  The vacuum modular Hamiltonian $K$ of the Rindler wedge in any relativistic
quantum field theory is given by the boost generator. Here we investigate the
modular Hamiltoninan for more general half-spaces which are bounded by an
arbitrary smooth cut of a null plane. We derive a formula for the second
derivative of the modular Hamiltonian with respect to the coordinates of the
cut which schematically reads $K" = T_{vv}$. This formula can be integrated
twice to obtain a simple expression for the modular Hamiltonian. The result
naturally generalizes the standard expression for the Rindler modular
Hamiltonian to this larger class of regions. Our primary assumptions are the
quantum null energy condition --- an inequality between the second derivative
of the von Neumann entropy of a region and the stress tensor --- and its
saturation in the vacuum for these regions. We discuss the validity of these
assumptions in free theories and holographic theories to all orders in $1/N$.
