On the Gravitational-Wave Energy Density in the Teleparallel Equivalent of General Relativity: Application to LIGO–Virgo–KAGRA Events

We compute the gravitational energy density of a linearized gravitational wave in the teleparallel equivalent of general relativity. For a plane wave in the transverse–traceless gauge we obtain the closed and exact expression [Formula: see text], and evaluate it on model polarizations [Formula: see text] and [Formula: see text] generated with source parameters consistent with ten LIGO–Virgo–KAGRA events spanning binary black holes, binary neutron stars and neutron-star-black-hole systems. Being a total derivative in the retarded time, the density is not positive definite and the energy it assigns to a region reduces to a flux across its boundary; as a local diagnostic, however, its morphology correlates with the nature of the source, contrasting the slow, growing oscillation of neutron-star systems with the compact profile that marks a black-hole merger. We argue that this quantity, built directly from the strain, may offer a template-independent diagnostic of gravitational-wave events.