Comment by jmyeet | Hacker News Reader

Comment by jmyeet | Hacker News Reader

There are several subtypes of neutron stars. My favorite is the magnear [1]. These are extremely rare and I believe don't last that long but while they do they have an unbelievable strong magnetic field. I'm talking a quadrillion times stronger than Earth's, strong enough to literally rip atoms apart from a sizeable distance.

The article mentions the equation of state. Fun fact: neutron stars are probably the most complex objects in the Universe. Black holes by comparison are quite simple: describle with three quantities (mass, spin, electric charge). An equation of state would tell us how large these can get, for example.

Consider the nucleus of a normal atom. We know and have mapped out electron shell structures. Nuclei too have structure but it's way more inscrutable and complex as you have to deal with the electric repulsion between protons, the strong interaction between quarks (and gluons) and the strong interaction between nucleons. AFAIK we don't really have a good model for this.

Now imagine that scaled up to something 20km across where gravity has also become a significant force and obviously we don't have a quantum model for gravity anyway.

In addition to all of that you have to deal with fluid dynamics. The article mentions nuclear pasta and theorized crystalline structure within a neutron star but in outer layers its likely it acts more like a fluid.

And then there's things can collide in unbelievable energetic interactions, such that we can detect the ripples in space-time billions of light years away. We're talking 5-10 Solar masses converted to energy in less than a second.

[1]: https://en.wikipedia.org/wiki/Magnetar

EDIT: fixed Solar mass typo

Quibbles:

> Black holes by comparison are quite simple: describle with three quantities (mass, spin, electric charge).

For an actual black hole (vs. theoretical-in-a-vaccuum one), I believe 2 other number are required - to specify which way the spin axis points. [EDIT - still not right. 11 numbers are needed to cover everything; see my Wikipedia cite below.]

> We're talking 50-10 Solar masses converted to energy...

Obvious "50-10" typo. But beyond ~6 Solar masses total, at least one of the two object will have long-ago collapsed into a black hole.

The spin axis isn't a valuable reference since it depends on your frame of reference, which is a concept that gets rather ambiguous as you get close to a black hole anyway.

Plus you can just "rotate" a black hole to get it to have the same spin axis as another black hole. You can't "rotate" or "translate" a black hole in space to make the other three numbers change. Those require ingesting matter or emitting hawking radiation and that is the only thing that changes those properties.

I'm figuring that the low-rent planets, stars, etc. in the vague vicinity of an actual black hole would provide a fine frame of reference.

> Plus you can just "rotate" a black hole to get it to have the same spin axis as...

Quip: If you have the tech & budget to meaningfully rotate a spinning black hole, then you've got the tech & budget to change the other parameters, too.

FWIW - Wikipedia's answer is that 11 numbers (or 2 scalars and 3 vectors) are needed to fully spec. a stable black hole - https://en.wikipedia.org/wiki/Rotating_black_hole#Types_of_b...

There is a cheap and even for current humanity achievable way to rotate a black hole; change your frame of reference. That is not only true for angular momentum but linear momentum and position. Those are entirely dependent on the observer and their frame of reference. Spin, magnetic charge and mass are not.

Two black holes who differ only by their position, linear and/or angular momentum but are equal in all other parameters are not distinguishable from simply seeing the same black hole twice from a different perspective.

Two black holes who differ in any of the three properties of mass, spin or magnetic charge are distinguishable by those properties (but even that is arguable to some extend).

edit: The rent prices of a planet don't matter since frame of reference is an actual term here, there is no frame of reference more valid than any other for determining the linear or angular velocity or the position of a black hole.

The quantity a = cJ/GM^2, the spin parameter of the Kerr metric, is not observer-dependent. No observer (or system of coordinates) can turn an axisymmetric system into a spherically symmetric one.

Also,

> Two black holes who differ only by their ... angular momentum ... are not distinguishable

is contradicted by

> Two black holes who differ in ... spin ... are distinguishable

(Spin) Angular momentum is J in my first line above.

Spin and Angular momentum are two very different things. Angular momentum measures the velocity of a black hole in, eg, an orbit. Spin measures the rotation of a black hole against it's rest frame.

These are independent quantities.

In a Kerr black hole spacetime there is no orbital angular momentum (OAM, L), only the intrinsic spin angular momentum (SAM, S). One can get OAM in a relativistic n-body black hole problem. Each of those black holes will have its own SAM.

See §5.11. ANGULAR MOMENTUM in Misner, Thorne & Wheeler (MTW) and in particular Box 5.6 D (Intrinsic Angular Momentum) and E (Decomposition of Angular Momentum into Intrinsic and Orbital Parts). The latter gives J = L + S. Admittedly, in MTW §33 the authors prefer to use S (e.g. eqn. 33.4) but that raises the important caveat for binary black hole (BBH) mergers at the end of Box 33.4 (I)(A)(4), which refers back to Box 5.6). Newer textbooks and other sources (including Wikipedia [1]) prefer J, although commonly it gets called spin angular momentum (as in [1] and my earlier comment). Carroll's textbook calls it the Komar angular momentum (near eqn. 6.73, referring to eqn. 6.48) and "spin (angular momentum)" (above eqn. 6.47). This is the sort of thing that annoys mathematicians and non-relativist physicists about relativists; confusion is completely understandable.

A binary black hole (BBH) is not a Kerr solution. No exact analytical solutions to the Einstein Field Equations for a BBH have been found, only approximations and numerical solutions (see the comprehensive review by Baker et al. at <https://arxiv.org/abs/1010.5260> and \vec{L} therein, notably at section D(2) in the second column on PDF p. 26, "In a related phenomenon, the direction of the total angular momentum (\vec{L} + \vec{S}_1 + \vec{S}_2) may change.").

No change of coordinates can turn a BBH into a Kerr solution; the former radiates gravitational waves (if there is no incoming gravitational radiation), the latter doesn't.

(Another way of distinguishing is in the algebraic symmetries of the Weyl curvature tensor. Kerr is a Petrov type D spacetime, BBH spacetimes are generically type I up to some degeneracy measure.)

Finally, I can tie this in to neutron stars: the (exterior) Hartle-Thorne metric is an approximation of the Kerr metric useful for relativistic stars without horizons (neutron stars, white dwarfs) and without regard to interior differentiation. Its usual write-down uses J, but sometimes S, and sometimes both (e.g. <https://arxiv.org/abs/1507.04264>, where at the top of p. 2 the authors give J = GS/c^3).

[1] <https://en.wikipedia.org/wiki/Kerr_metric#Overview>, "J represents its spin angular momentum" and see eqn (6) further down, "a = J/Mc".

You're still referring to two distinct properties with Angular Moment being one and Spin being the other. Because a black hole can in fact orbit things and that would give it angular momentum. The spin value is merely how fast it rotates around an axis (which you can define but that's just an observational data point) and is unrelated to the external movement in spacetime.

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