Entropy and gravity become closely linked, via black hole thermodynamics. The thermodynamic arrow of time is the direction of increased entropy.
Here is mathematician John Nash's interesting "Einstein field equation" where he talks about gravity "compression" waves:
http://www.stat.psu.edu/~babu/nash/intereq.pdf
Quote:

WaveLike Form of the Scalar Equation
It was discovered only recently by me that the scalar equation naturally derived from the tensor equation for vacuum, particularly in the case of 4 spacetime dimensions, has a form extremely suggestive of waves. The scalar derived equation can be obtained by formally
contracting the general vacuum equation with the metric tensor. This results at first in an equation involving G (the scalar derived from the Einstein tensor) and the Ricci tensor and the scalar curvature R. And G, being the scalar trace of the Einstein tensor, can be expressed in term of R but this expression involves the number of dimensions, n. So we get
as the scalar equation derived from the original vacuum equation this result:
[...]
And now two things are notable about the form of this resulting scalar equation: (1): If n = 2 there is a singularity and this simply corresponds to the fact that the Einstein Gtensor is identically vanishing if n = 2, so there isnt any derived scalar equation of this type for two dimensions. (2): For n = 4 we find the nice surprise that the scalar equation entirely simplifies and then asserts simply that the scalar curvature satisfies the wave operator (which is a d'Alembertian if we think in terms of 3 + 1 dimensions).
So the scalar equation is
[]R = 0 PROVIDED that n = 4
[...]
But I don't myself understand either renormalization or the general theory of quantization. (To me it seems like \quantum theory" is in a sense like a traditional herbal medicine used by \witch doctors". We don't REALLY understand what is happening, what the ultimate truth really is, but we have a \cook book" of procedures and rituals that can be used
to obtain useful and practical calculations (independent of fundamental truth).)

end quote.
The gravity tensor should be able to rotate into the electromagnetic tensor and the electromagnetic tensor should be able to rotate into the gravity tensor. Time should rotate into space and space should rotate into time:
Time
^



>space
G
^



>EM
Here is an interesting quote:
http://www.einsteinschrodinger.com/
Quote:

In the well established "General Theory of Relativity", the Einstein equations are the field equations which describe the allowed values of the gravitational field. In the Einstein equations, the gravitational field is not a single number but is instead represented by the metric g_ik, which is a 4x4 matrix containing 4x4=16 components. However it is required to be symmetric, meaning that
g_ik= g_ki (for every combination of i=0,1,2,3 and k=0,1,2,3)
Therefore, g_ik really only has 166=10 independent components.
Maxwell's equations are the field equations which describe the allowed values of the electromagnetic field. In Maxwell's equations, the electromagnetic field F_ik is also a 4x4 matrix containing 4x4=16 components. However, it is required to be antisymmetric, meaning that
F_ik= F_ki (for every combination of i=0,1,2,3 and k=0,1,2,3)
In this case, for elements along the diagonal of the matrix we have
F_ii = F_ii, which can only be true if they are zero. Therefore, F_ik has just 1664=6 independent components.
In the EinsteinSchrodinger theory, the field equations are written in terms of a matrix N_ik with no symmetry properties, so that it has a full 4x4=16 independent components. Therefore, it could potentially contain both the metric and the electromagnetic field. For example we could have,
N_ik=g_ik+F_ik
By this definition and the symmetry properties of g_ik and F_ik, it is easy to see that the symmetric part of Nik would be the metric
g_ik=(N_ik+N_ki)/2
and the antisymmetric part of N_ik would be the electromagnetic field
F_ik=(N_ikN_ki)/2
This method for combining the metric and the electromagnetic field is meant as a simple example and does not actually work...

end quote.
It does not work but it is still interesting...
