# The speed of light and gravity

#### Forestman

I know that according to the theory of special relativity that nothing with mass can travel at the speed of light because it gains mass, but what happens if when an object is accelerated by a gravitational field that it begins to get close to the speed of light? I guess what I am asking is, what stops gravity from being able to pull an object to the speed of light or faster. I know that this cannot happen, so that is why I am confused.

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#### Dmitry67

Well, words are slippery. I will try to give an oversimplified explanation.

Cravity CAN be so strong that t can 'accelerate objects faster then light'. It happens inside the black hole. WHen objects reach the horizon, they (gradually) dissapear from the view as even light is sucked inside the black hole.

The limitation (information can not be transfered faster then light) is applicable only to the local nearly-flat region of space and is not generally applicable to distant objects in the curved spacetime

#### Vals509

i am not sure about my answer but i believe that probably gravity can't get the object to the speed of light as the object will become too heavy for gravity to accelerate it and that the object might start to attract the gravitational field source rather than the vice versa defeating the entire purpose.

#### HallsofIvy

Homework Helper
The same thing that prevents any force from accelerating an object beyond the speed of light: Force= dp/dt where p is the momentum. As the speed of an object nears the speed of light its momentum increases without bound so greater and greater force is required to accelerate it.

(I started to write "F= ma" but that would require talking about "mass increasing" and many people who are more knowledgable about relativity than I am object to that.)

#### Dmitry67

The same thing that prevents any force from accelerating an object beyond the speed of light: Force= dp/dt where p is the momentum. As the speed of an object nears the speed of light its momentum increases without bound so greater and greater force is required to accelerate it.

(I started to write "F= ma" but that would require talking about "mass increasing" and many people who are more knowledgable about relativity than I am object to that.)
I think it would be more useful to learn the gravity is not a force at all.
For example, one picture like this one:
http://nrumiano.free.fr/Images/lightcones_E.gif
is much better then many wordy explanations.

#### Forestman

Thanks you guys, that does help clear a lot of things up in my mind.

#### A.T.

One way to think about it, is that everything already advances at light speed trough space-time. Forces or gravitation (space-time curvature) merely change the direction of that advance trough space-time. So light speed trough space is the maximum you get if you don't move trough time anymore.

#### Howard Rosen

The classic reason for why mass can not reach the speed of light is that since the mass continues to increase as you approach the speed of light you will need an infinite amount of enrgy to reach it. Since there is no such thing as an infinite amount of energy the mass can never reach the speed of light.

Howard

#### Nickelodeon

I get the impression that a lot of people interested in Special and General Relativity suddendly forget the significance of the 'relative' part of it all and start putting constraints on the physical universe without qualification.

There is a difference between observed phenomena and actual phenomena. For instance, some distant galaxies have an observed 'speed of separation' approaching 2c. If they 'observe' each other, then, assuming they can see each other at all, then they will presume the other is only going away at a max speed of c.

Using light as the information carrier you are only ever going to get observed max velocity approaching that of c for an object with mass.

The cause of gravity is still an open question, so perhaps whatever produces the gravity effect may be able to alter the characteristics of spacetime to accelerate mass beyond c.

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#### stevebd1

Gold Member
Another thing worth considering is that for a static black hole, as Dimtry67 stated, an infalling object attains c at the event horizon; for an infalling object falling from rest at infinity this can be expressed as the radial proper velocity where $v_{rel}=-\sqrt{2M/r}$ where v=c at the EH. This changes slightly for a rotating black hole where radial proper velocity equals-

$$v=-\frac{\sqrt{2Mr(r^2+a^2)}}{\rho^2}$$

where $\rho^2=r^2+a^2cos^2\theta$

which is used in Doran coordinates (which are basically Gullstrand-Painleve coordinates for a rotating black hole).

Here it seems that proper radial velocity exceeds c not just outside the event horizon but outside the ergosphere also. This seems in some way analogues to proper v>c for the distant expanding universe but in this case, it's a combination of extreme gravity and frame dragging so you appear to have a global effect and local effect where proper v can exceed c. The above Kerr equation for proper radial velocity reduces to the Schwarzschild solution when a=0 (i.e. no spin)

Source- http://arxiv.org/PS_cache/arxiv/pdf/0805/0805.0206v2.pdf [Broken] page 2

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