Finite-sized bodies are deformed in the presence of external tidal fields created, for instance, by surrounding objects. This is particularly important in the merging process of black holes or neutron stars, whereby the phase of the gravitational waveform produced is affected by such tidal Love numbers. This idea has been used to constrain the nuclear matter equation of state from the gravitational wave detection of binary neutron star mergers. It is a well known fact that non-rotating black holes in General Relativity (GR) have vanishing Love numbers. Nevertheless, this exact same spacetime is also a solution of a broad class of modified gravity theories, for which the linearized perturbations equations generically differ from those of GR. A direct consequence is that the tidal Love numbers depend not only on the object itself, but also on the gravitational theory supporting it, offering the possibility of ruling out theories with detections of gravitational waves from binary black hole mergers. I will discuss linear perturbations of f(R) gravity on the background of a Schwarzschild-AdS black hole, and determine the associated tidal Love numbers. While axial sector perturbations remain unaltered with respect to GR —and therefore the axial Love numbers vanish in the absence of a cosmological constant—, the polar sector is affected. Results for two cases of particular relevance will be highlighted: (i) the Schwarzschild spacetime, regarded as a solution in f(R) gravity, and (ii) the Schwarzschild-AdS solution in GR.

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Black Holes,Gravitation,Modified Gravity

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