# Neutron Stars and Special Relativity

## Main Question or Discussion Point

Neutron Stars and Special Relativity and General Relativity

Here is a question which I can't quite wrap my head around:

Suppose we have a Neutron Star that is borderline on the Chandrasekhar limit in its rest frame.

In another frame, the Neutron star is moving.

As a result, its density increases due to
1) Relativistic mass increase.
2) Length contraction.

So why does the Neutron star not form a black hole?

Technically, this question would apply for any object in any frame of reference that is moving sufficiently quickly.

So what am I missing here?

I suppose a general relativistic explanation is that Stress-Energy is a tensor, so matter what coordinate system you use, the criteria for black hole formation will not be met.

So,
1) Is this question well posed?
2) Where does special relativity break down?
3) Did I answer my own question?
4) What is the General Relativistic explanation?

I would like to hear your input.
Thanks.

Last edited:

Related Special and General Relativity News on Phys.org
George Jones
Staff Emeritus
Gold Member

Hao said:
I suppose a general relativistic explanation is that Stress-Energy is a tensor, so matter what coordinate system you use, the criteria for black hole formation will not be met.

3) Did I answer my own question?
Yes and yes

For simplicity, consider a spherically symmetric, non-rotating neutron star its rest frame. In this coordinate system, it has a has non-zero stress-energy tensor that satisfies Einstein's equation. Boosting this stress-energy tensor produces a non-zero stress-energy tensor that is also a solution of Einstein's equation, but this boosted solution is not a black hole solution.

Now consider a spherically symmetric black hole in one of the usual coordinate systems. This is a vacuum solution to Einstein's equation, so the stress-energy tensor is identically zero. This stress-energy tensor, too, can be boosted, but the the boost of something identically zero zero is something identically zero. Boosting the stuff on the right side of Einstein's equation results, however, in a "different" looking solution to Einstein's equation, i.e., there isn't a unique vacuum solution to Einstein's equation. In this black hole situation, one of the solutions (unboosted) has (explicit) spherical symmetry and one doesn't (boosted).

Neither of the black hole solutions look like the boosted neutron star solution.

The same considerations apply to rotating neutron stars and rotating black holes. For a synopsis of boosted black holes, see

http://mwrm.wustl.edu/Presentations/akcay_sarp_win.ppt.

"Boosting this stress-energy tensor produces a non-zero stress-energy tensor that is also a solution of Einstein's equation, but this boosted solution is not a black hole solution..."

I don't disagree, but how do we know this is so??

Why did I also get a BBC story at this website about a Sudanese man being forced to marry a goat??