Thermodynamic geometry analysis of new Schwarzschild black holes

This article puts forward a hypothesis.In this article, the derivative of the cosmological constant is positive, and there is a possibility that the constant evolves from negative in the early universe to positive in the later period. We see that when the black hole is an extreme black hole $r_{+}=r_{-}$, the curvature scalar vanishes to zero. In general, the curvature scalar is not equal to zero. When $r_{+}=3 r_{-}$, the curvature scalar is equal to negative infinity. According to Ruppeiner's theory, this time represents the phase transition of the system. It is very interesting that the divergence point of the curvature scalar happens to be the Davis transition point. We have found the phase transition point of the new Schwarzschild black hole.

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