Can Neutron Star Become Black Hole

[litespeed]

This is something of a trojan horse sort of post. Specifically, I already suspect the answer is no, but am not sure. However, assuming a Neutron star can not become a black hole through accretion of additional mass, that means Black Holes are generally created through momentum as the minimum mass needed accelerates in the initial collapse.

 

1) Does this mass accelerated by gravity increase as it approaches the speed of light, thus increasing the mass and gravity of the BH?

[Moontanman]

I think assuming a neutron star cannot become a black hole by accumulating mass is wrong. I see no reason a neutron star couldn't become a black hole by collecting mass. If a neutron star accumulated mass whether through collision with another neutron star or some other mass big enough to push it over the limit it should become a black hole. Even if it acquires this mass slowly over time it should become a black hole if it becomes massive enough.

[litespeed]

MT

 

I agree with you, but have never seen it stated elsewhere, and I will demure until more posters indulge us. In the mean time, I have another question about neutron stars. Are they entirely solid matter, or do they include space of any sort.

 

In elaboration, I have seen it said that an atom blown up to the size of a grape, and then blown up to the size of a NFL covered stadium, would have a nucleous the size of a grain of sand. I quess the various electrons would be even less cosequential. So an atom is almost entirely empty space.

 

I know that a neutron star is so dense it pushes electrons and protons together to form neutrons, and that only neutrons remain. However, I have yet to be informed if all these 'neutered' atoms are also squeezed together so that no empty space remains.

[freeztar]

This is something of a trojan horse sort of post. Specifically, I already suspect the answer is no, but am not sure. However, assuming a Neutron star can not become a black hole through accretion of additional mass, that means Black Holes are generally created through momentum as the minimum mass needed accelerates in the initial collapse.

 

From the wiki on neutron stars:

 

A typical neutron star has a mass between 1.35 and about 2.1 solar masses, with a corresponding radius of about 12 km if the Akmal-Pandharipande-Ravenhall (APR) Equation of state (EOS) is used.[1][2] In contrast, the Sun's radius is about 60,000 times that. Neutron stars have overall densities predicted by the APR EOS of 3.7 × 1017 (2.6 × 1014 times Solar density) to 5.9 × 1017 kg/m³ (4.1 × 1014 times Solar density),[3] which compares with the approximate density of an atomic nucleus of 3 × 1017 kg/m³.[4] The neutron star's density varies from below 1 × 109 kg/m³ in the crust increasing with depth to above 6 or 8 × 1017 kg/m³ deeper inside.[5]

 

In general, compact stars of less than 1.44 solar masses, the Chandrasekhar limit, are white dwarfs; above 2 to 3 solar masses (the Tolman-Oppenheimer-Volkoff limit), a quark star might be created, however this is uncertain. Gravitational collapse will always occur on any star over 5 solar masses, inevitably producing a black hole.

 

1) Does this mass accelerated by gravity increase as it approaches the speed of light, thus increasing the mass and gravity of the BH?

 

The resulting force of gravity is so strong that if an object were to fall from just one meter high it would hit the surface of the neutron star at 2 thousand kilometers per second, or 4.3 million miles per hour

 

Since the speed of light is 670,616,629 mph, relativistic effects would be negligible.

[maddog]

This is something of a trojan horse sort of post. Specifically, I already suspect the answer is no, but am not sure. However, assuming a Neutron star can not become a black hole through accretion of additional mass, that means Black Holes are generally created through momentum as the minimum mass needed accelerates in the initial collapse.

 

1) Does this mass accelerated by gravity increase as it approaches the speed of light, thus increasing the mass and gravity of the BH?

Both Neutron Stars and Black Holes are both remnants of the explosion of a star once its fuel is exhausted. When the stars mass is sufficient to explode in a Supernovae event or a simple Novae, the latter producing White Dwarf stars.

 

What determines whether the remnant will be a Neutron Star or Black Hole is dependent upon the mass of the original star. If the original star is above about 2 solar masses (twice the size of our sun). Then then end product produces a Black Hole over Neutron Star. Once the end product is produced it is pretty much static.

