centra

<font face="Arial, Helvetica">It is quite presumable from recent observations that there exi</font><font face="Arial, Helvetica">sts a </font><br /><font face="Arial, Helvetica"> huge black hole with millions of solar mass at the center of most <br /> galaxies. There are many scenarios proposed for the formation of such <br /> supermassive black holes. Among them, the scenario proposed by Zel\' <br /> dovich and Novikov in 1967 is a very attractive one, in which a tiny <br /> black holes formed in the very early universe grows very rapidly in a <br /> self-similar manner and becomes a giant black hole. <br /> Realistic black holes, especially those in the early universe when <br /> the expansion effects are far from negligible, should be modeled by <br /> black hole solutions that include matter fields in an expanding universe. </font><br /><font face="Arial, Helvetica"> In order to clarify the possibility of the scenario by Zel\'dovich and <br /> Novikov, we study the self-similar spherically symmetric solutions which <br /> are asymptotic to the Friedmann universe at spatial infinity. The (non)- <br /> existence of the solutions and the properties of the self-similar black <br /> holes in the presence of a scalar field or a perfect fluid are discussed. </font>