Trivial Entropy of Matter in Gravitation

Abstract: Expanding the black hole thermodynamics from the horizon to achronal Cauchy hypersurface, the general relation between the Einstein equation and thermodynamics is established. Starting from trivial entropy that is generalized by Bekenstein-Hawking entropy, the entropic mass of matter emerges naturally together with Unruh temperature. The key idea is that the cause of mass formation comes down to trivial entropy, and mass density is just the external manifestation of mass. The full Einstein equation with the cosmological constant is derived from the requirement that entropic mass and proper mass are equivalent. This perspective suggests that trivial entropy that causes mass in gravitation may be the best choice for the origin of space-time geometry.