The Non-vanishing Imprint of Gravitational Waves as the Result of Its Nonlinear Evolution in Space

Abstract

In this paper, we consider the nonlinear self-interaction of gravitational waves and its results, which appear in the spectral space. Many authors widely consider different nonlinear effects; among them, in the frame of the concept of "gravitational memory." We begin the study by analyzing harmonic waves. Theoretical analysis shows that higher harmonics do not have suitable conditions for energy accumulation. But our study shows another exciting result. It predicts the transformation of gravitational wave energy into a non-vanishing deformation of the metric on the background space (zero harmonic or generated static field in our terminology). In other words, the waves leave their imprint on the background space. Moreover, this imprint does not disappear after the damping of the gravitational impulse. In addition, it gradually accumulates contributions from various sources. The imprint of the Primordial Gravitational Wave turns to be much weaker than that in galaxies. The static field created in the latter can be associated with additional mass. In this study, we evaluate the effects numerically.