# How can a black hole bend light?

#### ShawnD

Black holes are currently thought to just be big things (lack of better word) of gravity that pull stuff in. If gravity relies on mass and light has no mass, how is light pulled into black holes?

Related Other Physics Topics News on Phys.org

#### Mumeishi

Because they bend space-time - the light moves in a straight path through curved space-time - right into the black hole. See Einstein for more details.

#### Zhou Yu

Basically anything that bends space time will cause light to bend, therefore even a large sun will bend light even though it will not be to the same extent as a black hole.

I guess if you think of space time as a 2D sheet, then place various celestial objects with a large mass on the sheet. They will cause a slight dent in the sheet, this is a simple analogy of what happens.

However if light travels too close to a black hole then it will not have the velocity required to escape the black hole. If this is true then on a 2D sheet representing space time, would the black hole create a bottomless abyss?

So does a black hold merely bend space time and create a bottomless pit or does it create a "rip" in space time?

Any information on such a topic would be most appreciated

#### pmb

Originally posted by ShawnD
Black holes are currently thought to just be big things (lack of better word) of gravity that pull stuff in. If gravity relies on mass and light has no mass, how is light pulled into black holes?
Light does have mass. You're thinking about rest mass which is different. In The Evolution of Physics - from Early Concepts to Relativity and Quanta, Albert Einstein and Leopold Infeld, Simone & Schuster (1938), page 221 - Einstein commented on an observation made by an observer inside an accelerating elevator that light is ‘weightless’ Einstein wrote
But there is, fortunately, a grave fault in the reasoning of the inside observer, which saves our previous conclusion. He said: “A beam of light is weightless and, therefore, it will not be affected by the gravitational field.” This cannot be right! A beam of light carries energy and energy has mass.
This same sentiment was expressed by Feynman in Feynman Lectures Vol - I, page 7-11. Section entitled Gravitation and Relativity
One feature of this new law is quite easy to understand is this: In Einstein relativity theory, anything which has energy has mass -- mass in the sense that it is attracted gravitationaly. Even light, which has energy, has a "mass". When a light beam, which has energy in it, comes past the sun there is attraction on it by the sun.
Pete

#### pmb

Originally posted by Zhou Yu
Basically anything that bends space time will cause light to bend, therefore even a large sun will bend light even though it will not be to the same extent as a black hole.
The bending of space is not what causes the bending of light. In fact Einstein's first calculation of the deflection of light by the sun did not take spatial curvature into account and yet there was still a deflection. When spatial curvature is added then there is more delfection. So curvature contributes to deflection but is not the sole cause of delfection. Also - Spacetime curvature is not a neccesary condition of the gravitational attraction of light.

Pete

#### Ambitwistor

Re: Re: How can a black hole bend light?

Originally posted by pmb
Light does have mass.
According to one definition of mass, light has mass. According to another, it doesn't. ShawnD is not wrong.

The specific question of how massless light can be deflected by gravity is answered in this FAQ:

http://math.ucr.edu/home/baez/physics/Relativity/SR/light_mass.html [Broken]

You're thinking about rest mass which is different.
"Rest mass" cannot be defined for light, which is never at rest. Light has zero invariant mass. Rest mass is a special case of invariant mass that applies to massive bodies.

Last edited by a moderator:

#### pmb

Re: Re: Re: How can a black hole bend light?

Originally posted by Ambitwistor
According to one definition of mass, light has mass. According to another, it doesn't. ShawnD is not wrong.
Show me where I said "ShawnD you are wrong" and I will delete it.
"Rest mass" cannot be defined for light, which is never at rest. Light has zero invariant mass. Rest mass is a special case of invariant mass that applies to massive bodies.
The so-called "invariant mass" is the name given to the magnitude of the total 4-momentum of a system of particles. The term "rest mass" is the name given to the m0 in

m0 = sqrt[E2 - (pc)2]/c2

If the 'system' of particles is one particle then the invariant mass is identical to rest mass.

However - I've never liked this definition of rest mass and as such I've always held that m0 should be refered to as proper mass. However most people on the internet don't know what the term proper mass means. However, since the term "A photon has zero rest mass" is a phrase which is widely used in physics and it clarifies that it is rest mass that is being refered to then I choose to use it. In fact Thorne and Blanchard explain this in their new text. I.e. from --
http://www.pma.caltech.edu/Courses/ph136/yr2002/chap01/0201.2.pdf (Note: T = tau. Z =zeta)
The above formalism is valid only for particles with nonzero rest mass, m != 0. The corresponding formalism for a particle with zero rest mass can be obtained from the above by taking the limit as m -> 0 and dT -> 0 with the quotient dZ = dT/m held finite.
where "m" here means "rest mass." I see no mention of the term invariant mass in that text. Its not a widely used term in all of relativity. In other texts it refers to systems of particles only.

As far as the FAQ goes - that is one person's opinion on this topic. For another person's opinion then see
http://www.astro.washington.edu/tmurphy/phys110/faqs/AB05.05.html
Question: If light can be pulled into a black hole due to huge gravity forces, does this necessarily mean that light has mass?

Answer: This is an exceedingly subtle question. The photon (particle representation of light) is called a massless particle, because it has no rest mass. It's never sitting still. So all its energy is energy of motion. Ordinary objects, like a pencil, have both a rest mass-energy: E = mc2, and an energy of motion (kinetic energy): E = (1/2) mv2. Note the remarkable similarity between these forms.

