# Relativistic mass, Gravity and Dark matter.

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It was observed that the velocities of stars did not decrease as you move away from a galaxies center and that the luminous mass did not create enough gravity. Originally this effect was written off as the galaxy absorbs light and planets and asteroids which do not create light would account for the missing mass. It turns out they do not and the missing mass problem became known as dark matter. The theory that some matter only interacts gravitationally and has helped form and shape galaxies.

I have a few questions:

Does an object which spins gain mass due to kinetic energy?

Can relativistic mass cause gravity?

I was thinking of this problem and wondered about relativistic mass of the galaxy due to rotational and translational kinetic energy of the components of the system. Some kind of emergent property of interplay between mass, kinetic energy and gravity. As you move quicker you gain more mass which increases gravity and then you go quicker... etc.

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It was observed that the velocities of stars did not decrease as you move away from a galaxies center and that the luminous mass did not create enough gravity. Originally this effect was written off as the galaxy absorbs light and planets and asteroids which do not create light would account for the missing mass. It turns out they do not and the missing mass problem became known as dark matter. The theory that some matter only interacts gravitationally and has helped form and shape galaxies.

I have a few questions:

Does an object which spins gain mass due to kinetic energy?

Can relativistic mass cause gravity?

I was thinking of this problem and wondered about relativistic mass of the galaxy due to rotational and translational kinetic energy of the components of the system. Some kind of emergent property of interplay between mass, kinetic energy and gravity. As you move quicker you gain more mass which increases gravity and then you go quicker... etc.

Does an object which spins gain mass due to kinetic energy? Yes. It is energy within a bound system. It adds to the rest mass of the object.

Can relativistic mass cause gravity? As per above example yes, but generally not and/or misunderstood.

Some kind of emergent property of interplay between mass, kinetic energy and gravity...(well stated) but I don't believe that is enough to account for dark matter and likely is a small effect that has already been taken into account

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Thanks for the reply J.C MacSwell.

Gravitationally what's the difference between relativistic mass and rest mass?

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Gravitationally what's the difference between relativistic mass and rest mass?

Mass and energy are subtle issues in general relativity and you should be aware of that.

Anyway, relativistic mass is not a concept employed much in modern physics. One usually talk just about mass meaning rest or invariant mass.

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Thanks for the reply J.C MacSwell.

Gravitationally what's the difference between relativistic mass and rest mass?

A particle's rest mass, mo is a source of gravity or spacetime curvature. A particle's relativistic mass, mr is also a source of gravity. It is given by mr = m0 / sqrt (1 - v2/c2) where v is relative velocity and c is the speed of light. Here a particle's "apparent" mass approaches infinity as its relative velocity approaches the speed of light.

However, as ajb points out, relativistic mass is not so popular with physicists. Relativistic momentum, p is preferred, where p = m0 v / sqrt (1 - v2/c2). Here a particle's mass remains constant and its momentum approaches infinity as its relative velocity approaches the speed of light. This method better represents the underlying physics.

For gravity, it is best to think in terms of energy, which is a source of gravity:

- A particle's rest energy, E0 is E0 = m0 c2.

- A particle's total energy, E is E = E0 / sqrt (1 - (v2/c2). So its total energy also approaches infinity as its relative velocity approaches the speed of light. This is one reason why no particle with mass can travel at the speed of light.

http://www.marksmodernphysics.com/

Edited by IM Egdall
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A particle's rest mass, mo is a source of gravity or spacetime curvature. A particle's relativistic mass, mr is also a source of gravity. It is given by mr = m0 / (1 - v2/c2) where v is relative velocity and c is the speed of light. Here a particle's "apparent" mass approaches infinity as its relative velocity approaches the speed of light.

However, as ajb points out, relativistic mass is not so popular with physicists. Relativistic momentum, p is preferred, where p = m0 / (1 - v2/c2). Here a particle's mass remains constant and its momentum approaches infinity as its relative velocity approaches the speed of light. This method better represents the underlying physics.

For gravity, it is best to think in terms of energy, which is a source of gravity:

- A particle's rest energy, E0 is E0 = m0 c2.

- A particle's total energy, E is E = E0 / (1 - (v2/c2). So its total energy also approaches infinity as its relative velocity approaches the speed of light. This is one reason why no particle with mass can travel at the speed of light.

http://www.marksmodernphysics.com/

Mr = M0 / sqrt( 1 - v^2/c^2 )

p = M0 * v / sqrt( 1 - v^2/c^2 )

E = E0 / sqrt( 1 - v^2/c^2 )

Edited by Sensei
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Thanks for the reply J.C MacSwell.

Gravitationally what's the difference between relativistic mass and rest mass?

I wish I could answer that precisely. I don't think we really know what mass is. Rest mass has well known effects in it's frame and of course effects in other frames that must be consistent with that.

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Mr = M0 / sqrt( 1 - v^2/c^2 )

p = M0 * v / sqrt( 1 - v^2/c^2 )

E = E0 / sqrt( 1 - v^2/c^2 )

Thank you for the corrections! I have edited my math accordingly.

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A spinning object would gain mass, and this would then cause more gravity.

In General Relativity, the solution for a rotating spherical object with no charge would be called the kerr metric, and you can learn about it at http://www.roma1.infn.it/teongrav/leonardo/bh/bhcap3.pdf

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The kinetic energy of rotation would create gravity. To be significant, it would require a rotation speed approaching c, which a piece of steel can't withstand, nor even a molecule of hydrogen.

Then, the rotating matter would still be visible. Maybe very little matter would create much gravity if its speed is very near to c...

I imagine only the gravitation of black holes to do this, and matter near their horizon is negligible as compared with the hole.

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The energy of mass whether at rest or in motion is product of mass and square of velocity of light.The energy of moving mass is more than that of mass at rest which is possible only if mass increases with velocity because in energy relation velocity of light is constant. It can be said that increase in mass is hybrid of mass and energy so can be named as mattenergy

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When electron and positron are annihilated in the moving carriage of train the energy liberated is more than when the pair is annihilated on platform which shows that there is increase in mass on motion because it is mass that is annihilated during pair interaction

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A spinning object would gain mass, and this would then cause more gravity.

In General Relativity, the solution for a rotating spherical object with no charge would be called the kerr metric, and you can learn about it at http://www.roma1.infn.it/teongrav/leonardo/bh/bhcap3.pdf

IIRC the Kerr Metric only applies to black holes. S'Child can be made to apply to any (non-rot non-charged) object not just BHs- but at present we are not able to extend Kerr Metric

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