Injecting particles into atmosphere to reflect sunlight, stratospheric aerosol injection (SAI), represents a potential technological solution to the threat of climate change. But could the cure be worse than the disease? Understanding low probability, yet plausible, high-impact cases is critical to prudent climate risk management and SAI deliberation. But analyses of such high impact outcomes are lacking in SAI research. This paper helps resolve this gap by investigating SAI's contributions to global catastrophic risk. We split SAI's contributions to catastrophic risk into four interrelated dimensions:1. Acting as a direct catastrophic risk through potentially unforeseen ecological blowback.2. Interacting with other globally catastrophic hazards like nuclear war.3. Exacerbating systemic risk (risks that cascade and amplify across different systems);4. Acting as a latent risk (risk that is dormant but can later be triggered).The potential for major unforeseen environmental consequences seems highly unlikely but is ultimately unknown. SAI plausibly interacts with other catastrophic calamities, most notably by potentially exacerbating the impacts of nuclear war or an extreme space weather event. SAI could contribute to systemic risk by introducing stressors into critical systems such as agriculture. SAI's systemic stressors, and risks of systemic cascades and synchronous failures, are highly understudied. SAI deployment more tightly couples different ecological, economic, and political systems. This creates a precarious condition of latent risk, the largest cause for concern. Thicker SAI masking extreme warming could create a planetary Sword of Damocles. That is, if SAI were removed but underlying greenhouse gas concentrations not reduced, there would be extreme warming in a very short timeframe. Sufficiently large global shocks could force SAI termination and trigger SAI's latent risk, compounding disasters and catastrophic risks. Across all these dimensions, the specific SAI deployment, and associated governance, is critical. A well-coordinated use of a small amount of SAI would incur negligible risks, but this is an optimistic scenario. Conversely, larger use of SAI used in an uncoordinated manner poses many potential dangers. We cannot equivocally determine whether SAI will be worse than warming. For now, a heavy reliance on SAI seems an imprudent policy response.