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Planck-scale effects on black hole structure by (Palatini) modified gravity theories

The Palatini formulation of classical theories of gravity amounts to consider the metric and affine (connection) structures as independent physical entities. The field equations are thus obtained by independent variations of the action with respect to both objects. While this reinterpretation of the theory is innocuous for General Relativity it has very important consequences for the physics of modified gravity theories (f(R) and beyond). Indeed, in such a case the connection is no longer given by the Christoffel symbols of the metric, the field equations are always second-order, and the theory is not affected by ghosts or any other dynamical instabilities. This has interesting effects on the (semi-)classical picture of the black hole structure, when Planck-scale effects, assumed to arise from the (conjectured) underlying quantum theory of gravity, are integrated in the gravity lagrangian. In this talk we shall sketch the main ideas of the Palatini formulation of several modified theories of gravity, and how the black hole structure is modified due to these effects.
 
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