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Hi, I'm looking for some help on where to start with this question:

The surface area of a Schwarzschild black hole is [tex]A=16 \pi R^2_c[/tex] where [tex]R_c[/tex] is the distance of the event horizon from the centre of the black hole. Show that for such a hole containing quantized matter, its entropy can be written

[tex]S = \frac{\xi k c}{4\pi h G}A[/tex]

where [tex]\xi[/tex] is a numerical constant.

I know that the enropy of a change is

[tex]S = \int_{initial}^{final} \frac{Q_{rev}}{T}[/tex]

and can show that using the de Broglie relation

[tex]\lambda dB <= 2R_c = \frac{4GM}{c^2}[/tex]

the energy is

[tex]\frac{hc^3}{4GM} <= E[/tex]

But I'm not sure where to go with proving that the entropy is the equation given.

The surface area of a Schwarzschild black hole is [tex]A=16 \pi R^2_c[/tex] where [tex]R_c[/tex] is the distance of the event horizon from the centre of the black hole. Show that for such a hole containing quantized matter, its entropy can be written

[tex]S = \frac{\xi k c}{4\pi h G}A[/tex]

where [tex]\xi[/tex] is a numerical constant.

I know that the enropy of a change is

[tex]S = \int_{initial}^{final} \frac{Q_{rev}}{T}[/tex]

and can show that using the de Broglie relation

[tex]\lambda dB <= 2R_c = \frac{4GM}{c^2}[/tex]

the energy is

[tex]\frac{hc^3}{4GM} <= E[/tex]

But I'm not sure where to go with proving that the entropy is the equation given.

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