 

There would be one exception where a Neutron Star could go black. That would be if a Neutron Star were part of a binary system where the Neutron Star could accrete material from the other star. Matter transfer is common with eclipsing binaries in close orbits. Were the Neutron Star to exceed 2 solar masses, it would become a Black Hole.

 

Note: This is the process I learned in Astrophysics when I was in school (and was the conventional wisdom, until the article I read in SciAm) -- this months issue on Naked Singularities.

 

I am not aware what are the defining rules (not even sure they are known yet) what makes a Naked Singularity over a Black Hole. From the article, they imply if creeping up to the limit allows an Event Horizon (Black) whereas if creation is abrupt (SuperNova) then maybe Naked (assuming pressure properly taken into account).

 

I know this muddies up the clarity. Well, that is science....

 

:coffee_n_pc:

 

maddog

[freeztar]

I have yet to be informed if all these 'neutered' atoms are also squeezed together so that no empty space remains.

 

I believe that is the case. The wiki article mentions the Pauli Exclusion Principle which suggests to me that the neutrons are squeezed together up to the point of physical limitations.

[litespeed]

Free - You provided: "... fall from just one meter high it would hit the surface of the neutron star at 2 thousand kilometers per second, or 4.3 million miles per hour." Since the speed of light is 670,616,629 mph, relativistic effects would be negligible.

 

I invite a mathematician to calculate the impact velocity from one kilometer above the surface.

[freeztar]

Free - You provided: "... fall from just one meter high it would hit the surface of the neutron star at 2 thousand kilometers per second, or 4.3 million miles per hour." Since the speed of light is 670,616,629 mph, relativistic effects would be negligible.

 

I invite a mathematician to calculate the impact velocity from one kilometer above the surface.

 

I knew somebody was going to call me out on that. :singer:

I'm not sure how they came to that number really. Figuring it out using Newton's method seems fairly straightforward, but using GR to incorporate pressure is another story. I, too, will await someone with more math prowess than I have.

[CraigD]

I invite a mathematician to calculate the impact velocity from one kilometer above the surface [of a neutron star].

You can calculate this by calculating the change in gravitational potential energy for a test body at a radius 1 meter greater than vs. equal to the radius of the primary body, the neutron star.

 

GPE is given by

[math]E = -\frac{Gm_pm_b}{r}[/math]

, where [math]G[/math] is the gravitational constant, [math]m_p[/math] the mass of the primary, [math]m_b[/math] the mass of the test body, [math]r[/math] the distance from the center of gravity of the system to the test body.

 

Change in GPE, then, is

[math]E = Gm_pM_b \left( \frac1{r_2} -\frac1{r_1} \right)[/math]

, where [math]r_1[/math] is the test body’s initial distance, [math]r_2[/math] its distance at impact.

 

Taking an “average” neutron star of 1.5 solar masses and surface radius 12000 m, and for ease of calculation a test body massing 1 kg, this evaluates:

 

[math]E \dot= 6.67 \times 10^{-11} \cdot 3 \times 10^{30} \cdot 1 \left( \frac1{12000} -\frac1{12001} \right) \dot= 1.4 \times 10^{12} \,\mbox{J}[/math]

 

Suspecting that this is associated with a speed for which relativistic effects are slight, we can calculate impact velocity [math]v[/math] with the classical equation for kinetic energy,

[math]E = \frac12 m_b v^2[/math]

 

getting

 

[math]v = \sqrt{\frac{2 E}{M_b}} \dot= 1.7 \times 10^{6} \,\mbox{m/s}[/math]

 

, close to wikipedia & freeztar’s example of [math]2 \times 10^{6} \,\mbox{m/s}[/math]

"... fall from just one meter high it would hit the surface of the neutron star at 2 thousand kilometers per second, or 4.3 million miles per hour."

which is indeed less than 1% of the speed of light.

 

More relevant than impact speed from 1 m above its surface, though, is impact speed from a great distance (it’s traditional in gravitational mechanics to assume “an infinite distance” to set an upper limit on such values). Recalculating with [math]r_1 = \infty [/math], [math]-\frac1{r_1} = 0[/math], and [math]E \dot= 1.67 \times 10^{16}[/math].

