The discussion revolves around identifying and understanding solutions related to black holes within the framework of general relativity, particularly focusing on the conditions under which these solutions exist and their characteristics. The scope includes theoretical aspects of black hole metrics and the nature of vacuum solutions.
Participants express differing views on the relationship between vacuum solutions and black holes, indicating that while some black holes are vacuum solutions, not all vacuum solutions correspond to black holes. The discussion remains unresolved regarding the criteria for identifying black hole metrics.
There are limitations regarding the assumptions made about the nature of vacuum solutions and the definitions of black holes, which are not fully explored in the discussion.
sadegh4137 said:hi
if you want to find the black hole solutions, what do you do?
has any solutions of $$R_\alpha\beta=0$$ a black hole?
As stated above, there are black hole solutions which solve the vacuum Einstein equations but the converse, as you have stated it, is clearly not true (a vacuum solution need not be a black hole solution). Just take the trivial solution (Minkowski space-time) as a counterexample.sadegh4137 said:has any solutions of $R_\alpha\beta=0$ a black hole?