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We investigate the amplification of the genuine tripartite nonlocality (GTN)and the genuine tripartite entanglement (GTE) of Dirac particles in thebackground of a Schwarzschild black hole by a local filtering operation underdecoherence. It is shown that both the physically accessible GTN and thephysically accessible GTE are decreased by the Hawking effect and decoherence.The "sudden" death of the physically accessible GTN occurs at some criticalHawking temperature, and the critical Hawking temperature degrades as thedecoherence strength increases. In particular, it is found that the criticalHawking temperature of "sudden death" can be prolonged by applying the localfiltering operation, which means that the physically accessible GTN can existfor a longer time. Furthermore, we also find that the physically accessible GTEapproaches to the nonzero stable value in the limit of infinite Hawkingtemperature for most cases, but if the decoherence parameter p is less than 1,the "sudden death" of GTE will take place when the decoherence strength islarge enough. It is worth noting that the nonzero stable value of GTE can beincreased by performing the local filtering operation, even in the presence ofdecoherence. Finally, we explore the generation of physically inaccessible GTNand GTE of other tripartite subsystems under decoherence, it is shown that thephysically inaccessible GTN cannot be produced, but the physically inaccessibleGTE can be produced, namely, GTE can pass through the event horizon of blackhole, but the GTN cannot do it. In addition, we can see that the generatedphysically inaccessible GTE can be increased by applying the local filteringoperation, even if the system suffers decoherence.

Amplification of genuine tripartite nonlocality and entanglement in the Schwarzschild spacetime under decoherence