## Description

Neutron stars have the ability to rotate rapidly and emit electromagnetic and gravitational radiation. The rapid rotation of these compact objects have a set limit known as the Kepler frequency, at which the star begins to shed mass at its equator as it approaches this limit. However, there is another phenomenon that sets a rotation frequency limit before the Kepler frequency. The instabilities driven by the gravitational-radiation reaction causes the star to emit gravitational waves that carry angular momentum away from the system. In particular, the Gravitational-Radiation Reaction (GRR) f -mode, m = 2, may set the limit of stable rotation. In this thesis, the Kepler periods and the GRR driven instability periods are determined for three relativistic models of different nuclear equations of state, DD2, ACB4 and GM1L. ACB4 has an equation of state that accounts for a strong first-order phase transition that predicts a new branch of compact objects known as mass-twin stars. DD2 is a relativistic mean field (RMF) model that describes the meson-baryon coupling constants to be dependent on the local baryon number density, where the mesons are M ∈ {σ,ω,ρ} and the baryons are B ∈ {n,p,Λ,Ξ,Σ,∆}. GM1L is also an RMF model that only treats the ρ meson coupling as density-dependent. The results show that the m = 2 f -mode instability periods set the limit of stable rotation for cold neutron stars (T ∼ < 1010 K) with masses 1 M ̄ − 2 M ̄. The m = 2 mode is excited at rotation periods between 1 and 1.4 milliseconds (∼ 20% to ∼ 40% higher than the Kepler periods of these stars). For cold mass-twin compact stars with masses 1.96 M ̄ − 2.10 M ̄, the m = 2 instability sets in at periods between 0.8 − 1 millisecond for (∼ 25% to ∼ 30% above the Kepler period). The difference between rotational speeds necessary to excite the m = 2 modes may distinguish conventional neutron stars from their mass-twin counter parts through observation, provided other instabilities, such as the r -mode, do not set an even tighter limit on rotation.