Propagation of high-frequency gravitational waves in vacuum: Nonlinear effects

Some High-Frequency Gravitational Waves Related to Exact Radiative Spacetimes

“…. .. For the high-frequency approximation we obtain from (13) in the leading order O(ǫ −1 ) the equation ( 6) which is identical with the wave equation in the vacuum case. The second-order contributions, that are O(1), represent an influence of the high-frequency gravitational waves and matter fields on the background,…”

“…Comparison of these approaches, and clarification of assumptions that have to be made in order to provide a consistent high-frequency approximation limit was also given by Araujo [11,12]. Elster [13] proposed an alternative method that is based on expanding null-tetrad components of the Weyl tensor. Recently, Burnett developed a weak limit approach [14] in which the high-frequency limit * Institute of Theoretical Physics, Charles University in Prague, V Holešovičkách 2, 180 00 Prague 8, Czech Republic can be introduced and studied in a mathematically rigorous way.…”

The Efroimsky formalism for weak gravitational waves adapted to high-frequency perturbations

“…Thus we recover Efroimsky's previous results, cf. (7), (8), (10). In general, however, expressing η in terms of h from the equation (19) becomes an extremely difficult task because it is no longer a linear equation for η.…”

“…Such waves also influence the cosmological background in which they propagate. Isaacson's work stimulated further contributions in which his method was reformulated using various formalisms, and explicitly applied to particular spacetimes (see, e.g., [6][7][8][9][10][11][12][13][14][15]).…”

The orthoprojection widths of some classes of periodic functions of two variables with a given majorant of the mixed moduli of continuity

“…Such waves also influence the cosmological background in which they propagate. Isaacson's work stimulated further contributions in which his method was reformulated using various formalisms, and explicitly applied to particular spacetimes (see, e.g., [6][7][8][9][10][11][12][13][14][15]). …”