An image that recurs to me often through many years is that of a continuity of something close to dimensionality such as SU(2) X U(1) or the SO(3,3) -> SO(3,1) x C of D R Lunsford above (which looks promising).
Going from the outside in:
In the continuity at and NEAR the surface of a gravitational body, the dimensions change from those in space-time (as interplanetary, interstellar and intergalactic space) and those in isotropic acceleration toward the center, and time such as geological time, within moons, planets and stars.
On the "outside" in space-time this continuity supports radiation in the energy part of the mass-energy relation, and the motion of material objects. The time domain is a part of the velocity dimension which is evident in the speed of light c and in the simpler paths trajectories and orbits of objects. The dimensions outside are as above, SU(2) X U(1) or the SO(3,3) -> SO(3,1).
On the "inside" within gravitational bodies it supports the existence of the massive part of the mass-energy equivalence, and a time domain in which that existence is not always guaranteed forever, as in stellar radiation and planetary radioactivity. The dimensions inside appear to be at least time, acceleration and an isotropic form, rotation, two surface dimensions (longitude and latitude).
I have not rationalized the continuity well though it appears to be true continuity. It seems to require approaching the subject field with almost diaphanous imagination because the field is not understood or well conceived by our neurons. It is like repairing an integrated circuit with fish's flippers or paws.
Part of the problem is that length is a construct of measuring sticks, and planetary sizes and orbits, etc. while its only fundamental and absolute form appears to be in the Planck length. Similarly, time is a construct of the rotation of the earth and fractions and multiples of that, while the only absolute and fundamental unit of time appears to be the Planck time. That is, pending this millenium's review of the whole of physics from the earliest languages to the attainment of the Moon.