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The interaction of petawatt (10(15) W) lasers with solid matter forms the basis for advanced scientific applications such as table-top particle accelerators, ultrafast imaging systems and laser fusion. Key metrics for these applications relate to absorption, yet conditions in this regime are so nonlinear that it is often impossible to know the fraction of absorbed light f, and even the range of f is unknown. Here using a relativistic Rankine-Hugoniot-like analysis, we show for the first time that f exhibits a theoretical maximum and minimum. These bounds constrain nonlinear absorption mechanisms across the petawatt regime, forbidding high absorption values at low laser power and low absorption values at high laser power. For applications needing to circumvent the absorption bounds, these results will accelerate a shift from solid targets, towards structured and multilayer targets, and lead the development of new materials.