Teaching General Relativity with sector models: the field equations

The field equations of the general theory of relativity state the connection between spacetime curvature and matter, often summarized as "matter curves spacetime". In this contribution we analyze the structure of the field equations from a pedagogical point of view and describe a formulation that is accessible in secondary school and undergraduate physics. This formulation of the field equations requires the concept of curvature in three dimensions and we show how this notion can be introduced using sector models. The field equations are illustrated using the black hole as an example.