The dynamical phase transitions of stellar systems and the corresponding
  kinetimacs
  External fields in Migromian dynamics (MD or MOND, Milgrom 1983) break the
Strong Equivalence Principle (SEP) and change the dynamics of self-bound
stellar systems moving in space-varying background gravitational fields. We
study two kinds of re-virialisation of the stellar systems: the violent phase
transition and the adiabatic phase transition for systems moving on radial
orbits, where the external field evolves from strong to weak and whose
corresponding dynamics changes from Newtonian to Milgromian. We find that the
time scale for the phase tranformation from Newtonian to Milgromian gravity
lies only within one to a few crossing times for low density globular clusters
with masses ranging from $10^4\msun$ to $10^6\msun$. Thus a globular cluster
can appear frozen in the Newtonian regime despite being in the Milgromian
regime for not longer than a few crossing times. We also study the kinematics
and anisotropy profiles of the systems. The velocity dispersions of the systems
are larger after the phase transitions, especially for the outer regions of the
stellar systems. Moreover, the isotropic systems become radially anisotropic,
especially for the outer parts, after the process caused by the dynamical phase
transition. Deeper Milgromian systems have more radially anisotropic velocity
dispersion functions. We also find that the final profiles of density, velocity
dispersion and anisotropy do not depend on the details of the phase transition.
I.e., the mass distribution and kinematics of the end-states of the globular
clusters do not depend on the rapidity of the transition from Newtonian to
Milgromian gravity. Thus, the transition from the Newtonian to the Milgromian
regime naturally induces a significant radially anisotropic velocity
distribution in a globular cluster.
