I Upper limit of relativistic spin?

[BWV]

Was curious at the upper limit for neutron stars,

found this article stating one was found at around 700 / s

https://www.newscientist.com/article/dn8576-fast-spinning-neutron-star-smashes-speed-limit/

did not see the size, the article is behind a paywall, but it would have taken a radius of about 7km for the speed to exceed 0.1C, which is far bigger than any neutron star, as far as I have read. So neutron stars cannot spin at relativistic speeds?

Not really sure how the radius of a black hole is measured, as the event horizon extends well beyond that point ( correct?) but did find this

a supermassive black hole at the center of galaxy NGC 1365 has had the radiation emitted from the volume outside of it detected and measured, revealing its speed. Even at these large distances, the material spins at 84% the speed of light.

https://www.forbes.com/sites/starts...at-almost-the-speed-of-light/?sh=1387d657735a

but only the rest mass of the black hole contributes to its gravitation, not the inertial mass, which for an object spinning at 0.84c would have the same gamma correction as an object traveling in a straight line at that speed? So given a big enough black hole (there is no theoretical upper limit correct?) it could spin at any arbitrary speed approaching c ?

 

[Vanadium 50]

For neutron stars, surely the answer depends on the EOS you assume.

I don't understand your argument about black holes. Certainly not "only the rest mass contributes to gravitation". Huh?

 

[BWV]

For neutron stars, surely the answer depends on the EOS you assume.

I don't understand your argument about black holes. Certainly not "only the rest mass contributes to gravitation". Huh?

EOS?

I thought, from a prior discussions here, that gravity comes from rest mass, not the frame-dependent mass due to relativistic effects, no?

 

[berkeman]

EOS?

https://arxiv.org/pdf/1910.05554.pdf

 

[Ibix]

EOS?

Equation Of State for neutron star matter. Basically, there'll be a spin rate where a neutron star flies apart, but I don't think we know what it is. Certainly I don't.

I thought, from a prior discussions here, that gravity comes from rest mass, not the frame-dependent mass due to relativistic effects, no?

Gravity comes from the stress-energy tensor, not the rest mass. In many cases the rest mass density is the only non-zero component of the tensor (or the only non-negligible one) so gravity kind of comes from the rest mass in those cases, but the source is always strictly the stress-energy tensor. It's definitely not the relativistic mass, though, as you note.

Rotation has an effect on the gravity of black holes, but it doesn't make it 'stronger' or 'weaker'. Rather, it makes free falling objects start to rotate around the hole. The effect is just detectable around Earth - that's one of the things Gravity Probe B looked at.

There is a maximum angular momentum per unit mass for black holes (the so-called extremal Kerr black hole). Attempting to increase its angular momentum will always increase its mass at least as much. I don't think any known real black holes are anywhere near extremal, but I could be wrong.

 

[BWV]

Equation Of State for neutron star matter. Basically, there'll be a spin rate where a neutron star flies apart, but I don't think we know what it is. Certainly I don't.

Gravity comes from the stress-energy tensor, not the rest mass. In many cases the rest mass density is the only non-zero component of the tensor (or the only non-negligible one) so gravity kind of comes from the rest mass in those cases, but the source is always strictly the stress-energy tensor. It's definitely not the relativistic mass, though, as you note.

Rotation has an effect on the gravity of black holes, but it doesn't make it 'stronger' or 'weaker'. Rather, it makes free falling objects start to rotate around the hole. The effect is just detectable around Earth - that's one of the things Gravity Probe B looked at.

There is a maximum angular momentum per unit mass for black holes (the so-called extremal Kerr black hole). Attempting to increase its angular momentum will always increase its mass at least as much. I don't think any known real black holes are anywhere near extremal, but I could be wrong.

Thanks, and the stress-energy tensor is invariant in difference reference frames, which is why the spin rate does not impact gravitation?

On the Kerr black hole, you mention attempting to increase its angular momentum will increase the mass - does that refer to relativistic effects, or that increasing angular momentum requires an addition of energy, which is part of the stress-energy tensor?

 

[Ibix]

Thanks, and the stress-energy tensor is invariant in difference reference frames, which is why the spin rate does not impact gravitation?

Tensors are invariant by definition. But the spin rate definitely affects the gravitational field - the more angular momentum the hole has the larger the frame dragging effect.

On the Kerr black hole, you mention attempting to increase its angular momentum will increase the mass - does that refer to relativistic effects, or that increasing angular momentum requires an addition of energy, which is part of the stress-energy tensor?

You can increase the angular momentum of a Kerr black hole, but not an extremal Kerr black hole.

You can't spin up a hole by getting hold of it and twisting, or strapping rockets to it, because there's nothing you can get hold of. You can only increase its spin by throwing in stuff on spinwise trajectories, but that increases its mass and its angular momentum, and when you reach an extremal hole it turns out that any attempt to do this increases the mass at least as much as the angular momentum.

 

[Vanadium 50]

Thanks, and the stress-energy tensor is invariant in difference reference frames, which is why the spin rate does not impact gravitation?

No, the stress-energy tensor transforms as a tensor.

And the angular momentum definitely does affect the gravitation: L²/2I contributes even to the T₀₀ term.