A new proposal regarding the heat generated by gravity in locally accelerating frames

For Rindler observers accelerating close to the horizon in local patches around a spacetime point, the matter-energy passing through the horizon increases the entropy and heat energy. Jacobson has showed that the Einstein equation can be derived from the consideration of this thermodynamic process. This, however, works only if the acceleration $a$ is much larger than the scale set by the curvature of the spacetime. It is explored here whether an extension is possible to the case with no lower bound on $a$. We show that this is possible if one assumes that in a locally accelerating frame, the matter-energy passing through null hypersurfaces could result in an increase in the heat energy and the entropy. Such a generalisation extends the thermodynamic derivation of gravity to include any non-freely falling observer. A new method of determining the temperature detected by such locally accelerating observers is also presented. By considering only the quantisation of sufficiently localised wave modes of a field, it is shown that the observer finds himself in a thermal environment.