  The interaction of petawatt ($10^{15}\ \mathrm{W}$) 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.
