2025/02/17 by M. Ali Akbar, Akbar, M. M., M. Self +1
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Cosmology and Gravitation Theories #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Geometric Analysis and Curvature Flows
paper · pdf · doi:10.48550/arxiv.2502.11428
openalex publication_date 2025/02/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that the system of vacuum Einstein equations (i.e., Ricci-flat metrics) with two hypersurface-orthogonal, commuting Killing vector fields in d ≥ 5 dimensions is invariant under the action of a one-parameter Lie group, and the group action on any metric can be expressed in a closed, universal form. This enables the generation of a one-parameter family of solutions from any given ``seed" solution of the system without solving additional equations, as well as one-parameter families of local steady Ricci solitons. This extends the Lie point symmetry in four dimensions, found earlier for axisymmetric static vacuum systems, and provides the first example of solution generation in higher-dimensional vacuum Einstein equations that can be realized purely algebraically.