The conclusion comes from combining a standard entropy calculation for a star, and a standard entropy calculation for a black hole. I can’t find a good example where they are worked through together, but the last page here provides an example. Treat the sun as an ideal gas, and its entropy is proportional to the number of particles, so it’s ~ 10^57. Entropy of a solar-mass black hole is the square of solar mass in units of Planck mass, so it’s ~ 10^76. So when a star becomes a black hole, its entropy jumps by about 10^20.
What’s lacking is a common theoretical framework for both calculations. The calculation of stellar entropy comes from standard thermodynamics, the calculation of black hole entropy comes from study of event horizon properties in general relativity. To unify the two, you would need to have a common stat-mech framework in which the star and the black hole were just two thermodynamic phases of the same system. You can try to do that in string theory but it’s still a long way from real-world physics.
For what I was saying about 0-branes, try this. The “tachyon instability” is the point at which the inter-brane modes come to life.
The conclusion comes from combining a standard entropy calculation for a star, and a standard entropy calculation for a black hole. I can’t find a good example where they are worked through together, but the last page here provides an example. Treat the sun as an ideal gas, and its entropy is proportional to the number of particles, so it’s ~ 10^57. Entropy of a solar-mass black hole is the square of solar mass in units of Planck mass, so it’s ~ 10^76. So when a star becomes a black hole, its entropy jumps by about 10^20.
What’s lacking is a common theoretical framework for both calculations. The calculation of stellar entropy comes from standard thermodynamics, the calculation of black hole entropy comes from study of event horizon properties in general relativity. To unify the two, you would need to have a common stat-mech framework in which the star and the black hole were just two thermodynamic phases of the same system. You can try to do that in string theory but it’s still a long way from real-world physics.
For what I was saying about 0-branes, try this. The “tachyon instability” is the point at which the inter-brane modes come to life.