Quantum gravity effective action: corrections to
\nclassical metrics and observational tests

General relativity is non-renormalizable, meaning that we lack a complete quantum theory
\nof gravity. However, working at energies below the Planck mass, which is the cutoff scale
\nof quantum gravity, we can resort to the effective field theory approach, implemented here
\nvia the Barvinsky-Vilkovisky unique effective action. The latter has been used to derive
\nquantum corrections to classical metrics, such as the Schwarzschild solution. In this thesis,
\nwe compute these corrections and extend the analysis to a static and electrically charged star
\nmodeled as a perfect fluid, considering distinct scenarios based on different applications of
\nthe perfect fluidity condition to the energy-momentum tensor components. Additionally, we
\nexplore gravastars and dark energy stars, proposed as compact objects alternative to classical
\nSchwarzschild black holes, arguing that quantum-induced hairs in their metrics may allow us
\nto experimentally distinguish between these objects. Finally, we examine gravitational lensing
\nobservables, namely the photon sphere radius and the deflection angle of bent light rays, and the
\ngravitational redshift, to validate the predicted quantum corrections. These findings provide a
\nframework for potential empirical tests to distinguish quantum-corrected metrics from classical
\nones, contributing to the broader understanding of quantum gravity phenomenology