We examine the Tolman temperature by using Carter's variational formalism of thermodynamics. restrict our interests to fluids in thermal equilibrium that heat does not propagate. show this condition presents a general formula for local gradient. suggest resolution recently addressed conflict when chemical potential vanish.

A foundational theorem due to Buchdahl states that, within general relativity (GR), the maximum compactness $\mathcal{C}\ensuremath{\equiv}GM/(R{c}^{2})$ of a static, spherically symmetric, perfect fluid object mass $M$ and radius $R$ is $\mathcal{C}=4/9$. As corollary, there exists gap between stars black holes (where $\mathcal{C}=1/2$). Here we generalize Buchdahl's result by introducing most...

Maxwellian approximations to linear general relativity are revisited in light of relatively recent results on the degrees freedom gravitational field. The well-known formalism obtained harmonic coordinates is compared with a under coordinate choice where each metric components corresponds coordinate-invariant can be exploited cast field equations into form, but such forms mere mirages -- as vec...

We present a streamlined axiom system of special relativity in first-order logic. From this axiom system we “derive” an axiom system of general relativity in two natural steps. We will also see how the axioms of special relativity transform into those of general relativity. This way we hope to make general relativity more accessible for the non-specialist.