TOV Equations for Neutron Stars 

For this project, I followed along the process presented by Reddy and Silbar in their 2004 paper "Neutron Stars for Undergraduates". The full paper is available here. Below are my proofs and derivations of some of the equations presented in the paper, since the equations in the paper are not always presented with full justification, and many such derivations are left as an exercise to the reader. Click here to visit the full project with code and results!

Is there a maximum mass to Neutron Stars? This project studies the mass and pressure distributions for neutron stars and white dwarves by numerically solving the Tolman-Oppenheimer-Volkov (TOV) equations, predicting the mass of the most massive neutron star to an error of within 0.2 solar masses when compared to current observations. To achieve this, a custom Runge-Kutta 4 (RK4) solver was built, and research into gravitational, quantum, nuclear and relativistic effects was conducted.  (May 2025, Summer of Year 1)