# What is the meaning of t=infinity at the black hole horizon?

Looking at the Kruskal diagram for black holes, it seems to me that at the horizon, all free falling objects cross the horizon at the same coordinate radius and time. Does this not mean that all objects crossing the horizon do so at the same time (i.e. two objects starting free fall at different locations must meet at the surface at the same instant because they cross at the same coordinate radius and time)? Since we can say 'two objects begin to fall at t=0', doesn't this mean that two objects at the same radius and coordinate time are 'the same event'

It just means the Schwarzschild coordinate system is faulty at the horizon because it assigns the same coordinates $(t,r,\theta, \phi)$=$(\infty,2m,\theta,\phi)$ to multiple events that are actually distinct events.