Research

# Negative Temperatures

The thermodynamic concept of temperature is defined by the following equation: $$T = \frac{\partial E}{\partial S}$$ where $E$ is the energy of the system and $S$ is the entropy. Now usually when the energy of a system increases or decreases it’s disorder, and hence it’s entropy, also increases or… Continue reading Negative Temperatures

Research

# Euler’s Theorem and the Smarr Relation

The area of a charged rotating (Kerr) black hole is given by $$\label{eqn:kerr-area-relation} A = 4\pi \left[ 2 M^2 + 2 (M^4 – L^2 – M^2 Q^2)^{1/2} – Q^2 \right]$$ This relation can be inverted to express the mass $M$ as a function of charge $Q$, area $A$ and angular momentum $L$: … Continue reading Euler’s Theorem and the Smarr Relation