# What happens if gravity accelerates a object to a speed faster than light?

Suppose a rock has an initial velocity of almost the speed of light when a planet or star's gravity starts accelerating it. (Need NOT be a black hole) Will its speed pass the speed of light or will it not accelerate any more?

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Not sure whether you want the answer from classical Newton plus special relativity or just general relativity.

From the classical Newton gravity standpoint where we can treat gravity as just another force, plus special relativity, we can simply use the relativistic energy-momentum equation where the change in both the time component and space components of 4-momentum approach infinity as the gamma factor, γ, approaches infinity as v with respect to standing on the ground approaches ‘c’. I’m pretty sure you already know that .....

Since you have mentioned having a physics degree, we can talk a bit about GR. The 4-acceleration involves both the 4-velocity and the ‘connection’ components (Christoffel symbols) that contains derivatives of the metric tensor. The following is the General Relativity equation for 4-acceleration:

aᵏ = d²xᵏ⁄dτ² = -⌈ᵏᵤᵥ(dxᵘ/dτ)(dxᵛ/dτ)

aᵏ = components of 4 acceleration

d²xᵏ⁄dτ² = components of 4-acceleration as second derivatives of some reference frame with respect to proper time

⌈ᵏᵤᵥ = connection components (first derivatives of metric tensor - solutions to field equations)

(dxᵘ/dτ)(dxᵛ/dτ) - permutations of components of 4-velocity

The equation contains the same 4-velocity as special relativity (derivative with respect to proper time) so we know its magnitude cannot be greater than ‘c’ regardless of the connection components. The observed acceleration is also coordinate dependent and connection dependent. Locally, where it counts, no matter what the gravity, local velocity of light cannot be exceeded.

• Jeffrey K
Lv 6
1 month agoReport

Neb, I was looking for a Newton gravity + special relativity explanation that I could explain to students. Your description confirmed my thoughts.
Thanks for the GR info. It is more correct but difficult to describe to a non physicist.

• Anonymous
1 month ago

Easy, it can't.  End of question

• Acceleration is dependent on the field strengths of gravity and magnetic field. A particle mass of light in free fall on earth would experience a greater velocity than light speed exiting from the sun.

Einstein gave an equation to what happens when a particle of light is moving towards a gravity field as follows;

C' = C + Phi .

where C is the speed of light in an inertial field.

Phi is the square root of GM/ R =where G is newton constant and M is the gravitational mass.

• goring
Lv 6
1 month agoReport

Phi ^2 varies hyperbolically

• It'll get closer and closer to the speed of light, but never quite reach it. Acceleration, just like velocity, gets reduced the closer your get to the speed of light. Relativistic speeds aren't linear, but asymptotic, meaning they have a maximum amount beyond which they can't rise.

• The rock will accelerate closer and closer to the speed of light, but will never reach that speed.  It will be 0.9c, 0.99c, 0.999c, 0.9999c, etc.

• You completely misunderstand the theory of relativity.

THINGS DO NOT HAVE A SPEED.

The only speed is relative to something else.

The rock cannot HAVE "an initial velocity of almost the speed of light". To a physicist this statement makes no sense at all.

It might be moving at a high speed relative to us. Perhaps. yet what speed relative to the planet?

all necessary to even start to analyze the process

• Jeffrey K
Lv 6
1 month agoReport

Good point. I should have said the rock has a speed near that of light relative to the planet and it is headed directly toward the planet.

• Mass increases with velocity such that at the speed of light the mass becomes infinite. Since gravitational attraction is related to mass, at some point your rock reaches a mass that starts attracting the planet or star and it's own acceleration slows down. The relationship between mass and velocity also means the energy required for an infinite mass to reach the speed of light is also infinite, it means it can never happen.

• neb
Lv 7
1 month agoReport

Except for the minor fact that mass doesn’t increase with velocity and you cannot create a black hole from relative motion.

• The first thing to take into account is that, at high velocities, mass increases. The greater the mass, the more inertia (resistance to change of velocity) the body has. At the speed of light, the body would have a theoretical mass of infinity -- the body would act like a massive black hole (maybe even implode the whole universe).

In other words, the Newtonian model of acceleration doesn't apply in the ways we know of.

• goring
Lv 6
1 month agoReport

its just the inverse;the smaller a mass becomes the faster it moves

• There is no speed faster than light. If matter could be accelerated to the speed of light it would turn into energy.

• nobody is quite sure. there are probably ways to exceed The Speed of Light. Vsauce claims Shadows do this.