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Inspiraling and merging binary neutron stars are not only important source ofgravitational waves, but also promising candidates for coincidentelectromagnetic counterparts. These systems are thought to be progenitors ofshort gamma-ray bursts (sGRBs). We have shown previously that binary neutronstar mergers that undergo {\it delayed} collapse to a black hole surrounded bya {\it weighty} magnetized accretion disk can drive magnetically-powered jets.We now perform magnetohydrodynamic simulations in full general relativity ofbinary neutron stars mergers that undergo {\it prompt} collapse to explore thepossibility of jet formation from black hole-{\it light} accretion diskremnants. We find that after $t-t_{\rm BH}\sim 26(M_{\rm NS}/1.8M_\odot)$ms[$M_{\rm NS}$ is the ADM mass] following prompt black hole formation, there isno evidence of mass outflow or magnetic field collimation. The rapid formationof the black hole following merger prevents magnetic energy from approachingforce-free values above the magnetic poles, which is required for the launchingof a jet by the usual Blandford--Znajek mechanism. Detection of gravitationalwaves in coincidence with sGRBs may provide constraints on the nuclear equationof state (EOS): the fate of an NSNS merger--delayed or prompt collapse, andhence the appearance or nonappearance of an sGRB--depends on a critical valueof the total mass of the binary, and this value is sensitive to the EOS.

GRMHD simulations of prompt-collapse neutron star mergers: the absence of jets