No abstract

We study the perturbations to General Relativistic black holes (i.e. those without scalar hair) in Horndeski scalar-tensor gravity. First, we derive the equations of odd and even parity perturbations of both the metric and scalar field in the case of a Schwarzschild black hole, and show that the gravitational waves emitted from such a system contain a mixture of quasi-normal mode frequencies from the usual General Relativistic spectrum and those from the new scalar field spectrum, with the new scalar spectrum characterised by just two free parameters. We then specialise to the sub-family of Horndeski theories in which gravitational waves propagate at the speed of light c on cosmological backgrounds; the scalar quasi-normal mode spectrum of such theories is characterised by just a single parameter µ acting as an effective mass of the scalar field. Analytical expressions for the quasinormal mode frequencies of the scalar spectrum in this sub-family of theories are provided for both static and slowly rotating black holes. In both regimes comparisons to quasi-normal modes calculated numerically show good agreement with those calculated analytically in this work.

We use the covariant formulation proposed in [1] to analyse the structure of linear perturbations about a spherically symmetric background in different families of gravity theories, and hence study how quasi-normal modes of perturbed black holes may be affected by modifications to General Relativity. We restrict ourselves to single-tensor, scalar-tensor and vector-tensor diffeomorphism-invariant gravity models in a Schwarzschild black hole background. We show explicitly the full covariant form of the quadratic actions in such cases, which allow us to then analyse odd parity (axial) and even parity (polar) perturbations simultaneously in a straightforward manner.

The recent detection of GRB 170817A and GW170817 constrains the speed of gravity waves c T to be that of light, which severely restricts the landscape of modified gravity theories that impact the cosmological evolution of the universe. In this work, we investigate the presence of black hole hair in the remaining viable cosmological theories of modified gravity that respect the constraint c T = 1. We focus mainly on scalar-tensor theories of gravity, analyzing static, asymptotically flat black holes in Horndeski, Beyond Horndeski, Einstein-Scalar-Gauss-Bonnet, and Chern-Simons theories. We find that in all of the cases considered here, theories that are cosmologically relevant and respect c T = 1 do not allow for hair, or have negligible hair. We further comment on vector-tensor theories including Einstein Yang-Mills, Einstein-Aether, and Generalised Proca theories, as well as bimetric theories.

The decay timescales of the quasinormal modes of a massive scalar field have an intriguing behaviour: they either grow or decay with increasing angular harmonic numbers , depending on whether the mass of the scalar field is small or large. We identify the properties of the effective potential of the scalar field that leads to this behaviour and characterize it in detail. If the scalar field is non-minimally coupled, considered here, the scalar quasinormal modes will leak into the gravitational wave signal and will have decaying times that are comparable or smaller than those typical in General Relativity. Hence, these modes could be detectable in the future. Finally, we find that the anomalous behaviour in the decay timescales of quasinormal modes is present in a much larger class of models beyond a simple massive scalar field. * mlagos@kicp.uchicago.edu † pedro.ferreira@physics.ox.ac.uk ‡ oliver.tattersall@physics.ox.ac.uk 1 From the publicly available data in [16], one can check that, for any given azimuthal number m, the QNM are such that |ω I | grows with for all values of the BH's dimensionless spin a = J/M 2 .