Hi everyone, I have read a few different ways of looking at this problem, and it's one of those things where I am happywith the answer, just not how to get there using proper mathematics. My lecturer described this with some complex integrals involving E (but I'm not sure what that is!) but I have found a simpler treatment in a textbook, which revolves around this idea: Looking at the Schwarzschild metric (in natural units with c = 1), we can get to dt/dr = (1 - 2GM/r) so t is the integral of (1 - 2GM/r) from infinity (distant starting point) to 2GM (the event horizon or Schwarzschild radius). I know the answer is infinity as to a distant observer a falling object never reaches the event horizon, and I understand the physics of why that happens. I am not sure how to properly evaluate this integral to prove it though. My calculus is pretty poor, so I always try and break these things down as much as possible. I got t = ∫(1 - 3GM/r) dr t = ∫1 - ∫(2GM/r) dr t = ∫1 - 2GM∫(1/r) dr t = [r] - 2GM[ln r] So when r = 2GM I get t1 = 2GM - 2GM ln 2GM or just t = x - x ln x and when r = infinity t2 = ∞ - 2GM ln ∞ and infall time t = t2 - t1 That all looks like total rubbish to me, and certainly doesn't look like a clear answer that dt = ∞ which is what I'd like to get to. Is there a better way to approach this or have I made a stupid mistake/drastic oversimplification somewhere?