  We demonstrate how observables of slowly rotating neutron stars can be used
to constrain the nuclear equation of state. By building a Bayesian framework we
demonstrate how combining different types of neutron star measurements,
motivated by the upcoming multi-messenger era, provide informative posterior
distributions of commonly used equation of state parametrizations. Exemplarily,
we chose the Read et al. four parameter model that is widely used to represent
realistic equations of states in neutron star physics. Since future
observational campaigns will not only provide mass, radius and rotation rate
measurements, but also neutron star oscillation modes, a unified framework to
analyze the joint knowledge becomes necessary. While several attempts exist in
the literature, the here presented framework explicitly takes into account
rotational effects by using state-of-the-art universal relations for their
oscillation spectra. To demonstrate its performance we apply it to observables
that take into account rotational effects to best possible precision and use
our independent model for the reconstruction. Only a few high precision neutron
star measurements are required to put tight constraints on the underlying
equation of state.

General Relativity and Quantum Cosmology