What does this equation mean?

What general relativity does not generally hand over is a local, coordinate-independent tensorial density for the energy carried by the gravitational field itself. Only pseudotensors serve that role, and a pseudotensor’s value at a point depends on the coordinate system used to compute it, a fact treated carefully in modern reviews of quasi-local energy-momentum [ 7 ] . A genuinely coordinate-independent, globally conserved energy exists only under a much stronger condition: the spacetime must admit a timelike Killing vector field $\xi^\mu$ , an actual continuous isometry of the full geometry, not a convenient choice of coordinates. Komar’s construction turns that Killing vector into a covariant surface-integral charge conserved along the resulting flow [ 5 ] , and the general statement tying conserved quantities to Killing vectors is standard material in the field’s own textbooks [ 15 ] .