In this talk, I will present the computation of the one-loop four-graviton amplitudes with a massive abelian vector field circulating in the loop. For the gravity part we employ the Landau-Lifschits metric density approach. Within this framework, we will see that the resulting contact-terms-free n-gon numerators exhibit a manifest double-copy structure, provided the external gravitational trees satisfy this property. This structure enables the direct construction of the corresponding amplitudes with a massive scalar in the loop.