How Long Until You Hit the Black Hole?

[wackypete]

Homework Statement

Starting from rest at a great distance, you plunge straight towards a black hole of mass M. You set your watch to noon as you determine that you are crossing the horizon. How much more time do you have (as measured on your watch) until the instant of crunch?

Homework Equations

Nothing else is given in the problem. I thought I would need to know the metric.

The Attempt at a Solution

If I understand correctly the metric tells me how to measure distance and time so I would just integrate from the r=horizon to r=0 to get the time? Am I on the right track?

 

[azatkgz]

I think yes.You should integrate.