Two-Dimensional Einstein Manifolds in Geometrothermodynamics

Figure 1

The three qualitatively different types of radial functions. The horizontal axis corresponds to the energy, while the vertical represents the radius of the circumference. We observe that only the curves corresponding to negative values of the exponent𝛼are positive definite in the full physical domain, that is, positive values of energy and volume.

(a)

(b)

(c)

(d)