A Please help solve the equation in black hole f(R) theories

AI Thread Summary
The discussion centers on solving an equation related to black hole f(R) theories, referencing a specific paper. The user reports discrepancies between their attempts and the results presented in the paper, particularly at zero order. They provide detailed input and output equations, highlighting potential errors in their calculations. Suggestions for resolving the issue include checking for missing terms, sign errors, and verifying the correctness of inputs and derivatives. Consulting with a colleague or expert in the field is also recommended for further clarification.
Boy_saber
Messages
1
Reaction score
0
In the paper https://arxiv.org/abs/1210.4699. How to solve this equation?

1.jpg


I've tried it, it's not same as in this paper. Even zero order still not the same.
This is what I try to do at zero order.

input

$$E=E_0\left(r_0\right)$$
$$H=H_0\left(r_0\right)$$
$$b=b\left(r_0\right)$$
$$R=R_0\left(r_0\right)$$
$$\Phi =\Phi _0\left(r_0\right)$$
$$r=r_0$$
$$g^{11}=1-\frac{b}{r}$$
$$\Box f_R=H g^{11} \left(\frac{\partial R}{\partial r_0}\right){}^2+E \left(\left(1-\frac{b}{r}\right) \left(\frac{\partial R}{\partial r_0} \left(-\frac{\partial \Phi }{\partial r_0}\right)+\frac{\frac{\partial R}{\partial r_0}}{r}+\frac{\partial }{\partial r_0}\frac{\partial R}{\partial r_0}\right)+\frac{\left(1-\frac{\partial b}{\partial r_0}\right) \frac{\partial R}{\partial r_0}}{r}\right)$$

output

$$-\frac{b\left(r_0\right) H_0\left(r_0\right) R_0'\left(r_0\right){}^2}{r_0}+\frac{b\left(r_0\right) E_0\left(r_0\right) R_0'\left(r_0\right) \Phi _0'\left(r_0\right)}{r_0}-\frac{E_0\left(r_0\right) b_0'\left(r_0\right) R_0'\left(r_0\right)}{r_0}-\frac{b\left(r_0\right) E_0\left(r_0\right) R_0'\left(r_0\right)}{r_0^2}-\frac{b\left(r_0\right) E_0\left(r_0\right) R_0''\left(r_0\right)}{r_0}+H_0\left(r_0\right) R_0'\left(r_0\right){}^2-E_0\left(r_0\right) R_0'\left(r_0\right) \Phi _0'\left(r_0\right)+\frac{2 E_0\left(r_0\right) R_0'\left(r_0\right)}{r_0}+E_0\left(r_0\right) R_0''\left(r_0\right)$$

Where did I make a mistake?
 
Space news on Phys.org


It is difficult to pinpoint the exact mistake without more context and information about the specific equation and problem being solved. However, it is possible that there may be a missing term or a sign error in the output equation. It is also important to carefully check all the inputs and their derivatives to ensure they are correct. It may also be helpful to consult with a colleague or a subject expert for further assistance in solving the equation.
 
Abstract The Event Horizon Telescope (EHT) has significantly advanced our ability to study black holes, achieving unprecedented spatial resolution and revealing horizon-scale structures. Notably, these observations feature a distinctive dark shadow—primarily arising from faint jet emissions—surrounded by a bright photon ring. Anticipated upgrades of the EHT promise substantial improvements in dynamic range, enabling deeper exploration of low-background regions, particularly the inner shadow...
Back
Top