  Derrick-type virial identities, obtained via dilatation (scaling) arguments,
have a variety of applications in field theories. We deconstruct such virial
identities in relativistic gravity showing how they can be recast as
self-evident integrals of appropriate combinations of the equations of motion.
In spherical symmetry, the appropriate combination and gauge choice guarantee
the geometric part can be integrated out to yield a master form of the virial
identity as a non-trivial energy-momentum balance condition, valid for both
asymptotically flat black holes and self-gravitating solitons, for any matter
model. Specifying the matter model we recover previous results obtained via the
scaling procedure. We then discuss the more general case of stationary,
axi-symmetric, asymptotically flat black hole or solitonic solutions in General
Relativity, for which a master form for their virial identity is proposed, in a
specific gauge but regardless of the matter content. In the flat spacetime
limit, the master virial identity for both the spherical and axial cases
reduces to a balance condition for the principal pressures, discussed by Deser.
