Changes between Version 8 and Version 9 of u/JCFeb0713
- Timestamp:
- 02/14/13 15:52:07 (12 years ago)
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u/JCFeb0713
v8 v9 38 38 || [[latex(A)]] || black hole surface area || 39 39 || [[latex(g)]] || black hole surface gravity || 40 || [[latex(\Omega _H)]] || horizon angular velocity ||41 || [[latex(J _H)]] || black hole angular momentum ||42 || [[latex(\ bar{\mu})]] || red shifted chemicalpotential ||43 || [[latex( \bar{\theta})]] || red shifted temperature ||40 || [[latex(\Omega)]] || horizon angular velocity || 41 || [[latex(J)]] || black hole angular momentum || 42 || [[latex(\phi)]] || electric potential || 43 || [[latex(Q)]] || electric charge || 44 44 45 45 Correspondence between Temperature and Entropy with surface gravity and area … … 49 49 || Third Law || [[latex(g > 0)]] || [[latex(T > 0)]] || 50 50 51 Black hole 'entropy' 52 [[latex(S = \frac{k_B A}{4 l_p^2})]] 51 Black hole 'entropy' should be proportional to area. Dimensional analysis gives: 52 53 [[latex(S_{BH} = \frac{k_B A}{4 l_p^2})]] 53 54 54 55 where … … 56 57 [[latex(l_p=\sqrt{G\hbar/c^3})]] 57 58 59 and S,,BH,, stands for Bekenstein-Hawking entropy (not Black Hole). 60 58 61 59 62 60 63 Bekenstein's thought experiment... 61 When lowering a particle into a black hole, information about the particle is lost, so entropy of black hole should increase. This corresponds to an increase in area of64 When lowering a particle into a black hole, information about the particle is lost, so entropy of black hole should increase. This corresponds to an minimal increase in area of 62 65 63 66 [[latex(dA >= 8 \pi \frac{G m r}{c^2} )]] … … 71 74 [[latex(d S >= 2 \pi k_B)]] 72 75 73 ''1 bit of information lostas the particle merges with the black hole''76 ''1 possible microstate is lost to system as the particle merges with the black hole'' 74 77 75 78 If we assume that this change in energy occurs linearly over the particle's compton radius then we have … … 102 105 [[latex(T = \frac{\hbar a}{2\pi k_B c})]] 103 106 104 Verlinde supposes that the entropy is stored on a holographic screen bounding emerged part of space...105 107 106 108 [[Image(JC3.png, width=600)]] … … 115 117 [[Image(JC2.png, width=600)]] 116 118 119 What should be the temperature of the screen? 120 117 121 If we assume that the number of degrees of freedom is proportional to the area of the enclosed space like an event horizon 118 122 119 [[latex(N=\frac{A c^3}{G\hbar})]]123 [[latex(N=\frac{A}{l_p^2})]] 120 124 121 125 and that the temperature is determined by the equipartition rule … … 128 132 [[latex(E=Mc^2)]] 129 133 130 we recover 134 we get 135 136 [[latex(T=\frac{2 l_p^2 Mc^2}{k_B A} = \frac{G \hbar M}{k_B 2\pi R^2 c} 137 138 and 139 131 140 [[latex(F=G\frac{Mm}{R^2})]] 132
