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schaefera
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From another post on this forum, we have an excerpt of Susskind's "The Black Whole War":
To figure the increase in mass, let's figure the energy of the photon and then convert that to an equivalent mass.
Photon energy is E = hf and if wavelength is Rs/SUB], from v = f x wavelength, frequency (f) is c/Rs/SUB] so E = hf becomes hc/Rs/SUB]. (1)
From E =mc2, dividing energy by c2 gives mass, so the change in mass becomes h/Rsc. (2)
The Schwarzschild radius is given by Rs - 2MG/c2 (3)
and substituting the above change in mass for the photon, substituting (2) in (3) increases the radius 2hG/Rsc3...
Later on, the book says that solving the equations for the increase in area of the black hole horizon, you can see that the area is always increasing by one square Planck length for each piece of information which falls in, regardless of the black hole's size. But don't the equations all involve R(s), meaning that the increase in area is not always the same for all black holes? For example, the increase in radius involves the initial radius itself.
To figure the increase in mass, let's figure the energy of the photon and then convert that to an equivalent mass.
Photon energy is E = hf and if wavelength is Rs/SUB], from v = f x wavelength, frequency (f) is c/Rs/SUB] so E = hf becomes hc/Rs/SUB]. (1)
From E =mc2, dividing energy by c2 gives mass, so the change in mass becomes h/Rsc. (2)
The Schwarzschild radius is given by Rs - 2MG/c2 (3)
and substituting the above change in mass for the photon, substituting (2) in (3) increases the radius 2hG/Rsc3...
Later on, the book says that solving the equations for the increase in area of the black hole horizon, you can see that the area is always increasing by one square Planck length for each piece of information which falls in, regardless of the black hole's size. But don't the equations all involve R(s), meaning that the increase in area is not always the same for all black holes? For example, the increase in radius involves the initial radius itself.
