Solving higher curvature gravity theories

Understand

Solving field equations in the context of higher curvature gravity theories is a formidable task.

• However in many situations, e.g., in the context of $f(R)$ theories the higher curvature gravity action can be written as Einstein-Hilbert action plus a scalar field action.
• We show that not only the action but the field equations derived from the action are also equivalent provided the spacetime is regular.
• We also demonstrate that such equivalence continues to hold even when gravitational field equations are projected on a lower dimensional hypersurface.