Recent content by djymndl07

Sure. Please see This paper for reference.

Kislev developed black hole metric in quintessence field by considering $T^t_t=T^r_r$ for energy momentum tesor corresponding to quintessence. Is there any action for the quintessence fild that gives such energy momentum tensor after varying with respect to $g^{\mu \nu}$?

In the article https://arxiv.org/abs/1112.1682 effective potential in equation 16 is approximated for early universe and obtained equation 21 and for later time in equation 26. Some constraints are given in equation 4 and 5. Can anyone explain how this approximations are made? I was trying to...

It is often seen in research papers that values of quintessence state parameter $\omega$ is taken between -1 and -1/3. However $\omega=-1$ corresponds to the cosmological constant and -1/3 corresponds to dust phase. Why these two cases are excluded in studying BH extended phase space thermodynamics?

I have been thinking this for quite a few time. At this point we know that our universe is going through an accelerated expansion phase. I was also doing some work on blackhole thermodynamics, specially P-V criticality, heat capacity, Joule Thomson expansion, heat engine etc. These...

I have this expression, $$T=2 P r-\frac{q^2}{4 \pi r^3}+\frac{1}{4 \pi r}$$. Now I want to solve this equation for ##r## perturbatively. This will give the expression $$r=\frac{T}{2 P}-\frac{1}{4 \pi T}+\frac{P \left(8 \pi P q^2-1\right)}{8 \left(\pi ^2 T^3\right)}+.......$$. I was reading...

I am trying to recreate the ##T-P## plane of figure 3 in the article black hole Joule-Thomson in Mathematica. I am following the procedure but cannot obtain the graph. I don't know exactly where am i doing wrong. Can any one tell me how to fix it? My notebook is attached here.

I have a function ##f(\text{r})\text{=}-\frac{a Q^4}{20 r^6}-\frac{c}{r^{3 \omega +1}}-\frac{2 M}{r}+\frac{8}{3} \pi P r^2+\frac{Q^2}{r^2}+1;## and an expression $$\text{Tinv2}=\frac{2^{2/3} \pi ^{4/3} a Q^4}{9 \sqrt[3]{3} V^{7/3}}+c 2^{2 \omega -\frac{2}{3}} \left(\frac{3}{\pi...

I got some way to do that in mathematica. Thank you everyone for the reply. One can see the link Here if interested.

Yes, numerically I can do that. but some analytical solution, even if it is an approximate one would be better.

a,c,Q,M, ##\omega## Are arbitrary constants. ##\omega## lies between -1 and -3. Other constants may take any positive value.

Hello there, I am trying to solve the Following equation for r, $$2 a Q^4+5 r^4 \left(3 c (\omega +1) r^{1-3 \omega }-2 r (r-3 M)-4 Q^2\right)=0$$ Clearly this is unsolvable. But if we substitute a=0 and c=0 we get one of the solution, ##r=\frac{1}{2} \left(\sqrt{9 M^2-8 Q^2}+3 M\right)##. Can I...

I am not sure if it is right to ask this question or not. Kindly let me know if it isn't. Actually I was going through the article Shadow Thermodynamics. I was trying to recreate the image fig 5 and 6 in mathematica. The idea is that we have to draw circles of radius ##r_s## given by equations...

Thanks a lot

Look at the following Image. The results are okay but clearly the plot colors does not match with the color bar. for example the color bar is showing only single color. the value 0.4 in color bar corresponds to the radius 0.8 which is different color in the plot. Another issue is that I don't...