Photons and Black holes

Question

A black hole is listed as "a region of spacetime exhibiting such strong gravitational effects that nothing—not even particles and electromagnetic radiation such as light—can escape from inside it" One thing i don't understand is how photons cannot escape from them. If they don't have mass, then how can gravity exert any force on them?

Answer 1

Newtonian gravity is one thing, Einstein's General Relativity is another. In Newtonian gravity the force acts on massive particles according to the inverse square force law well known.

In GR things are different. In GR gravity isn't a force but a property of spacetime. The key idea is: freely falling particles - those feeling just gravity and not any other interaction - follows geodesics of spacetime.

So first of all: what is spacetime? In the mathematical terms, spacetime is a smooth Lorentzian manifold endowed with some extra structure. It is just the result of bringing space and time together in a cohesive way, that proved to be the right way to match observations.

It is a four-dimensional space, with a metric $g_{\mu\nu}$ which describes its geometry. Einstein's GR is based on the fact that the effects of gravity are encoded on $g_{\mu\nu}$ which is the unknown in Einstein's Field Equations.

Points of spacetime are called events. So spacetime is comprised of all possible happenings. On such spacetime many geometric notions can be developed. One of them is the worldline, it is a one-parameter family of events, a continuous sequence of events if you like. The history of a particle (massive or massless) is described by a worldline containing all the events on its history.

What are geodesics then? Geodesics are the straightest paths possible in spacetime. In a flat space like a plane, geodesics are straight lines really, but in a curved space that won't happen. In a sphere for example, geodesics are the great circles.

Now it is a postulate that massive particles follow the so-called timelike worldlines, because they have speed less than that of light, while massless particles will follow the so-called lightlike worldlines, because they have the speed of light. So freely falling massive particles will move in timelike geodesics and freely falling massless particles will move in lightlike geodesics.

Either way, the point of GR is: the geometry of spacetime determined by the distribution of energy through Einstein's Field Equations will determine the spacetime geodesisc which in turn will change how particles travel in the absence of other interactions. That is how they feel gravity, and that is how light feels gravity.