We present new parallel emptiness checks for LTL model checking. Unlike existing parallel emptiness checks, these are based on an SCC enumeration, support generalized Büchi acceptance, and require no synchronization points nor repair procedures. A salient feature of our algorithms is the use of a global union-find data structure in which multiple threads share structural information about the automaton being checked. Our prototype implementation has encouraging performances: the new emptiness checks have better speedup than existing algorithms in half of our experiments.