This is high enough that we should use a relativistic calculation for kinetic energy,

[math]E = m_b c^2 \left( 1 - \frac{1}{\sqrt{1-\left( \frac{v}{c} \right)^2}} \right)[/math]

, which gives an impact velocity of about 0.4 c, about 12000000 m/s.

 

Although a very high speed, this is still not enough to produce a dramatic mass dilation – a factor of about 1.19, (a 19% increase), so we can see that the original post’s question

1) Does this mass accelerated by gravity increase as it approaches the speed of light, thus increasing the mass and gravity of the BH?

incorrectly assumes that bodies falling toward the surfaces of compact bodies such as neutron stars or the event horizons of black holes (which requires a separate calculation, but one yielding a larger yet similar result) always reach high relativistic speeds.

 

It’s also necessary to realistically consider conditions around a star-mass body like a neutron star. Because our test body would not be alone, but part of a large accretion disk, it would almost certainly collide many times with similar bodies, preventing it from approaching this upper limit value of 0.4 c.

 

I think the answer to the title question “Can Neutron Star Become Black Hole”, is “yes, but before it became a black hole, it would cease being a neutron star. An explanation would require a separate, fairly lengthy post, which I’ll get to as time permits, and invite anyone who can spare the time now the pleasure of writing.

[maddog]

I believe that is the case. The wiki article mentions the Pauli Exclusion Principle which suggests to me that the neutrons are squeezed together up to the point of physical limitations.

As your Wiki link describes the Pauli Exclusion principle applies to all Fermions (spin 1/2 particles) and thus applies to Neutrons.

 

To get a sense of what a Neutron Star is like, the best example I know is a Sci Fi novel Dragon's Egg by Dr. Robert L. Forward. At first this may seem off topic, just hear me out. The novel is about creature that live on the Neutron Star. Dr. Forward is very descriptive about how a body of mass would behave on the surface of such an object.

 

maddog

[Pyrotex]

Wow! Somebody else has read "Dragon's Egg". Excellent!

It is a fantastic novel, and would be still even if the good Dr. Forward were not one of America's premier theoretical physicists, specializing in gravitational theory and modeling. I say that to impress on you that all the "science" in the novel is as close to REAL, UNDERSTOOD science as you could get in the days when the novel was published. It may still be very accurate.

 

I met Robert Forward once. Very friendly and outgoing guy.

[CraigD]

Wow! Somebody else has read "Dragon's Egg". Excellent!

Yeah, “Dragon's Egg” is IMHO a true hard SF classic, which along with most of Forward’s fiction and non-fiction, are among my favorite books.

It is a fantastic novel, and would be still even if the good Dr. Forward were not one of America's premier theoretical physicists, specializing in gravitational theory and modeling.

I think its safe to say that Forward ranks high in actual science knowledge among even hard SF writers. He was a bona fide PhD of Physics. However, his life’s work was always focused on the applied, making him I think more of what we’d now call a technologist than a theoretical physicist.

 

I find his vision of the near-term future of technology one of the most compelling. My own vision of the future of technology is taken nearly verbatim from Forward’s (most of it described in his alternating fiction/nonfiction book “Indistinguishable from Magic”), updated as the future unfolds.

I met Robert Forward once. Very friendly and outgoing guy.

I’m envious, having missed the opportunity myself, as Robert Forward died in 2002. :)

 

Another hard SF romp concerning neutron stars is Steven Baxter’s “Flux” – though, unfortunately, knowing in advance that it involves a neutron star spoils one of the book’s major plot devices, as read in its original, until 2/3rds or so of the way through, the reader is lead to believe that its characters are biologically normal humans living in a strange world.

 

The physics of either book, or better still a comparison of both, would make for a good thread. :confused:

 

Important to the real science of neutron stars, though, is to note that in both books, exotic science and technology, and an abundance of luck, is needed for a normal human observer to even detect that the story taking place on the neutron star is occurring. Though the books do a compelling job of speculating that life on a neutron star is possible – and arguable superior in dramatic ways to our low-gravity kind of life – they in no way assure that such life actually exists, or that if it does, we’ll ever be able to detect, (as described in “Dragon’s Egg”) interact with, or, (as described in “Flux”) create it.

