Isolated objects in quadratic gravity

Quadratic curvature terms are commonly introduced in the action as first-order corrections of General Relativity, and, in this thesis, we investigated their impact on the most simple isolated objects, that are the static and spherically symmetric ones. Most of the work has been done in the context of Stelle's theory of gravity, in which the most general quadratic contractions of curvature tensors are added to the action of General Relativity without a cosmological constant. We studied this theory's possible static, spherically symmetric and asymptotically flat solutions with both analytical approximations and numerical methods. We found black holes with Schwarzschild and non-Schwarzschild nature, naked singularities which can have either an attractive or repulsive gravitational potential in the origin, non-symmetric wormholes which connects an asymptotically flat spacetime with an asymptotically singular one, and non-vacuum solutions modeled by perfect fluids with different equations of state. We described the general geometrical properties of these solutions and linked these short-scale behaviors to the values of the parameters which characterize the gravitational field at large distances. We studied linear perturbations of these solutions, finding that most are unstable, and presented a first attempt to picture the parameter space of stable solutions. We also studied the Thermodynamics of black holes and described their evaporation process: we found that either evaporation leads black holes to unstable configurations, or the predictions of quadratic gravity are unphysical. We also considered the possibility of generalizing Stelle's theory by removing the dependence from the only mass-scale present by including a new dynamical scalar field, making the theory scale invariant. Having a more complex theory, we did not investigate exotic solutions but limited ourselves to the impact of the new additional degrees of freedom on known analytical solutions. It was already known that in a cosmological setting this theory admits a transition between two de Sitter configurations; we analyzed the same problem in the context of static and spherically symmetric solutions and found a transition between two Schwarzschild-de Sitter configurations. In order to do that, we studied both linear perturbations and the semiclassical approximation of the path integral formulation of Euclidean quantum gravity. At last, we tried to extract some phenomenological signatures of the exotic solutions. In particular, we investigated the shadow of an object on background free-falling light, and a possible way of determining the behavior close to the origin using mass measurements that rely on different physical processes. We show that, whenever these measurements are applied to the case of compact stars, in principle it could be possible to distinguish solutions where different equations of state describe the fluid.