But the most honest answer to your question is yes--light has mass. I say this, running against the physics grain (photons have no mass), because the photon in all respects behaves as if it has mass. It is affected by gravity (light is deflected by gravity). It carries momentum. It creates dimples in spacetime (albeit tiny), like any mass or energy does. The fact that it has no rest mass is irrelevant in many respects, because it never travels any slower than light speed!
That link you posted has many conceptual errors in it. I.e.
Sometimes people like to say that the photon does have mass because a photon has energy E = hf where h is Planck's constant and f is the frequency of the photon.
Theoretically this has never been the case. That's more of a poor-man's view of the physics. In all truely rigorous definitions and derivations the term relativistic mass refers to the ratio of momentum to speed. A.P. French was right on the mark in his text on this point. However he refers to this ratio as inertial mass, not relativistic mass. To be precise, relativistic mass, m, is defined such that mv is a conserved quantity. So anything which has momentum has mass. For a rigorous definition and for the derivations see

The Classical and Relativistic Concepts of Mass,, Erik Eriksen and Kjell Voyenli, Foundations of Physics, Vol. 6, No. 1, (1976).

Or see any text on relativity.

Trying to define mass as the m in

m = sqrt[E2 - (pc)2]/c2

is a circular arguement since p is defined in terms of this m.

Staff Emeritus
Gold Member

Integral

#### pmb

Originally posted by Integral

Integral
These are two different topics which are related. The other thread has to do with whether a particle's mass increases with speed. This thread has to do with whether light has mass and as such is the reason why it is deflected by gravity. This, however, is often taken to be the same question. However it was not so to Einstein. In fact Einstein would not have used relativistic mass in the first case but would use relativistic mass in the present case.

#### chroot

Staff Emeritus
Gold Member
pmb, Ambi --

Let's not have another discussion about the definition of mass; the one you already had was already unnecessary. pmb, stop arguing about definitions, and stop acting like your way is the only way -- you know it isn't. Ambitwistor, please stop egging him on.

- Warren

#### pmb

pmb, stop arguing about definitions, and stop acting like your way is the only way -- you know it isn't.
- Warren
If you got the impression that I think my way is the only way then you got the wrong impression. I've never made that claim nor have I ever had that thought it, especially since I believe that definitions are beyond question. There is calculation, historical fact and modern usage (e.g. texts, journals etc). That is what I've discussed.

Also, when someone asks a question which requires repeating something I've explained in the past it would be rude and improper to ignore that person. Especially since there is a fundamental rule of learning: The more you explain something the better you understand it. If you are a teacher, or have tutored, then you know that all too well.

Pete

#### chroot

Staff Emeritus
Gold Member
Originally posted by pmb
If you got the impression that I think my way is the only way then you got the wrong impression. I've never made that claim nor have I ever had that thought it
Pete,

You said specifically that
Light does have mass. You're thinking about rest mass which is different.
This would indicate to me (and anyone else reading this thread) that you would disagree with anyone who says "light is massless" -- since that's exactly what you just expressed.

Please stop arguing definitions unless the meaning is clearly relevant to the discussion (in this case, the arugment just isn't relevant).

- Warren

#### pmb

Please stop arguing definitions unless the meaning is clearly relevant to the discussion (in this case, the arugment just isn't relevant).
I'll do better than that

#### FZ+

The bending of space is not what causes the bending of light. In fact Einstein's first calculation of the deflection of light by the sun did not take spatial curvature into account and yet there was still a deflection. When spatial curvature is added then there is more delfection. So curvature contributes to deflection but is not the sole cause of delfection. Also - Spacetime curvature is not a neccesary condition of the gravitational attraction of light.
Wait... are you sure this is right? If I remember correctly, and there is a good chance that I'm not, GR puts gravitational attraction in terms of distorted spacetime. You can't have any gravitational attractive, massive or not, without such spacetime distortion, or implicitly taking into account of spatial curvature.

#### †ony

So is it possible for light to orbit a black hole if it goes by at just the right distance and speed relative to the black hole?

#### sea_wizard

i like that idea of the light not existing but the force of the black holes spinnig around it and creating the perception of it.then the force would have created the light because of liking it

if the existence of the present depended on the existence of light because the posibilty of the existence of the present among the infinite of time is like that to get one over infinite and do you think is possible to get aleatorium numbers from 1 to 10 and get 0000...0000 and so on for ever well i dont know maybe the ... has big gaps of 0s because everybody was too pissed off with what they were seeing as to not even one of the most simple souls would want to see light, but then again if we are here in the middle of eternity is because at least theres something that is etenal.
of course because of the beauty of light it grows stronger every time

of course this is just what i think i really expect not to be taken too seriously

#### chroot

Staff Emeritus
Gold Member
Originally posted by †ony
So is it possible for light to orbit a black hole if it goes by at just the right distance and speed relative to the black hole?
Yes. That orbital distance is 1.5 times the black hole's Schwarzschild radius.

- Warren

#### jasono

since black absorbs light could there be a colour so black that it not only takes in all the light but bends any light towards it?

#### nasageek

A black hole not only absorbs light and matter, it also distorts space time so much it bends light.

#### rcgldr

Homework Helper
Since the speed of light is unaffected by large masses, just bent, how do we know that it's gravity bending a beam of light as opposed to some sort of (yet unknown) refaction effect unrelated to gravity?

### Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving