Dim Stars: Are There Almost-Black Holes in the Universe?

In summary, if there were a star that was almost, but not quite massive enough to become a black hole, gravitational time dilation would make it appear very dim. This is because time would pass slower within the star compared to outside of it, resulting in a lower energy output. However, such stars do not exist in the universe as there are only neutron stars, which are extremely small in size. It is possible for neutron stars to exhibit intrinsic redshift, and there is evidence of this in observed cases. The greatest time dilation due to gravity at the surface of a stable neutron star would be about 1/3, meaning that one second on the star would be equivalent to three seconds outside of it. This would cause the star to emit
  • #1
mrspeedybob
869
65
If there were a star which was almost, but not quite massive enough to become a black hole it seems as though gravitational time dilation should make it appear very dim. If time dilation resulted in 1/1000 of the time passing within the star as passes for us, we should see a star emitting 1/1000 the energy that it's mass would otherwise suggest. Do we see such stars in the universe?
 
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  • #2
Just an off-the-wall question from a non-astronomer: Would these "almost black holes" exhibit an intrinsic red-shift? I think I remember that Halton C. Arp proposed that for explaining the red-shift of quasars.
 
  • #3
mrspeedybob said:
If there were a star which was almost, but not quite massive enough to become a black hole it seems as though gravitational time dilation should make it appear very dim. If time dilation resulted in 1/1000 of the time passing within the star as passes for us, we should see a star emitting 1/1000 the energy that it's mass would otherwise suggest. Do we see such stars in the universe?

No, such objects can only be Neutron Stars, which are extremely tiny in size, yet comparable to the mass of the Sun. There are no stars that are still fusing elements in their cores that are anywhere close to being a black hole.

Your question should apply to a neutron star though. I would expect to see significant redshift on radiation coming from a neutron star.
 
  • #4
mrspeedybob said:
If there were a star which was almost, but not quite massive enough to become a black hole it seems as though gravitational time dilation should make it appear very dim. If time dilation resulted in 1/1000 of the time passing within the star as passes for us, we should see a star emitting 1/1000 the energy that it's mass would otherwise suggest. Do we see such stars in the universe?

A star that is not quite a black hole is a neutron star. The energy that comes off of a neutron star is red shifted, but I don't know how much.

Last I looked only one neutron star had been directly observed. (Usually we see the glow of the surrounding matter.) But that should enough to get a real figure.
 
  • #5
mrspeedybob said:
If there were a star which was almost, but not quite massive enough to become a black hole it seems as though gravitational time dilation should make it appear very dim. If time dilation resulted in 1/1000 of the time passing within the star as passes for us, we should see a star emitting 1/1000 the energy that it's mass would otherwise suggest. Do we see such stars in the universe?

The smallest a neutron star can get before run away collapse occurs is r0=9M/4 or 2.25M in order to have positive tangential pressures (according to the Schwarzschild interior metric, this is the point that the time dilation at the very interior of the star becomes zero). If we consider the gravitational redshift-

[tex]z=\frac{1}{\sqrt{1-\frac{2M}{r}}}-1=\frac{\lambda_o-\lambda_e}{\lambda_e}[/tex]

where z is the redshift, [itex]\lambda_o[/itex] is the wavelength observed and [itex]\lambda_e[/itex] is the wavelength emitted. The above can be rewritten-

[tex]\lambda_o=(z\cdot\lambda_e)+\lambda_e[/tex]

if we consider a 3 sol mass as an absolute maximum, then M=4430.55, then you can pretty much work out what z would be and what the emitted wavelength of light would be shifted to.

Regarding gravitational time dilation, this would be expressed as-

[tex]d\tau=dt\sqrt{1-\frac{2M}{r}}[/tex]

so the greatest time dilation due to gravity at the surface of a stable neutron star at the very boundary of collapse would be 0.333 or ~1/3.
 
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  • #6
  • #7
Duh.

What's M? What's z?
 
  • #8
ImaLooser said:
Duh.

What's M? What's z?

I believe M = mass, and Z = the measure of redshift.
 
  • #9
Yes, but, just to clarify, M is expressed in units of solar mass.
 
  • #10
I don't think it would appear dim to us. Light would travel very slowly away from it when released because of massive gravity pulling backwards, but as soon as the light moves far enough away it would resume its 'speed of light' pase. And reach us just like a normal star. Unless gravity pulled back some photons and not others it would have the same luminosity
 
  • #11
Rorkster2 said:
I don't think it would appear dim to us. Light would travel very slowly away from it when released because of massive gravity pulling backwards, but as soon as the light moves far enough away it would resume its 'speed of light' pase. And reach us just like a normal star. Unless gravity pulled back some photons and not others it would have the same luminosity

It appears you have a mistaken view of "gravitational redshift". It is true when we say photons "climb out of the gravitational potential" of a massive object. But this does not mean their velocity is changed...they still travel at c. What happens is just what's been mentioned above: redshift. This term comes from the optical part of the EM spectrum where red is a longer wavelength than, say, blue. This means the WAVELENGTH of the light has been stretched out and its "color" will be different (redder). Light never "slows down" or "resumes its pace", at least in this kind of example.
 
