Newman–Janis algorithm

{{short description|Technique to find exact solutions to Einstein field equations}}

In general relativity, the Newman–Janis algorithm (NJA) is a complexification technique for finding exact solutions to the Einstein field equations. In 1964, Newman and Janis showed that the Kerr metric could be obtained from the Schwarzschild metric by means of a coordinate transformation and allowing the radial coordinate to take on complex values. Originally, no clear reason for why the algorithm works was known.{{Cite journal|last1=Newman|first1=E. T.|last2=Janis|first2=A. I.|date=June 1965|title=Note on the Kerr Spinning Particle Metric|url=https://aip.scitation.org/doi/10.1063/1.1704350|journal=Journal of Mathematical Physics|volume=6|issue=6 |pages=915–917|doi=10.1063/1.1704350 |bibcode=1965JMP.....6..915N }}

In 1998, Drake and Szekeres gave a detailed explanation of the success of the algorithm and proved the uniqueness of certain solutions. In particular, the only perfect fluid solution generated by NJA is the Kerr metric and the only Petrov type D solution is the Kerr–Newman metric.{{cite journal|arxiv=gr-qc/9807001|first1=S. P.|last1=Drake|first2=P.|last2=Szekeres|year=2000|title=Uniqueness of the Newman–Janis Algorithm in Generating the Kerr–Newman Metric|journal=General Relativity and Gravitation |volume=32 |issue=3 |pages=445–457 |doi=10.1023/A:1001920232180 |bibcode=2000GReGr..32..445D |s2cid=123507909 }}

The algorithm works well on ƒ(R) and Einstein–Maxwell–Dilaton theories, but doesn't return expected results on Braneworld and Born–Infield theories.{{Cite journal|last1=Canonico|first1=Rosangela|last2=Parisi|first2=Luca|last3=Vilasi|first3=Gaetano|date=2011|title=The Newman Janis Algorithm: A Review of Some Results|journal=Proceedings of the Twelfth International Conference on Geometry, Integrability and Quantization |volume=12 |url=https://projecteuclid.org/euclid.pgiq/1436815617|language=EN|publisher=Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences|pages=159–169|doi=10.7546/giq-12-2011-159-169|s2cid=124148817 }}