Modified gravity theories in the strong-field regime

4 problems

• Is a massive graviton with cosmological mass a consistent theory?

  Contested

  Giving the graviton a tiny mass, comparable to the inverse age of the universe, changes gravity at the largest distances. Versions without unstable ghost modes exist, but they may violate causality or lack any consistent high-energy completion.

• Do black holes carry scalar hair from spontaneous scalarization?

  Open

  In some theories a black hole becomes surrounded by a cloud of a new scalar field once it is small enough or spins fast enough. This would change how binaries emit gravitational waves.

• Does a black hole second law hold beyond effective field theory?

  Partially resolved

  In Einstein's theory a black hole's horizon area never decreases, which is why area acts as entropy. For theories with extra curvature terms a growing entropy is now proved when the extra terms are small corrections, but not when they are treated as exact.

• Are scalar-Gauss-Bonnet and higher-curvature theories well-posed in black hole mergers?

  Partially resolved

  To simulate merging black holes in a modified theory, its equations must give a unique, stable evolution from given starting data. Some popular theories lose this property when gravity becomes strong.