Abstract
Among the Scalar-Tensor modified theories of gravity, DHOST models could play a special role for dark energy while being consistent with current observations, notably those constraining the speed of gravitational waves. Schwarzschild-de Sitter black holes were shown to be exact solutions of a particular subclass of quadratic DHOST theories, while carrying a nontrivial scalar profile that linearly evolves in time and hence potentially providing exciting new phenomenological windows to explore this model. We investigate the physical perturbations about such black holes and find that the odd-parity tensor perturbations behave in a way indistinguishable to GR. On the other hand, the effective metric for the (even-parity) scalar perturbations is singular, indicating that those exact black hole solutions are infinitely strongly coupled and cannot be trusted within the regime of validity of the DHOST effective field theory. We show how this strong coupling result is generalizable to a whole class of solutions with arbitrary manifolds both for DHOST and Horndeski.
Highlights
The discovery of the cosmic accelerated expansion has motivated numerous studies on modifications of gravity in the infrared
In agreement with [40], we show that such solutions are stable against odd-parity perturbations
For the stealth black hole solutions in the shift-symmetric quadratic degenerate higher-order scalar-tensor (DHOST) theories on the other hand, the effective scalar fluctuations are always everywhere and all the time degenerate and those solutions can never and nowhere be trusted. These types of pathologies are very similar in nature to those observed about the exact static black solutions found in massive gravity [31], where it was shown that solutions that perfectly mimic general relativity (GR) black hole solutions, do so by effectively suppressing the graviton mass on those backgrounds and making the additional d.o.f. present in massive gravity infinitely strongly coupled
Summary
The discovery of the cosmic accelerated expansion has motivated numerous studies on modifications of gravity in the infrared. The even-parity perturbations differ due to the presence of the scalar field and while the diagonalized would-be tensor modes could a priori be stable, the diagonalized scalar mode sees a singular effective metric, indicating the stealth black hole solution in the shift-symmetric quadratic DHOST theories can not be trusted. For the stealth black hole solutions in the shift-symmetric quadratic DHOST theories on the other hand, the effective scalar fluctuations are always everywhere and all the time degenerate and those solutions can never and nowhere be trusted These types of pathologies are very similar in nature to those observed about the exact static black solutions found in massive gravity [31], where it was shown that solutions that perfectly mimic GR black hole solutions, do so by effectively suppressing the graviton mass on those backgrounds and making the additional d.o.f. present in massive gravity infinitely strongly coupled. The Lagrangian of the shift-symmetric DHOST theory up to quadratic order is given by [5]
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