Throw something straight up and it usually comes back. Throw it faster than a certain speed and it escapes the body's pull and does not return. That speed is called the escape velocity.
For a body of mass and radius , the escape velocity is : km/s at the Earth's surface and km/s at the Sun's.
Keep the mass the same and shrink the radius, and the escape velocity grows until it reaches . Then not even light can get out.
Solving for gives , called the Schwarzschild radius.
This value, found from Newtonian mechanics, happens to agree with the radius from the Schwarzschild solution of general relativity. For the mass of the Sun it is about km; for the mass of the Earth, about mm.
The sphere at this radius is called the event horizon. Nothing sits on its surface; it is the boundary inside which events can no longer reach the outside.
Line up the light cones at various places on a spacetime diagram whose horizontal axis is the distance from the centre. Far away the cones point up, and one can move outward or inward.
Nearer the horizon, the cones tilt toward the centre. Motion is confined to the inside of the cone, so the possible directions lean toward the centre too.
At the horizon, even outgoing light stays at the same distance. Inside it, every direction within the cone leads toward the centre, and no direction leads back out.
The horizon has no marker and no wall, and someone falling passes through without hitting anything. For someone in free fall it is no different from the inside of a box where gravity has vanished.
What they do feel is the tidal force, the pull differing between feet and head. For a black hole of solar masses, the difference at the horizon across a m body reaches m/s², and the body is stretched out.
At the horizon the tidal force is weaker the more massive the black hole. For the black hole of about million solar masses at the centre of our galaxy it is about m/s², and crossing would not be felt at all.
For someone watching from far away, the faller's clock runs slower the nearer it gets to the horizon. The light the faller sends shifts further to the red and grows dim.
On the distant clock, the faller takes an infinite time to reach the horizon. The faller's image stops just short of it, fades and disappears.
On the faller's own clock, the time to cross the horizon is finite. The two accounts describe the same spacetime from two frames, and each clock reading is correct in its own frame.