New algorithm of measuring gravitational wave radiation from rotating binary system

TL;DR

This paper introduces a novel approach called modified linearized general relativity (MLGR) to measure gravitational wave radiation from binary systems without tensor formalism, providing new theoretical insights and explicit power calculations.

Contribution

The paper develops MLGR and constructs a new paradigm for measuring GW radiation using mass potentials, offering a different theoretical framework from traditional tensor-based methods.

Findings

GW radiation intensity has a prolate ellipsoid shape.

Radiation power on the axis is twice that on the equator.

Total GW power matches electromagnetic dipole radiation in rotating systems.

Abstract

In order to investigate the gravitational wave (GW) radiation, without appealing to the tensorial formalism of the linearized general relativity, we formulate the so-called modified linearized general relativity (MLGR). As an application of the MLGR, we construct a novel paradigm of measuring the GW radiation from a binary system of compact objects, to theoretically interpret their phenomenology. To do this, we formulate the mass scalar and mass vector potentials for the merging binary compact objects, from which we construct the mass magnetic field in addition to the mass electric one which also includes the mass vector potential effect. Next, defining the mass Poyinting vector in terms of the mass electric and mass magnetic fields, we construct the GW radiation intensity profile possessing a prolate ellipsoid geometry due to the merging binary compact objects source. At a given radial distance from the binary compact objects, the GW radiation intensity on the revolution axis of the binary compact objects is shown to be twice that on the equatorial plane. Moreover, we explicitly obtain the total radiation power of the GW, which has the same characteristic as that of the electromagnetic wave in the rotating charge electric dipole moment. We also find that, in no distorting limit of the merging binary compact objects, the compact objects do not yield the total GW radiation power, consistent with the result of the linearized general relativity.