Assignment Solutions in Physics, Physical Chemistry, Astrophysics, Computer Simulation, and Numerical Calculation

Black Hole Formation by Accommodation of Photons

Questions:

a) Give a rough estimate of the maximum number N of photons that could be accommodated in region of space of volume V before they’d collapse to form a black hole. You can assume that the region is approximately spherical and of size L~V^{1/3}.

b) In part (a) you should have found that

What property of the system does the particular value of γ single out as the determining factor in how many particles the system can accommodate?

c) The number N is essentially the number of bits of information a finite system can contain according to our present understanding of the laws of physics. Such a system will have 2^{N} quantum states. Estimate the theoretical limit to the number of terabytes of data that could be stored on a device the size of a typical hard drive.

d) Given that the radius of the observable universe is some 50 billion lightyears, estimate the maximum number of bits of information it might contain?

Solution:

a) Schwarzschild radius of a simple black hole occupied with N photons,is given by,