2024/05/24 by Jash Desai, Desai, Jash, Gabriel Herczeg +5 · 3 citations
Biochemistry, Genetics and Molecular Biology · Chemistry · #Cancer, Hypoxia, and Metabolism #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Protein Degradation and Inhibitors #Synthesis and Catalytic Reactions
paper · pdf · doi:10.48550/arxiv.2405.15946
openalex publication_date 2024/05/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It was recently conjectured that a certain vacuum Kerr-Schild spacetime, which may be regarded as a self-dual analog of the Kerr metric, is equivalent to the self-dual Taub-NUT instanton. We confirm this conjecture by applying the Cartan-Karlhede algorithm to each metric and showing that for suitable choices of null tetrad, the algorithm leads to the same invariants and linear isotropy groups for both, establishing their equivalence. While it is well-known that the Taub-NUT solution and its self-dual version admit a double Kerr-Schild form, the observation that the self-dual Taub-NUT instanton admits a single Kerr-Schild form has only been made very recently. The two metrics we compare may be regarded as either complex metrics with Lorentzian (1,3) signature or real metrics with Kleinian (2,2) signature; here we take the latter view. Significant simplifications occur when the null tetrads are chosen to consist of two pairs of complex conjugate null vectors rather than four real independent ones. As a bonus, our work provides the first example of applying the Cartan-Karlhede algorithm using a null tetrad of this type.