Reversible and Irreversible Transformations in Black-Hole Physics

The concepts of irreducible mass and of reversible and irreversible transformations in black holes are introduced, leading to the formula $E^2=m_{\mathrm{ir}}^{}{}_{}{}^2+\left(\frac{L^2}{4m_{\mathrm{ir}}^{}{}_{}{}^2}\right)+p^2$ for a black hole of linear momentum $p$ and angular momentum $L$.