  Emergent modified gravity presents a new set of generally covariant
gravitational theories in which the space-time metric is not directly given by
one of the fundamental fields. A metric compatible with the modified dynamics
of gravity is instead derived from covariance conditions for space-time in
canonical form. This paper presents a significant extension of existing vacuum
models to the case of a scalar field coupled to emergent modified gravity in a
spherically symmetric setting. Unlike in previous attempts for instance in
models of loop quantum gravity, it is possible to maintain general covariance
in the presence of modified gravity-scalar couplings. In general, however, the
emergent space-time metric depends not only on the phase-space degrees of
freedom of the gravitational part of the coupled theory, but also on the scalar
field. Matter therefore directly and profoundly affects the geometry of
space-time, not only through the well-known dynamical coupling of stress-energy
to curvature as in Einstein's equation, but even on a kinematical level before
equations of motion are solved. This paper introduces further physical
requirements that may be imposed for a reduction of modified theories to more
specific classes, in some cases eliminating certain modifications that would be
possible in a vacuum situation. With minimal coupling, results about the
removal of classical black-hole singularities in vacuum emergent modified
gravity are found to be unstable under the inclusion of matter, but alternative
modifications exist in which singularities are removed even in the presence of
matter. Emergent modified gravity is seen to provide a large class of new
scalar-tensor theories with second-order field equations.
