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
extractive_keyphrases: applied the asymptotic conditions to derive the schwarzschild metric in the expanding universe black hole charged black holes follow the same procedure to derive the metric reissner–nordström black holes in friedman–robertson–walker universe rewrite the metric from the cosmic coordinates system to the schwarzschild coordinates system solving the full einstein equations study the motion of the planet
abstractive_keyphrases: asymptotic conditions to derive the schwarzschild metric deduce the metric for a reissner–nordström black hole in the expanding universe extend the mcvittie's solution into charged black holes mcvittie's solution reissner–nordström black hole study the influences of the evolution of the universe on the size of the black hole