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We rigorously derive the quadrupole formula within the context of theEinstein-Vlasov system. The main contribution of this work is an estimate ofthe remainder terms, derived from well-defined assumptions, with explicitlystated error terms that depend on the solution's boundedness and decayproperties, and the distance to the source. The assumptions are linked toestablished properties of global solutions of the Einstein-Vlasov system as in\cite{LT}. Prior derivations of the quadrupole formula have relied onpost-Newtonian analysis and lacked comparisons with global solution properties.The importance of the no-incoming-radiation condition is emphasizedunderscoring the need for solutions satisfying this condition. This work thusaddresses the limitations of existing results and provides motivation forfurther research on global solution properties of the Einstein-Vlasov system.

Proof of the Einstein quadrupole formula for solutions of the Einstein-Vlasov system close to Minkowski spacetime