“The resulting formulation is based on a 4D Hodge-Laplacian operator with a spatiotemporal diffusion tensor and convection field, augmented by a small temporal perturbation to ensure nondegeneracy.”

“The Schwarzschild exterior maximizes the event horizon formation time $ΔT_{\text{eh}}=\frac{19}{6}m$ among all asymptotically flat, static, spherically-symmetric black holes with the same ADM mass $m$ that satisfy the weak energy condition.”

“The system was tested in different simulated and real outdoor environments, obtaining results near 90% of coverage in the majority of experiments.”

“The method provides a large class of exterior solutions of the constraint equations that can be matched to given interior solutions, according to the existing gluing techniques.”

“Related images were released by leaker and prototype collector Kosutami, showing prototypes with pink and yellow shells, but the inside of the charging case and the earbuds themselves remain white.”

“The main contribution is the derivation of unified gradient estimates that connect the near-boundary and far-field regions through a characteristic length scale determined by the Robin parameter, yielding a global description of how boundary effects penetrate into the exterior domain.”