Abstract
We develop the effective theory for perturbations around black holes with scalar hair, in two directions. First, we show that the scalar-Gauss-Bonnet theory, often used as an example exhibiting scalar black hole hair, can be deformed by galileon operators leading to order unity changes to its predictions. The effective theory for perturbations thus provides an efficient framework for describing and constraining broad classes of scalar-tensor theories, of which the addition of galileon operators is an example. Second, we extend the effective theory to perturbations around an axisymmetric, slowly rotating black hole, at linear order in the black hole spin. We also discuss the inclusion of parity-breaking operators in the effective theory.
Highlights
Future gravitational wave experiments are expected to find a large number of black hole merger events, and to measure their gravitational wave signals to high precision
We develop the effective theory for perturbations around black holes with scalar hair, in two directions
We have shown above how the presence of the cubic galileon operator modifies the properties of the hair generated by a scalar Gauss-Bonnet (sGB) coupling
Summary
Future gravitational wave experiments are expected to find a large number of black hole merger events, and to measure their gravitational wave signals to high precision. (3) A third approach is to parametrize the deviations from general relativistic expectations in a model-independent way This can take the form of a phenomenological parametrization such as [27,28,29,30,31,32], or a parametrization at the level of the action governing the dynamics of black hole perturbations [33,34,35,36,37]. We answer the first question by showing how the scalar-Gauss-Bonnet model can be deformed to yield a wide variety of predictions; an effective theory description is a useful way to parametrize the possibilities. J, . . . label instead the angular coordinates (θ, φ) on the S2-sphere
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