Guler, SinemKaraca, Fatma2026-01-312026-01-3120250202-28931995-0721https://doi.org./10.1134/S0202289324700464https://hdl.handle.net/20.500.12662/10733We first prove the existence of the gradient Ricci-Yamabe soliton (briefly GRYS) by constructing an explicit example endowed with the Robertson-Walker metric. Then we focus on the physical properties of the gradient Ricci-Yamabe solitons satisying Einstein's field equations, under the assumptions of different subspaces of Gray's decompositions. For instance, we prove that if a GRYS space-time satisfying Einstein's field equations, in which the gradient of the potential function psi is a unit-timelike torse-forming vector field, belongs to the subspaces B and B', then it is a Robertson-Walker space-time with vanishing shear and vorticity. Moreover, its possible local cosmological structures are of Petrov types I, D, or O. Finally, we obtain the equations of state of a perfect-fluid space-time admitting the GRYS whose velocity field is a unit-timelike Killing vector field.eninfo:eu-repo/semantics/closedAccessArticle10.1134/S02022893247004642-s2.0-85219643382361Q32831WOS:001440356400009Q3