  We construct a static and spherical excited state without singularities in
renormalizable quantum gravity with background-free nature asymptotically. Its
diameter is given by a correlation length of the quantum gravity, longer than
the Planck length by 2 orders of magnitude, and it has a Schwarzschild tail
outside. The quantum gravity dynamics inside is described by employing a
nonperturbative expression of higher-order corrections assumed from a physical
requirement that the dynamics disappear at the edge where it is in strong
coupling. A running coupling constant that is a manifestation of nonlinearity
and nonlocality is managed by approximating it as a mean field that depends on
the radial coordinate. If the mass is several times the Planck mass, we can set
up a system of linearized equations of motion for the gravitational potentials
incorporating the running effect and obtain the excited state as its solution.
It may be a candidate for dark matter, and will give a new perspective on black
hole physics.
