# Non-Comulative nature of Mass-Radius curves of Neutron Stars

For finding the mass-radius curve of neutron stars, we can solve TOV Equations which are constraint equations got by solving Einsteins equations. The boundary conditions are $$m(r=0)=0$$ and $$\rho(r=0)=\rho_c$$. Then we put a physical condition that for $$r\rightarrow r_*$$(radius of star), $$\rho\rightarrow 0$$, and by this we can get the limiting radius $$r_*$$ and mass $$m_*$$ and plots like

and for density

I understood and took it from MIT OCW

One can also do the same process for Modified Gravities and more involved $$P(\rho)$$ matter equations

• I have seen many places where the mass-radius curve looks like

• Confusion: Why isn't the mass of neutron star cumulative as radius increases, i.e. it must be $$0$$ at $$r=0$$ and reach its maximum at $$r=r_*$$? Maybe I am not getting the right interpretation of these curves. So, I would be grateful for some explanation or references.

• What can be the other perimeters for which we can draw the ($M_* - R_*$) curve? Bcoz $M_*, R_*$ is the result of solving TOV equations with initial conditions and a physical boundary constraint. So I guess the change in initial condition i.e. central density might be the perimeter! Commented Mar 31, 2022 at 20:59