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In classical textbooks for GR, Schwarzschild and Kerr spacetimes are adequately described. In which books or articles, it is mostly believed that Reissner-Nordstrom, Kerr-Newman, Schwarzschild-de Sitter, Kerr-de Sitter spacetimes are well described?

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  • $\begingroup$ I think as a general rule GR books will cover the basic metrics in detail and leave it up to you to research special cases. Are you still interested in photon spheres? If so note that a spherically symmetric static system has a metric $ds^2 = -f(r)dt^2 + dr^2/f(r) + r^2d\Omega^2$ for some function $f(r)$, and the effective potential for massless particles is $V(r)=\frac{L^2}{r^2}f(r)$. The photon sphere is the position of the maximum in $V(r)$. You can get $f(r)$ for the de Sitter-Schwarzschild metric from Wikipedia. $f(r)=1-\frac{2M}{r}-\frac{\Lambda}{3}r^2$ $\endgroup$ – John Rennie Jun 15 '17 at 16:24
  • $\begingroup$ Photon spheres are not problem now. I need the above mentioned metrics' properties discussed in some reliable sources (mostly articles). Of course there are many works devoted to these popular metrics. There should be some popular ones. $\endgroup$ – Constantin Jun 15 '17 at 16:49

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