Gravitational Bending of Light
Q: How much does gravity affect light? How does this relate to black holes?
A: The way gravity affects the motion of objects --- whether planets, falling apples, or particles of light --- is by warping the space-time through which they move. If there is no non-gravitational influence acting on an object, an object will travel in the straightest possible path through space-time. But since space-time itself is gravitationally warped, an object’s trajectory is deflected from what it would be without the warping. That is Einstein’s picture of gravity.
Anything that has mass, or energy of any kind, warps space-time in its vicinity (well, actually everywhere, but to a greater extent close by). So the Sun warps space-time and that causes the trajectories of thing moving near the Sun to be deflected. If an object is moving faster than the “escape velocity” from the Sun, the object will be deflected, but not enough to keep it from travelling farther and farther from the Sun. On the other hand, if an object is moving slower than the escape velocity, it will deflected so much that it gets trapped in an orbit.
The escape velocity from a body depends on the mass of that body and how far away you are from the body. At the surface of the Sun, the escape velocity from the Sun is about 618 miles per second, whereas at the location of the Earth the escape velocity from the Sun it is “only” about 26 miles per second. Notice that both of these escape velocities are much less than the speed of light. Light in empty space always goes 186,000 miles per second. So light that starts at the surface of the Sun or anywhere outside the Sun will always escape from the Sun rather than orbiting it.
On the other hand, suppose there is a “star” which has the same mass as the Sun, but a radius of, say, 1 mile. The gravity at its surface would be so strong that the escape velocity from its surface would be greater than the speed of light. In fact, for any place within 1.9 miles of the center of that “star” (called the Schwarzschild distance for that star) the escape velocity would be greater than the speed of light. Moreover, not only is it impossible for an object closer to the star than its Schwarzschild distance to escape, it cannot even remain at the same distance from the center of the star by orbiting, it inexorably gets pulled into the center. Indeed, the material of star itself suffers the same fate: it gets pulled all the way into the center. This situation is called a “black hole”. It is a region of space where the gravity is so strong that nothing --- even something going the speed of light –- can escape, but instead gets sucked into the center.
-Stephen Barr
