  A novel theory was proposed earlier to model systems with thermal gradients,
based on the postulate that the spatial and temporal variation in temperature
can be recast as a variation in the metric. Combining the variation in the
metric due to the thermal variations and gravity, leads to the concept of
thermal gravity in a 5-D space-time-temperature setting. When the 5-D Einstein
field equations are projected to a 4-D space, they result in additional terms
in the field equations. This may lead to unique phenomena such as the
spontaneous symmetry breaking of scalar particles in the presence of a strong
gravitational field. This theory, originally conceived in a quantum mechanical
framework, is now adapted to explain the galaxy rotation curves. A galaxy is
not in a state of thermal equilibrium. A parameter called the "degree of
thermalization" is introduced to model partially thermalized systems. The
generalization of thermal gravity to partially thermalized systems, leads to
the theory of many-body gravity. The theory of many-body gravity is now shown
to be able to explain the rotation curves of the Milky Way and the M31
(Andromeda) galaxies, to a fair extent. The radial acceleration relation (RAR)
for 21 galaxies, with variations spanning three orders of magnitude in galactic
mass, is also reproduced.
