeling effort is needed to accurately represent the NSBH merger process and its role in the formation of gravitational waves.