  We identify a new kind of physically realizable exceptional point (EP)
corresponding to degenerate coherent perfect absorption, in which two purely
incoming solutions of the wave operator for electromagnetic or acoustic waves
coalesce to a single state. Such non-hermitian degeneracies can occur at a
real-valued frequency without any associated noise or non-linearity, in
contrast to EPs in lasers. The absorption lineshape for the eigenchannel near
the EP is quartic in frequency around its maximum in any dimension. In general,
for the parameters at which an operator EP occurs, the associated scattering
matrix does not have an EP. However, in one dimension, when the $S$-matrix does
have a perfectly absorbing EP, it takes on a universal one-parameter form with
degenerate values for all scattering coefficients. For absorbing disk
resonators, these EPs give rise to chiral absorption: perfect absorption for
only one sense of rotation of the input wave.
