On the Positive Energy Theorem for Stationary Solutions to Fourth-Order Gravity

Abstract

In this paper we prove a positive energy theorem related to fourth-order gravitational theories, which is a higher-order analogue of the classical ADM positive energy theorem of general relativity. We will also show that, in parallel to the corresponding situation in general relativity, this result intersects several important problems in geometric analysis. For instance, it underlies positive mass theorems associated to the Paneitz operator, playing a similar role in the positive $Q$-curvature conformal prescription problem as the Schoen-Yau positive energy theorem does for the Yamabe problem. Several other links to $Q$-curvature analysis and rigidity phenomena are established.

We have corrected typos

References in corpus (4)

• Einstein Gravity from Conformal Gravity
• Sign of Green's function of Paneitz operators and the Q curvature
• Masse des opérateurs GJMS
• Energy in Fourth Order Gravity