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Tidal forces in dirty black hole spacetimes

Black holes can be inserted in very rich astrophysical environments, such as accretion disks. Although isolated black holes are simple objects in general relativity, their accretion disks may significantly enrich the field configurations of their surroundings. Alternative theories of gravity can lead to novel black hole solutions, which can be represented by small deviations in the metric due to an effective stress-energy tensor. Among the key aspects of the interaction of black holes with their surroundings, stand tidal forces phenomena. We study the tidal forces of spherically symmetric black holes in the presence of effective matter fields, dubbed as dirty black holes. These effective fields can generically represent usual or exotic matter associated to a variety of gravity theories. We show that this dirtiness leads to characteristic imprints in the tidal forces, which are absent in the case of a black hole surrounded by vacuum. We apply our results to particular cases, such as black holes coupled to linear and nonlinear electrodynamics theories and a Schwarzschild black hole surrounded by a spherical shell.