1
$\begingroup$

I understand that black holes have so much stress-energy, that even light cannot escape them. Now based on that, I would understand it so, that it the black hole gets near enough to anything, the black hole will pull it inside itself. So basically nothing that is near enough the black hole, no macro object can stay intact, because the black hole will spaghettify it and pull it inside itself.

I have read this:

https://www.quora.com/What-is-the-biggest-singular-object-in-the-observable-universe

It says that the biggest observable object in the universe is a quasar, that has a black hole inside it.

Now how is that possible, would the black hole not pull the quasar's material inside the black hole itself? Would the black hole not spaghettify all the material in the quasar and pull it inside?

Question:

  1. How can any singular macro object (like a quasar) stay intact with a black hole inside it?

  2. How can a black hole exist inside any singular macro object without spaghettifying and pulling all the material from the macro object inside the black hole?

$\endgroup$
  • $\begingroup$ Q: How do the Earth and the other planets keep from falling in to the Sun? A: They orbit the Sun. Despite the Sun's enormous gravity, it actually is substantially harder to send a spacecraft from Earth to the Sun than it is to send one completely out of the Solar System. $\endgroup$ – user205719 Sep 7 '18 at 17:28
  • $\begingroup$ @besmirched can you please tell me how this relates to my question where a black hole is inside the quasar? $\endgroup$ – Árpád Szendrei Sep 7 '18 at 17:30
  • $\begingroup$ I meant to suggest that the reason why everything in an active galactic nucleus doesn't just fall in to the black hole all at once is, that most of the stuff orbits the black hole. What I don't know how to explain is, why those orbits slowly decay, so that there always is a stream of in-falling matter to feed the quasar. $\endgroup$ – user205719 Sep 7 '18 at 18:34
  • $\begingroup$ @besmirched so you are saying that the quasar's material is orbiting the black hole from far away? $\endgroup$ – Árpád Szendrei Sep 7 '18 at 18:43
  • 1
    $\begingroup$ Quasars and other active galactic nuclei have a lot of stuff orbiting the central black hole. However, there is also an accretion disk there where matter is interacting with itself that it loses energy through friction that it spirals inwards. This releases a lot of energy. $\endgroup$ – Anders Sandberg Sep 7 '18 at 19:04
2
$\begingroup$

Imagine filling a bathtub and then pulling the plug. For a while there would be water in a bathtub with a hole at the bottom. But the water would not be 'staying intact' it would be draining, it just will not happen instantaneously.

Likewise, a single object with a black hole inside of it would not be staying intact, it would be accreting matter onto the black hole. And since there are various limits on the rate at which material could be absorbed by the black hole, it will not be instantaneous and it could possibly take billions of years or more to 'pull all the material inside'.

One should be aware of the following aspects of black hole material accretion:

  1. Angular momentum, energy, entropy transport. Even inside the 'singular body' most elements of matter would have enough angular momentum (per unit of mass) so that cannot fall into the black hole directly. As matter moves toward the black hole its high angular momentum is transported outwards by stresses (turbulence, viscosity, magnetic fields). Gravitational energy of falling matter is converted into heat and other forms of energy and transported across the medium. Accretion physics is a complex interplay of many phenomena: gravity, viscosity, turbulence, radiation and magnetic fields.

  2. There is a simple hydrodynamic limit for accretion rate (conceptually similar to the limit for the amount of water that could drain through the hole in a bathtub): $$ \dot{M}\approx 4\pi r_\text{sonic}^2 \rho_\infty a_\infty, $$ where $r_\text{sonic}=\frac{GM}{a^2_\infty}$ is the 'sonic radius', $\rho_\infty$ and $a_\infty$ is the density and sound speed reasonably far away from the black hole. Although in most astrophysical cases this limit is never realized.

  3. Radiative pressure on the infalling matter. As matter falls into black hole a portion of its mass energy is converted into radiation (with an efficiency $\eta$ in various cases ranging from about 5% to over 10%). This radiation exerts pressure on the infalling matter in the direction opposing gravitational pull. Thus there is a limit: Eddington luminosity when pressure of radiation balances gravitation:$$ L_\text{Edd}=4 \pi \frac {G M \mu m_p c}{\sigma_T},$$where $\sigma_T$ is Thompson crossection, $\mu$ is the number of nucleons per electron, $m_p$ is the mass of proton and $M$ is the mass of black hole. This provides critical mass accretion rate: $$\dot {M}=\frac{L_\text{Edd} c^2}{\eta}.$$ This is the value relevant to accretion inside quasars. (Since this value is obtained for spherical symmetry, actual anisotropic flows could exceed this limit).

As an example somewhat closer to home let us consider the black hole of about $10^{-5} M _\odot$ (about 3 Earth masses) inside the Sun. Such model was proposed in 1975 as a solution for solar neutrino problem:

  • Clayton, D. D., Dwek, E., Newman, M. J., & Talbot Jr, R. J. (1975). Solar models of low neutrino-counting rate: the central black hole. The Astrophysical Journal, pdf online.

Of course, since neutrino oscillations have been observed, this model is mainly of historical interest, but it does gives us some figures: it would take several hundred millions years for such a black hole to double its mass by accreting matter in the center of the Sun. Ultimately it comes down to a simple fact: such a black hole would have a Schwarzschild radius of about 3cm and it takes a lot of time to stuff several Earths worth of matter through such a small hole. Of course, as the mass of the black hole grows, so would the accretion rates, but even then the process would have taken billions of years.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.