[litespeed]

Graig - You wrote: "...Although a very high speed, [.4c] this is still not enough to produce a dramatic mass dilation – a factor of about 1.19, (a 19% increase)..."

 

It is, however, sufficient to address my original question, paraphrased: "Does this mass dialation increase the grivitation of the total system; or is it a separate effect?"

 

Bassically, I am thinking about the limits of BH physics. Specifically, their gravitation is so extreme that I wonder about two things:

 

1) Could light, theoretically, go into orbit someplace near or past the event horizon; after all, it never gets back out.

2) Mass dialation could be so extreme that, at some point, even the BH would not have enough gravitational force to actually crush it into a singularity. [PS - I do not believe infinities of any sort exist in our universe, including singularities. But thats just me.]:evil:

[freeztar]

It is, however, sufficient to address my original question, paraphrased: "Does this mass dialation increase the grivitation of the total system; or is it a separate effect?"

 

Short answer: no

"Mass dilation" is a confusing term, imho. Relativistic mass is a better term, but it is still confusing. Remember that mass and energy are related. So, when we consider "mass dilation" it is really a measure of an increase in energy rather than "gravitational mass". The wiki on mass in SR does a better job of explaining it.

 

The term relativistic mass is also used, and this is the total quantity of energy in a body or system (divided by c2). The relativistic mass (of a body or system of bodies) includes a contribution from the kinetic energy of the body, and is larger the faster the body moves, so unlike the invariant mass, the relativistic mass depends on the observer's frame of reference. However, for given single frames of reference and for closed systems, the relativistic mass is also a conserved quantity.

 

Because the relativistic mass is proportional to the energy, it has gradually fallen into disuse in among physicists[1]. There is disagreement over whether the concept remains pedagogically useful.[2][3]

 

1) Could light, theoretically, go into orbit someplace near or past the event horizon; after all, it never gets back out.

 

No. *Everything* within the event horizon proceeds to the singularity. Well, at least that's what theory predicts. It's impossible to know what exactly is going on inside the event horizon as no information can be extracted. In other words, if we sent a probe across the event horizon, it would have no way of transmitting data back to us.

 

2) Mass dialation could be so extreme that, at some point, even the BH would not have enough gravitational force to actually crush it into a singularity. [PS - I do not believe infinities of any sort exist in our universe, including singularities. But thats just me.]:evil:

 

Again, mass dilation is a confusing term and I recommend reading up on it. Energy does not increase a body's gravity.

 

If you are interested in BH, I'd recommend doing a search for that here. There are some nice discussions on BH in this very forum. :)

[CraigD]

Graig - You wrote: "...Although a very high speed, [.4c] this is still not enough to produce a dramatic mass dilation – a factor of about 1.19, (a 19% increase)..."

 

It is, however, sufficient to address my original question, paraphrased: "Does this mass dialation increase the grivitation of the total system; or is it a separate effect?"

Yes, mass dilation increases the mass of individual bodies in a system, and thus increases the mass of the total system. For example, if no matter was lost or gained, but the temperature of, say, a planet, were decreased, the speed of its molecules would decrease, their mass dilation decrease, the mass of the entire planet decrease, and the gravitational force exerted by it on a test body of constant mass would decrease. Such a decrease would be very small, and practically, be insignificant compared to its unavoidable gains and losses of matter.

 

Although the speeds of orbiting and infalling bodies around a neutron star or other dense body are greater than those associated with heat on planets, the increase of mass and resulting gravity due to mass dilation is, I think, similarly insignificant. Compared to the total mass of the central body and its accretion disk, the total mass of infalling bodies accelerated to a high speed is very small, and not significant compared to the mass of new matter accreted from interstellar space, or expelled by outgoing radiation, radiation pressure, and much more energetic, explosive events.

1) Could light, theoretically, go into orbit someplace near or past the event horizon; after all, it never gets back out.

