document: In this Letter, we extend the McVittie's solution into charged black holes. We first deduce the metric for a Reissner–Nordström black hole in the expanding universe; several special cases of our solution are exactly the same as some solutions discovered previously. In the previous work [6] we have applied the asymptotic conditions to derive the Schwarzschild metric in the expanding universe, which is exactly the same as that derived by McVittie by solving the full Einstein equations. That demonstrates the power of this simple and straight-forward approach. In this Letter we follow the same procedure to derive the metric for the Reissner–Nordström black holes in Friedman–Robertson–Walker universe. We then study the influences of the evolution of the universe on the size of the black hole. Finally, in order to study the motion of the planet, we rewrite the metric from the cosmic coordinates system to the Schwarzschild coordinates system.
doc_bio_tags: O O O O O O O O O B I I O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O B I I I I I I I I I I I I O O O O O O O O O O O B I I I I O O O O O O O O O O O O O O B I I I I I I I O O B I I I I I O O O O O O O O O O O O O O O O B I O O O O B I I I I I O B I I I I I I I I I I I I