  • #12
stevebd1 said:
Tso the greatest time dilation due to gravity at the surface of a stable neutron star at the very boundary of collapse would be 0.333 or ~1/3.

Does this mean that one second passes on the nutron star for every 3 seconds outside of it? If so, then I'd think that that would indeed dim the star by a factor of 3. Regardless of red shift, the star would produce one third the number of photons in 1 second that it would in 3. And an observer on the neuron star would see the rest of the universe as sped up, and three times as bright.
 
  • #13
Bobbywhy said:
It appears you have a mistaken view of "gravitational redshift". It is true when we say photons "climb out of the gravitational potential" of a massive object. But this does not mean their velocity is changed...they still travel at c. What happens is just what's been mentioned above: redshift. This term comes from the optical part of the EM spectrum where red is a longer wavelength than, say, blue. This means the WAVELENGTH of the light has been stretched out and its "color" will be different (redder). Light never "slows down" or "resumes its pace", at least in this kind of example.

Sorry to say but i believe your wrong. First off, light can indeed change its speed. For example, in near absolute zero it is possible to slow photons to a crawl, and also 'speed of light' refers to its speed when traveling threw a vaccuum, not its constant speed. Next, you are right in saying that the redshift and blueshift waves are a derived from its frequnecy, however in this example you also have to include the fact that light DOES slow down, because black holes change light momentum from going 'forward' to 'backwards', and a near black hole object would be in the very close inbetween where it slows down but does not quite go 'backward'
 
  • #14
Rorkster2 said:
Sorry to say but i believe your wrong. First off, light can indeed change its speed. For example, in near absolute zero it is possible to slow photons to a crawl, and also 'speed of light' refers to its speed when traveling threw a vaccuum, not its constant speed.

It is a well known fact that light does indeed change speeds in a material, but when anyone says that the speed of light doesn't change or is invariant they are referring to the velocity in a vacuum, which is c always.

Next, you are right in saying that the redshift and blueshift waves are a derived from its frequnecy, however in this example you also have to include the fact that light DOES slow down, because black holes change light momentum from going 'forward' to 'backwards', and a near black hole object would be in the very close inbetween where it slows down but does not quite go 'backward'

This is incorrect. The change in momentum in no way affects the speed of light. As for the forward and backward stuff, I'm not sure what you are getting at.
 
  • #15
The time dilation factor goes by (1 + z), so a neutron star with a gravitational redshift of .33 would be time dilated by 1/1.33, or basically it would take 1.33 seconds to emit the same amount radiation as it would radiate in 1 second if not redshifted.
 
  • #16
Chronos said:
Yes, but, just to clarify, M is expressed in units of solar mass.

Aha. Well, I'm duh again because I don't know what it means to express radius of an object in units of mass.
 
  • #17
ImaLooser said:
Aha. Well, I'm duh again because I don't know what it means to express radius of an object in units of mass.

The radius isn't being expressed in units of mass. You are dividing the mass by the radius because more mass packed into a smaller radius means more gravity and more time dilation.
 
  • #18
ImaLooser said:
Aha. Well, I'm duh again because I don't know what it means to express radius of an object in units of mass.

In the paper posted by Chronos, M refers to mass, in the post I made, M is the geometric unit of mass, sometimes referred to as the gravitational radius where M=Gm/c2 where G is the gravitational constant, m is the mass in SI units (i.e. kg) and c is the speed of light in m/s.
 
  • #19
Rorkster2 said:
because black holes change light momentum from going 'forward' to 'backwards'

If a photon is considered to be without mass how can light have momentum?

note: my only exposure to physics has been in an AP mechanics class and in the books I've read over this summer. (i won't begin more formal study until i begin college next fall)
 
  • #20
grantwilliams said:
If a photon is considered to be without mass how can light have momentum?

note: my only exposure to physics has been in an AP mechanics class and in the books I've read over this summer. (i won't begin more formal study until i begin college next fall)

The momentum and energy of a photon is determined by the frequency. Higher frequency photons have more momentum and energy. You can read a bit more here: http://en.wikipedia.org/wiki/Photon#Physical_properties

If that isn't detailed enough or doesn't answer your question just say so.
 

1. What are dim stars?

Dim stars are stars that are significantly less bright than other stars in the universe. They emit much less light and energy than other stars, making them difficult to detect and study.

2. Are dim stars the same as black holes?

No, dim stars are not the same as black holes. Black holes are objects with such strong gravitational pull that not even light can escape. Dim stars, on the other hand, still emit some light and energy.

3. How do we know if a dim star is a black hole?

We can determine if a dim star is a black hole by observing its behavior and surrounding environment. If the star is in a binary system and its companion star is being pulled towards it, it is likely a black hole. We can also look for evidence of a strong gravitational pull and the absence of any light or radiation.

4. Are there a lot of dim stars in the universe?

Yes, there are a lot of dim stars in the universe. In fact, dim stars may outnumber bright stars by a factor of 100 to 1. This is because dim stars can be difficult to detect, especially if they are not in a binary system.

5. What is the significance of dim stars in the study of black holes?

Dim stars play an important role in our understanding of black holes. They can help us identify potential black holes and study their behavior and characteristics. Additionally, dim stars can provide us with valuable information about the formation and evolution of black holes in the universe.

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