Black hole inside a star -- How long for it to consume the star?

In summary, the conversation discusses the problem of how long it would take for a small black hole to consume an ordinary star if it was located at the center of the star. Equations and assumptions are presented to try and determine a solution, but there are some uncertainties and variables that need to be considered. It is suggested to use better formulas and consider the compressibility of the star's atmosphere. It is also noted that the rate of star mass falling across the black hole's event horizon would increase as the variables increase.
  • #1
Vrbic
407
18

Homework Statement


It is my idea so I hope there is no problem in assignment.
How long takes small black hole to eat an ordinary star, if the black hole sit in the center of star?

Homework Equations


We probably should suppose that star is ideal fluid (incompressible).
(1) ##\frac{dm}{dt}=A\rho v##, where ##\frac{dm}{dt}## is mass falling onto black hole per unit time, ##A## is area of the hole a ##\rho## is density of the star and ##v## is speed of falling matter on the horizon.
(2) ##A=4\pi R^2##
(3) ##R_g=\frac{2Gm}{c^2}##, where ##m## is mass of black hole, ##G## is gravitation constant and ##c## is speed of light.
##F=G\frac{m_1m_2}{r^2}=m_2a => a=G\frac{m_1}{r^2}##
(4) ##v=G\frac{m}{r^2}t##

The Attempt at a Solution


So if I put (1) - (4) together I got
##\frac{dm}{m}=2\pi G\rho t dt##
and from that integrating from ##m_0## mass of black hole to ##m_0+M_0## where ##M_0## is mass of star, I have got ##t=\sqrt{\frac{1}{k}\ln{\frac{m_0+M_0}{m_0}}}##.
What do you mean about it?

a) If I would use ##\rho(r)## and better formulae for ##v##? Is equation (1) general?
b) May I use such speed of falling into black hole as a reasonable approximation?
c) Generally, is it alright?
 
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  • #2
Hi Vrbic:

I am not an expert, and I am curious about what others might respond. Since no one else has yet responded, I thought I might offer a few comments.

Vrbic said:
We probably should suppose that star is ideal fluid (incompressible).
I would expect a star to be mostly a hot gaseous atmosphere and therefore compressible. I do not know at what temperature and pressure the atmosphere might have a phase change to an incompressible liquid.

Re (1): (a) If the BH mass M is >> star mass m, then it may be OK to assume that M is a constant. However, If M is not much much greater than M, then M will increases as star mass falls pass the BH event horizon (EH). (b) I assume that by A you mean the surface area of the BH EH. A will also increases as star mass falls across the EH. (c) As these variables increase, the rae of star mass faliing across the EH also increases.

I hope this helps some.

Regards,
Buzz
 
  • #3
Buzz Bloom said:
Hi Vrbic:

I am not an expert, and I am curious about what others might respond. Since no one else has yet responded, I thought I might offer a few comments.I would expect a star to be mostly a hot gaseous atmosphere and therefore compressible. I do not know at what temperature and pressure the atmosphere might have a phase change to an incompressible liquid.

Re (1): (a) If the BH mass M is >> star mass m, then it may be OK to assume that M is a constant. However, If M is not much much greater than M, then M will increases as star mass falls pass the BH event horizon (EH). (b) I assume that by A you mean the surface area of the BH EH. A will also increases as star mass falls across the EH. (c) As these variables increase, the rae of star mass faliing across the EH also increases.

I hope this helps some.

Regards,
Buzz
Thank you for your comment, I hope someone will help us :-)
 
  • Like
Likes Buzz Bloom

Related to Black hole inside a star -- How long for it to consume the star?

1. How does a black hole form inside a star?

When a massive star runs out of fuel and can no longer produce energy through nuclear fusion, the inward pull of gravity causes it to collapse in on itself. If the star is more than three times the mass of our Sun, it will continue to collapse into a point of infinite density known as a singularity, thus forming a black hole.

2. How long does it take for a black hole to form inside a star?

The amount of time it takes for a black hole to form inside a star depends on its mass. For a star with the mass of our Sun, it can take millions of years for the collapse to occur. However, for a more massive star, the process can happen much more quickly, in a matter of seconds.

3. How long does it take for a black hole to consume a star?

The rate at which a black hole consumes a star also depends on its mass. For a black hole with the mass of our Sun, it would take several trillion years to consume a star similar to our Sun. However, for a supermassive black hole, it can consume a star in a matter of days or weeks.

4. Can a black hole consume an entire star?

Yes, a black hole can consume an entire star. In fact, it is one of the primary ways in which black holes grow in size. As the black hole consumes the star, it also releases a tremendous amount of energy and radiation, making it visible to telescopes and other instruments.

5. What happens to the material consumed by a black hole inside a star?

When a black hole consumes a star, its immense gravitational pull tears the star apart and pulls the material into its event horizon, the point of no return. The material is then compressed and heated to extreme temperatures, emitting high-energy radiation before disappearing beyond the event horizon.

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