# If light approaches a black hole will it accelerate?

1. Feb 16, 2014

### hayden47

If light approaches a black hole will it accelerate? I think this question ties in with whether light has mass or not. Does light have mass? It seems accepted that light has momentum, but this is not consistent with saying that photons are mass-less (momentum=mass*volume). Could someone clear this up or is it actually a contradiction? Mass is a requirement for gravity also. I've always heard that not even light can escape a black hole which is gravitational force, so wouldn't a black hole have enough force to accelerate light?

2. Feb 16, 2014

### Staff: Mentor

Photons are massless. The relationship between energy, momentum, and mass is $m^2 c^2=E^2/c^2-p^2$. For photons $p=E/c$ so the mass is 0 despite having both energy and momentum.

3. Feb 16, 2014

### hayden47

Oh I see. I'm still confused then of how gravity can affect light if it does not have mass (such as a black holes' effect on light).

4. Feb 16, 2014

### Staff: Mentor

Why should that matter?

First, Newtonian gravity is experimentally known to be wrong wrt the effect of gravity on light.

Second, in GR gravity curves spacetime and spacetime clearly affects light.

Third, even if you ignore the previous two points it takes 0 force to accelerate something without mass, so the fact that the Newtonian force is 0 doesn't imply that the acceleration is 0.

5. Feb 16, 2014

### hayden47

6. Feb 16, 2014

### Staff: Mentor

Light does not accelerate. It always moves at c in a vacuum. It will, however, gain energy by falling into the gravity well and be blueshifted.

7. Feb 17, 2014

### bahamagreen

If you are imagining that the light that can't escape the BH is traveling away from the BH and being slowed down or stopped by the BH's gravitational acceleration... and therefore supposing that the reverse would be that the BH can accelerate light moving close or toward the BH, then maybe this line of thinking may be causing the problem.

Look for something about light cones, and how they change "orientation" around a BH.

Here is an example - http://www.phy.syr.edu/courses/modules/LIGHTCONE/schwarzschild.html [Broken]

The light that can't escape the BH does not have a radial direction component away from the BH in its future light cone... the light cones can be oriented so that their "outer" edge is tangent to the event horizon.

(I've probably butched this description, but I think it is the concept needed here).

Last edited by a moderator: May 6, 2017
8. Feb 17, 2014

### hayden47

Acceleration is a change in velocity. Velocity is a measurement of direction and speed. The website you pointed me to says "The Einstein Theory correctly predicted the amount of the deflection of starlight". Is this acceleration?

9. Feb 17, 2014

### phinds

No. As Drakkith said, light always travels at exactly c in a vacuum. It also always travels in a "straight line", BUT ... a "straight line" in a high gravity field is a "straight line in spacetime" and that is not quite what you normally mean by "straight line". The deflected path IS a "straight line in spacetime", which in more formal parlance is called a "geodesic".

10. Feb 17, 2014

### Staff: Mentor

And how much force does it take to accelerate a massless object. What does Newtons 2nd law say?

Sure it would. Plug 0 in for the mass, what is the gravitational force? How does that compare to your answer above?

Newtonian gravity gives the wrong behavior for light, but not because of it being massless.

11. Feb 17, 2014