All Higher-Dimensional Majumdar–Papapetrou Black Holes

We prove that the only asymptotically flat spacetimes with a suitably regular event horizon, in a generalised Majumdar–Papapetrou class of solutions to higher-dimensional Einstein–Maxwell theory, are the standard multi-black holes. The proof involves a careful analysis of the near-horizon geometry and an extension of the positive mass theorem to Riemannian manifolds with conical singularities. This completes the classification of asymptotically flat, static, extreme black hole solutions in this theory.

Heat Treatment of Duplex Stainless Steel 2205 by Inserting Nano Nd2FeB14 in HIP Manifolds Under the Scope of Category Theory

In this paper, improving mechanical properties of duplex stainless steel by spinodal reaction inhibitors has been discussed. Spinodal gaps can be minimized when the host particles are minimized to the nanoscale. The Cahn-Hilliard Equation and the Allen-Cahn Equation on Manifolds with Conical Singularities can be related to manifolds produced by hot isostatic pressing (PM HIP) are used to improve mechanical strength. Spinodal reactions will be Inhibited by magnetic treatment and Nd-Fe-B Magnets. Grain refiners will be used to retard spinodal reactions. Mathematically, category theory is used to establish links between these different concepts.