- #1
Emilie.Jung
- 68
- 0
The metric
$$ds^2=-R_1(r)dt^2+R_2(r)dr^2+R_3(r)r^2(d\theta^2+sin^2d\phi^2)$$
when changed to
$$ds^2=-R_1(r)dt^2+R_2(r)(dr^2+r^2d\Omega^2)$$
upon setting ##R_2(r)=R_3(r)##, the later metric holds the name of isotropic metric.
My question what is the difference between the first and the second metric, so that, the first is standard meanwhile the second is called isotropic? We know that isotropy means no preferred direction, but I cannot see how isotropy holds in the secondbut not the first.
Note: I already checked wikipedia, where it doesn't say much about what is an isotropic metric by itself.
$$ds^2=-R_1(r)dt^2+R_2(r)dr^2+R_3(r)r^2(d\theta^2+sin^2d\phi^2)$$
when changed to
$$ds^2=-R_1(r)dt^2+R_2(r)(dr^2+r^2d\Omega^2)$$
upon setting ##R_2(r)=R_3(r)##, the later metric holds the name of isotropic metric.
My question what is the difference between the first and the second metric, so that, the first is standard meanwhile the second is called isotropic? We know that isotropy means no preferred direction, but I cannot see how isotropy holds in the secondbut not the first.
Note: I already checked wikipedia, where it doesn't say much about what is an isotropic metric by itself.