In
general relativity
General relativity, also known as the general theory of relativity, and as Einstein's theory of gravity, is the differential geometry, geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of grav ...
, the Newman–Janis algorithm (NJA) is a
complexification
In mathematics, the complexification of a vector space over the field of real numbers (a "real vector space") yields a vector space over the complex number field, obtained by formally extending the scaling of vectors by real numbers to include ...
technique for finding
exact solutions to the
Einstein field equations
In the General relativity, general theory of relativity, the Einstein field equations (EFE; also known as Einstein's equations) relate the geometry of spacetime to the distribution of Matter#In general relativity and cosmology, matter within it. ...
. In 1964, Newman and Janis showed that the
Kerr metric
The Kerr metric or Kerr geometry describes the geometry of empty spacetime around a rotating uncharged axially symmetric black hole with a quasispherical event horizon. The Kerr metric is an exact solution of the Einstein field equations of gen ...
could be obtained from the
Schwarzschild metric
In Einstein's theory of general relativity, the Schwarzschild metric (also known as the Schwarzschild solution) is an exact solution to the Einstein field equations that describes the gravitational field outside a spherical mass, on the assumpti ...
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.
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.
The algorithm works well on ''ƒ''(''R'') and Einstein–Maxwell–Dilaton theories, but doesn't return expected results on
Braneworld and
Born–Infield theories.
See also
*
Birkhoff's theorem (relativity)
References
Algorithms
Exact solutions in general relativity
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