{"knowledge_schema": {"broad_category": "Physics \u2192 Theoretical Physics \u2192 General Relativity and Alternative Theories", "refinement": "This problem involves deriving field equations from an action principle in a theory of gravity that incorporates non-metricity while excluding torsion and curvature.", "specific_scope": "The focus is on varying the action with respect to the metric tensor to obtain the field equations that relate the geometry of spacetime to the matter content, specifically in a non-metric compatible framework.", "goal": "To derive the field equations from the given action that describe the dynamics of the gravitational field in the presence of non-metricity."}, "summary": "In this problem, we are tasked with deriving the field equations from a given action that describes a theory of gravity characterized by non-metricity, while torsion and curvature are absent. The action includes a non-metricity scalar and the matter action. By performing a variation of the action with respect to the metric tensor, we aim to find the resulting field equations that relate the geometry of spacetime to the energy-momentum tensor of matter. The final field equation will express how the non-metricity influences the dynamics of the gravitational field."}