(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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?

2. Relevant 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##

3. 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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# Homework Help: Black hole inside a star -- How long for it to consume the star?

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