Why light can't escape from a blackhole if they have no mass?
I can understand why you would ask this question, given that the Newtonian equation for the force of gravity is:
This equation describes WHAT gravity does to objects that have mass. But it does not explain HOW gravity works. Gravity works, because objects that have any mass cause curves in space-time. The effect that this curvature has on other objects (that are, also, causing curves to space-time) is to cause them to deviate from their normally straight trajectory to a curved trajectory. This mutual curving and trajectory deviations is what we call gravity.
Photons of light are not exempt from this effect. We have many scientific observations that confirm that, though photons have no mass, they must follow these curvatures of space-time. A scientist named Karl Schwarzschild , discovered that, in a black hole, space-time can be so extremely curved that any light following this curvature cannot escape but, instead, doubles back on itself. This is why light cannot escape from a black hole.
Light is curved by a gravitational field. Time slows down in the presence of gravity, the affect of time slowing bends the light. In a black hole the gravity is so great light cannot escape.
One of the predictions of Einsteins theory of relativity was that light would be bent by gravitational forces. Einstein's theory was that gravity would bend space. The bending of space would also bend light waves by slowing down time. Pictures of stars taken during an eclipse verified Einstein's predictions.
In a black hole the gravity would be so great that space would be bent to the extent that time will stop. With no time light itself can not escape the black hole. The singularity the boundary of the black hole is a point where time slows down to zero.
The effect of gravity on time has been verified by many experiments. But the effect of gravity on time is difficult to understand as time is usually thought of as a constant instead of the variable quantity it is.
An example is the common practice of using light years as a measure of time when it can actually only be used as measure of distance.
The singularity of the Black hole bends space to the extent that nothing can escape the boundary of the Black Hole. Time itself stops at the boundary and with no time light can not move.
Newtonian gravity describes gravity as a force which is related to mass. This is not actually true, particularly close to a black hole.
Newton describes gravity as a force. Einstein proved this to be incorrect.
Mass, energy and momentum all curve the fabric of 4 dimensional space time. Also, gravity is equivalent to acceleration. Gravity is actually a direct consequence of all bodies moving in a gravitational field follow geodesics. A geodesic is the 4 dimensional equivalent of a straight line.
Photons have no mass and as a consequence travel at the speed of light. In fact as a consequence of this they don't experience the passage of time. They also have to follow geodesics which is why gravity bends light.
Every object has an escape velocity. This is the velocity required to completely escape a gravitational field.
The Schwarzschild solution to Einstein's field equations of General Relativity appears to have a singularity for any object of mass
The Schwarzschild radius of a body smaller than
At or inside the Schwarzschild radius, no geodesic can leave the black hole. Thus effectively the escape velocity is the speed of light. This means that nothing can leave a black hole, not even light.