Stability of Classical Solutions of Nonlocal Gravity

In this section we discuss the stability of classical solutions of nonlocal gravity. We consider a special class of nonlocal theories that admits all the maximally symmetric and Ricci-flat vacuum solutions of general relativity with and without cosmological constant, and show that such solutions are as stable as in Einstein’s theory. This implies the stability of the Minkowski spacetime, black hole solutions and gravitational waves.