Tempero-gravitational Wave

For completeness sake,

We have from Maxwell,

$\nabla.E=\cfrac{\rho}{\varepsilon_o}$

$\nabla.B=0$

$\nabla\times E+\cfrac{\partial B}{\partial t}=0$

$\nabla\times B-\cfrac{1}{c^2}\cfrac{\partial E}{\partial t}=\cfrac{1}{c^2}\cfrac{J}{\varepsilon_o}$

and so, analogously,

$\nabla.T=\cfrac{\rho_{\small{T}}}{\varepsilon_{\small{To}}}$

where $T$ is the temperature force field strength per unit temperature particle (defined later in this post).  $\rho_{\small{T}}$, the negative temperature particle density enclosed inside the closed area for which $\nabla.T$ is defined.

$\nabla.G_W=0$

where a gravitational field is produced by spinning negative temperature particles.

$\nabla\times T+\cfrac{\partial G_W}{\partial t}=0$

$\nabla\times G_W-\cfrac{1}{c^2}\cfrac{\partial T}{\partial t}=\cfrac{1}{c^2}\cfrac{J_T}{\varepsilon_{\small{To}}}$

where $J_T$ is the negative temperature particle flow density.

Furthermore, $\varepsilon_{\small{To}}$ is to be interpreted as the resistance to establishing a temperature force field in free space by a temperature particle, $T_m$.   Such a force field, experienced by other temperature particles, is spherical, centered at $T_m$,

$T=F_{\small{/T_m}}=\cfrac{T_m}{4\pi \varepsilon_{\small{To}}r^2}$

per unit temperature particle.  $T$ is a Newtonian force per unit temperature particle $T_m$, experienced by other temperature particle inside the temperature field.  $T$ by itself is no longer temperature but a vector quantity.  It is possible to define a scalar potential field, $T_s$, by defining zero potential at infinity (ie. $r\rightarrow\infty$, $T_s\rightarrow0$); as just the derivations of electric and gravitational potentials.

We have a tempero-gravitational wave; a coupled pair of heat and gravitational energy; a wave oscillating between these two forms of energies; travelling at light speed $c$.

Note:   宝莲灯; spinning negative temperature particles.