If we start from,
T(x)=A√xT(x)=A√x
A body experiences gravitational effect wholly due the mass behind it, the net effect of all mass above the sphere containing the hot mass is zero.
If we introduce the concept of thermal mass, where
Mthermal=T4(x)={A√x}4Mthermal=T4(x)={A√x}4, numerically
We have the total MthermalMthermal behind the body at point xx from the center of TT.
MT=∫x04πx2T4(x)dx=C∫x04πx21x2dx=C.4πxMT=∫x04πx2T4(x)dx=C∫x04πx21x2dx=C.4πx
where C=A4C=A4 is a constant.
Then we consider a hot body of total equivalent mass C.4πxC.4πx, what is its thermal gravity outwards? If we consider spheres of area
4πx24πx2
and the total thermal gravitational flux through them from a unit mass of TT, assuming space is empty and nothing else affects the flux between xoxo and xx,
gTo.4πx2o=gT.4πx2gTo.4πx2o=gT.4πx2
and that at x=xox=xo, GT=gTo.4πx2oGT=gTo.4πx2o
gT=GT4πx2gT=GT4πx2 per unit mass
GTGT increases with equivalent mass by C.4πx
gT=GT4πx2C.4πx
Let GTo=GTC
gT=GTox
This gravity is in the direction of x, outwards. This is the result from the post "Thermal Gravity And Lost Innocence" previously, that is to say the equivalent Thermal Mass concept
Mthermal=T4(x)
assumes that gT=GTox. This Thermal Mass generates a positive gravity outwards.