As with many questions I’m unable to even begin to answer rigorously, I’ve dedicated a lot of thought to this question, arriving at a conclusive “maybe – I don’t know”. :)

 

If General Relativity is as predictive as experiments to date confirm, I suspect, but am unable to calculate, that such orbits might be short-lived, because the photons or other particles would lose energy through the emission of gravitational waves. Because gravitational waves can in theory escape from within the event horizon of a black hole, this should in principle be detectable, though currently beyond human technological capability.

 

My main interest in this is due to the possibility of using gravity as optical elements in very large telescopes. For this purpose, it would not be necessary for photons to orbit (outside of the event horizon, as once within, they’re unavailable for detection outside it) a black hole or other compact massive body, but only be significantly deflected by it. Arranged and/or sampled carefully, I suspect that this could be used to gain telescopic data much greater than that currently obtained by present day observations of gravitational lensing. The pinnacle of my speculation in this direction is summarized in the post “an exotic variation” of the thread 5823.

2) Mass dialation could be so extreme that, at some point, even the BH would not have enough gravitational force to actually crush it into a singularity. [PS - I do not believe infinities of any sort exist in our universe, including singularities. But thats just me.]:evil:

I think it’s important to understand that mainstream physics is by no means certain of the existence of singularities. Rather, my read of it is that most physicist believe that the physics that predicts singularities – the “smooth” classical physics of General Relativity – fail on the scales and energies that exist at the centers of black holes. Unfortunately, the physics that most believe can describe these conditions, quantum particle physics, have yet to compellingly include gravitational interactions, which are so inconsequential on the usual scale of quantum physics, but so important in the case of black hole cores. Thus, one tends to find the best physicist speculating that these conditions are “quantum foam” and similar evocative but vague hints at a description.

 

My personal hunch is that black hole cores are “quark-gluon seas” different from those of ordinary hadrons (protons, neutrons, etc.) only in consisting of vastly more particles, and being subject to gravitational interactions of which we can scarcely imagine using conventional physics. Until theory can better answer the tremendously difficult questions of quantum gravity, I think guesses and hints are the best anyone will be able to offer on the subject of black hole cores.

 

Fortunately – or unfortunately, depending on you point of view – reality seems bent on sparing us a great need to know the details black hole cores, as such information is for all practical purposes causally disconnected from everything outside the black hole’s event horizon. Black holes, it appears, are nature’s ultimate black boxes. :)

[freeztar]

Yes, mass dilation increases the mass of individual bodies in a system, and thus increases the mass of the total system. For example, if no matter was lost or gained, but the temperature of, say, a planet, were decreased, the speed of its molecules would decrease, their mass dilation decrease, the mass of the entire planet decrease, and the gravitational force exerted by it on a test body of constant mass would decrease.

 

This disagrees with what I posted above and my understanding of "mass dilation". I'm going to go ahead and assume my knowledge is incomplete, rather than your's.

 

With massive bodies traveling a significant fraction of c, is it not the energy that causes the mass dilation? I understand [math]m=\frac{E}{c^2}[/math], but I'm still confused as to how this translates to more gravitation. Does this mean that increased energy itself can cause increased gravitation? :confused:

 

I'm obviously missing something significant here and perhaps I need to ponder this for a bit (and do some more reading). Of course, some further elaboration on your (or anyone else's) part would not go unappreciated. ;)

 

EDIT: Nevermind, I was being dense (no pun intended). I get it now after doing some reading. Specifically, this helped me:

 

Note further that in accordance with Einstein’s Strong Equivalence Principle (SEP), all forms of mass and energy produce a gravitational field in the same way.[9] So all radiated and transmitted energy retains its mass. Not only does the matter comprising Earth create gravity, but the gravitational field itself has mass, and that mass contributes to the field too.

[Moontanman]

Moderation note: moved this post and its replies to the new thread 18322, because they apply to physics in general, not just to neutron stars and black holes

 

How about this thought experiment, if you had a neutron star that was within 1% of being massive enough to be a black home and you accelerated it to .9999% of the speed of light would it become a black hole? more importantly if it did become a black hole would it stop being a black hole if you decelerated it back to an apparent standstill?