Many dark energy (DE) models are based on a scalar field with timelike gradient. If one hopes to learn something about scalar field DE from astrophysical black holes (BHs) then one needs to consider BH solutions with timelike scalar profiles. In this talk we begin with a review of the systematic construction of the effective field theory (EFT) describing perturbations around Minkowski and cosmological backgrounds with timelike scalar profiles. We then extend
the EFT to arbitrary backgrounds. Finally, as an application of the
general EFT, we study odd-parity perturbations around a spherically
symmetric, static black hole background with a timelike scalar field
responsible for DE.
Eugeny Babichev
