Escape Velocity of a Neutron Star: Relativistic Calculation

[TheSodesa]

Homework Statement

Calculate the escape velocity on the surface of the neutron star in the previous problem ($m = \frac{2}{3} \cdot 2,1 \cdot M_{\odot}$; $R = 15km$).

Hint: Basic physics. Note, however, that the escape velocity is not going to be small when compared to the speed of light.

Homework Equations

Relativistic kinetic energy:
\begin{equation}
K = \gamma mc^2 - mc^2 = \sqrt{(pc)^2 + (mc^2)^2} - mc^2
\end{equation}

Standard Newtonian potential energy:
\begin{equation}
V_N = -G\frac{mM}{r}
\end{equation}

Relativistic potential energy:
\begin{equation}
V_R = ?
\end{equation}

The Attempt at a Solution

My idea was to set the kinetic and potential energies to be equal, and solve for the speed as usual. The problem is, I don't know (how to derive) the expression for a relativistic potential, which I'm probably going to need because, you know, it's a neutron star we're talking about here.

I found a source (since none of my books were of any use), that simply multiplies the standard Newtonian potential with the Lorentz-factor $\gamma$, but I'm not sure that's allowed.

Is it, and if so, why?

 

[TheSodesa]

Scratch everything I said. I got the wrong result because of an input error... No such thing as a relativistic potential, apparently.

GG, calculator with a small screen.