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Recently Fuller & Shi proposed that the gravitational collapse ofsupermassive objects ($M \gtrsim 10^4M_\odot$) could be a cosmological sourceof $\gamma$-ray bursts (GRBs). The major advantage of their model is thatsupermassive object collapses are far more energetic than solar mass-scalecompact mergers. Also, in their proposal the seeds of supermassive black holes(SMBHs) thus formed could give rise to the SMBHs observed at the center of manygalaxies. We argue here that, besides the generation of GRBs, there could welloccur a strong generation of gravitational waves (GWs) during the formation ofSMBHs. As a result, the rate of such GW bursts could be as high as the rate ofGRBs in the model by Fuller & Shi. In this case, the detection of GRBs andbursts of GWs should occur with a small time difference. We also argue that theGWs produced by the SMBHs studied here could be detected when the LaserInterferometric Space Antenna (LISA) becomes operative.Comment: 10 pages (AAS Latex macros v5.0.2), 2 eps figures. The Astrophysical  Journal (accepted

Possible Strong Gravitational Wave Sources for theLISAAntenna