View source for 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 in general relativity|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.<ref>{{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 }}</ref>
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]].<ref>{{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 }}</ref>
The algorithm works well on ''ƒ''(''R'') and Einstein–Maxwell–Dilaton theories, but doesn't return expected results on [[Brane cosmology|Braneworld]] and [[Born–Infeld model|Born–Infield theories.]]<ref>{{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 }}</ref>
== See also ==
{{Portal|Physics|Mathematics|Astronomy|Science}}
* [[Birkhoff's theorem (relativity)]]
== References ==
{{Reflist}}
[[Category:Algorithms]]
[[Category:Exact solutions in general relativity]]
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