- #1
PeteSampras
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Homework Statement
Compute the specific heat of black hole
Homework Equations
##T=\frac{2}{r_+}-3/2048 r_+^2-\frac{6r_+^3M^2}{(M+r_+^6)^2}##
##f(r)=1-\Big (\frac{r^2}{64}+\frac{Mr^4}{M+r^6} \Big ) ^{1/2}##
##r_+## is the horizon where ##f(r=r_+)=0##.
The Attempt at a Solution
I tried to obtain use ##C= \Big ( \frac{dT}{dM_+} \Big )^{-1}=\frac{dM_+}{dr_+}(\frac{dT}{dr_+})^{-1} ##
where ##M_+## is obtained from ##f(r_+)=0##
For compute ## (\frac{dT}{dr_+})^{-1}## in the specific heat, Do i have to evaluate ##M_+=-r_+^6(r_+^2-64)/(r_+^2+64r_+^4-64)## by the term ##M## in the equation ##T=\frac{2}{r_+}-3/2048 r_+^2-\frac{6r_+^3M^2}{(M+r_+^6)^2}##??