A novel absorption mechanism for linearly polarized lasers propagating in relativistically underdense solids in the ultrarelativistic (a ~ 100) regime is presented. The mechanism is based on strong synchrotron emission from electrons reinjected into the laser by the space charge field they generate at the front of the laser pulse. This laser absorption, termed reinjected electron synchrotron emission, is due to a coupling of conventional plasma physics processes to quantum electrodynamic processes in low density solids at intensities above 10(22) W/cm(2). Reinjected electron synchrotron emission is identified in 2D QED-particle-in-cell simulations and then explained in terms of 1D QED-particle-in-cell simulations and simple analytical theory. It is found that between 1% (at 10(22) W/cm(2)) and 14% (at 8 × 10(23) W/cm(2)) of the laser energy is converted into gamma ray photons, potentially providing an ultraintense future gamma ray source.