Pseudoenergy, Superenergy, and Energy Radiation via Gravitational Waves in General Relativity

For slowly spinning matter the rate of energy loss via radiation of gravitational waves is estimated in General Relativity (GR) within a generally covariant superenergy approach. This estimation differs from Einstein’s Quadrupole Formula (EQF) by a suppression factor ($\mathrm{\Pi }\ll 1$). For a symmetric two-body-like distribution of scalar matter $\mathrm{\Pi }$ is estimated to be $\ll (v\mathrm{/}c{)}^2(r\mathrm{/}R{)}^2$, where $v$ is orbital velocity of the bodies, $c$ - velocity of light, $r$ - radius of each body, and $R$ – the inter-body distance. This contradiction with EQF is briefly discussed.