# Schwarzschild Black holes

1. Homework Statement

2. Homework Equations
$$d\tau = dt\sqrt{1-\frac{r_s}{r}}$$

and

$$\frac{dr}{d(ct)} = 1 - \frac{r_s}{r}$$

3. The Attempt at a Solution
First of all I worked out the Schwarzschild radius to be $$2.964*10^4$$m.

From this I plugged it into the first of the two equations above, along with $$d\tau = 30$$, and $$dt = 300$$ (years in both cases, but it'll cancel), and rearranged to give r as $$2.994*10^4$$m, i.e. 300m outside the Schwarzschild radius.

From here I plugged these new numbers into the second equation that I've given in order to give $$\frac{dr}{d(ct)} = 0.01$$. I assume that this means a fraction of c.

I'm not entirely convinced though. Can someone check what I've done please. Have I used the correct meanings of $$d\tau and dt$$? Is the second equation that I've given the correct one to use? If not could someone point me in the right direction?

Thanks for anyone who helps out.