Search for new physics with rare charm decays at LHCb

The LHCb experiment is playing a crucial role in the study of rare and forbidden decays of charm hadrons, which are unique probes for hints of physics beyond the Standard Model. These proceedings present results of the search for semileptonic three-body decays of the form $D_{(s)}^+ \rightarrow h^\pm \ell^+\ell^{(')\mp}$, where $h^\pm$ is a charged pion or kaon and $\ell^{(')\mp}$ is an electron or a muon. Furthermore, studies of the four-body neutral meson charm decays $D^0 \rightarrow \pi^+ \pi^- \mu^+ \mu^-$ and $D^0 \rightarrow K^+ K^- \mu^+ \mu^-$ are discussed. Prospects for leptonic and semileptonic rare charm decays at LHCb in the future are presented in the end.