A closed universe model containing a constant and positive vacuum energy density (cosmological constant) has been studied. By analyzing the McVittie metric, it can be shown directly that for an expanding universe, the Hubble parameter at the event horizon for all static symmetric black holes is the same. As for the cosmological constant, black holes will not expand as the universe expands. In addition, the existence of the Hubble voltage is also explained which can affect the speed of the universe's expansion in certain areas.
                        
                        
                        
                        
                            
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