Why can't Light Escape Black Holes?

[DRC12]

If light is transmitted by photons and photons are massless and gravity only affects particles with mass, then why can't light escape black holes' giant gravitational force?

 

[Mark M]

Gravity doesn't only affect particles with mass. In general relativity, the stress-energy tensor is the source of gravitation. Since photons have energy, they also gravitate.

 

[DRC12]

I swear a read that massless particles weren't affected by gravity but it must've just been that they don't create their own gravitational fields. Ether way that clears that up thanks

 

[Mark M]

I swear a read that massless particles weren't affected by gravity but it must've just been that they don't create their own gravitational fields. Ether way that clears that up thanks

They don't gravitate or have gravitational fields in Newtonian gravity. In general relativity, gravity is equated with the geometry of spacetime. So, massless particles also curve spacetime and will gravitate to each other. Even though it is very small, two photons in empty space will attract each other.

 

[DRC12]

But doesn't the mass of an object affect how much it warps spacetime? so how could photons curve spacetime, or is it based on their energy?

 

[Mark M]

But doesn't the mass of an object affect how much it warps spacetime? so how could photons curve spacetime, or is it based on their energy?

Energy. Remember that the rest energy associated with the mass of a particle is E = mc^2, so mass makes by far the largest contribution since c^2 is an enormous number. That's why Newtonian gravity is such a great approximation. However, in GR, other forms of energy make a small contribution, too. An object with more kinetic energy will have a stronger gravitational field (or it will curve spacetime more, if you like), although the difference is very negligible. So, photons still interact gravitationally because of their other forms of energy, but since they are massless this is much weaker than, say, a rock.

 

[Naty1]

An object with more kinetic energy will have a stronger gravitational field (or it will curve spacetime more, if you like),

This is an ok description as a start but is technically incorrect; if it were correct, a particle traveling at sufficient velocity could turn into a black hole. Better to say:more KE, then more curvature, NOT more gravity.

A succinct description was given in another discussion:

A single particle moving at a high velocity will not become a black hole. A pair of particles colliding can become a black. Relative to some observers, you are right now moving at 99.999999% of the speed of light. But you are not a black hole [and will not become one]. Not to yourself, and not to the observer at which you are moving at such a high velocity - because being a black hole is frame independent.

It is worth mentioning that the source of gravity in general relativity is the stress energy momentum tensor {SET}. So mass, energy,stress, momentum and also pressure have gravitational effects. Only those component sources in the frame of the SET contribute to gravitational curvature; additional curvature, such as from KE, might loosely be considered 'gravity', but is technically a different type of spacetime curvature.
One especially interesting example of gravity is the negative pressure attributed to dark energy: such negative pressure is repulsive! It is believed to be the cause of cosmological expansion.

An observational example of gravity bending light is 'gravitational lensing'...and was a major factor in confirming Einstein's prediction...Wikipedia discusses it.

 

[Mark M]

Thanks Naty. I should've been a bit mire careful with my terminology, and used momentum instead of KE. And thanks for the quote.

 

[CCWilson]

Isn't it because massive gravitation deforms spacetime so much that with respect to an outside observer, time has almost stopped within a black hole? Since light's speed is constant per unit of time, that means its progress toward the outside world would be almost infinitely slow.

 

[Vorde]

Isn't it because massive gravitation deforms spacetime so much that with respect to an outside observer, time has almost stopped within a black hole? Since light's speed is constant per unit of time, that means its progress toward the outside world would be almost infinitely slow.

Not really, the 'time-slowing' way of looking at a black-hole is only valid outside the event horizon, and then only if you are really careful with your words.

The much better way to put it is that black holes bend space so much that within the event horizon, every possible path is pointed inwards.

The analogy is that it is a hill so steep that you cannot possible walk up it, no matter how strong you are, you must walk down.

 

[hover guy]

First of all there is a difference between the rest mass and the relativistic MASS, in general relativity an object which moves with a velocity shall experience an in crease in its mass. Similarly the rest mass of a photon is zero but yet its energy provides its mass (m=hf/c2).The second thing is that , its more important to know how gravity actually works, gravity is nothing but curves and disturbances caused by the gravitational field with the space time, also see gravitational lensing, it will justify Ur questions .

 

[hover guy]

i wonder what happens to a photon once it comes to rest and its rest mass becomes zero, such that no gravity can act on it, so should the photon have escaped , just after it was sucked?

 

[Vorde]

i wonder what happens to a photon once it comes to rest and its rest mass becomes zero, such that no gravity can act on it, so should the photon have escaped , just after it was sucked?

Photons can't come to rest. They are always moving at c.

 

[CCWilson]

Not really, the 'time-slowing' way of looking at a black-hole is only valid outside the event horizon, and then only if you are really careful with your words.

But we are outside the event horizon. I assume that for a hardy observer inside the event horizon, time goes on as usual from his standpoint, and light travels at its usual speed. Right?

 

[Vorde]

Time always goes on 'as usual' from any standpoint. It's just that you might see someone else's time differ from yours. Likewise, light always travels at the same speed c.

 

[Naty1]

Thanks Naty. I should've been a bit mire careful with my terminology, and used momentum instead of KE. And thanks for the quote.

That 'curvature issue' is a subtle point I sure did not understand until Dr Greg here spent some time a few years ago explaining it to me in these forums. I would not even bother to mention it but there are frequent questions why a superfast particle can't become a black hole...

Here are a few more relevant comments I saved:

PeterDonis: “..if one is inferring from either the relativistic mass or the stress-energy tensor that an object's behavior as a source of gravity depends on its state of motion relative to you, one is inferring incorrectly.

This sounds like pervect, but I did not record the poster:

The stress-energy tensor takes into account both the object's rest energy and the object's motion (and pressure and internal stresses in the object) in such a way that the [space time] curvature caused by the object is frame-invariant. The sign of the metric is opposite for the timelike and spacelike terms, so you generally expect the timelike and spacelike components to have somewhat opposite effects. But this doesn’t mean that a hot object doesn’t have different trajectories in a gravitational field than an identical cold object.

DrGreg summarized a perspective:

So, to summarize, "spacetime curvature" refers to the curvature of the graph paper, regardless of observer, whereas visible {apparent, observer dependent} curvature in space is related to the distorted, non-square grid lines drawn on the graph paper, and depends on the choice of observer. In the absence of gravity, spacetime [graph paper] is always "flat" whether you are an inertial observer or not; non-inertial observers will draw a curved grid on flat graph paper.

And good separate discussion is here for those interested:

Does the speed of moving object curve spacetime?
https://www.physicsforums.com/showthread.php?t=602644

 

[Naty1]

time has almost stopped within a black hole?

That is a coordinate dependent effect at the horizon...That means using certain coordinate descriptions time appears to be a singulariy at the horizon. For other coordinate
descriptions there is no such effect. Even with Schwarzschild coordinates which are
usually used for non rotating non charged black holes, a hovering [stationary] observer [either near the horizon or millions of miles distant] detects such a timelike horizon while a free falling observer does not detect any horizon whatsoever. The former gets fried
by radiation, the latter sees none; this is entirely analogous to the Unruh effect.