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For fifty years after the creation of the general theory of relativity in all calculations, only the Schwarzschild solution was used, which describes a spherically symmetric black hole, characterized only by mass. The idea that sufficiently realistic black hole models should have rotation is not new. Everyone understood that the influence of rotation had to be taken into account, but no one could correctly decide the rotation should depend on two parameters - the mass of the black hole (denoted by the letter M) of the Einstein equation. Actually, a complete solution of the equations of the gravitational field, taking into account the angular momentum of the hole (indicated by the letter a). In addition, this solution should be asymptotically flat, i.e., away from the black hole, space-time should become flat. Although space is never flat, but at a certain distance - to the observed influence of a black hole, we can assume that it is flat. Like all assumptions in mathematical modeling, the rejection of them leads to a revision of the entire model. Therefore, the assumption of asymptotically flat space in mathematical models of black holes is still preserved, since it does not have a significant effect on the structure of a black hole, but it turns out to be inadmissible when considering a model of a space in which a black hole is an element of a more complex structure. The equations of the gravitational field turned out to be so complex mathematically that no one was able to find a single exact solution that satisfies these simple requirements for a long time. Only in 1963, Roy P. Kerr, an Australian mathematician who worked then at the University of Texas (USA), found a complete solution of the equations of the gravitational field for a rotating black hole. For the first time in nearly fifty years after Einstein’s fundamental work, astrophysicists finally received a mathematical description of the geometry of space-time surrounding a massive rotating object. By 1975, the uniqueness of the Kerr solution was proved. In the same way as all possible solutions for black holes with only mass (M) are equivalent to the Schwarzschild solution, and all possible solutions for black holes with mass and charge (M and Q) are equivalent to the Reisner-Nordstrom solution, all possible solutions with mass and moment of momentum (M and a) should be equivalent to Kerr's decision.


Field Equations Describing Black Holes

The sun has a mass - M and angular momentum - and therefore in the future we will consider the structure of the sun in the Kerr solution.

Authors: Gordeev S.I., Voloshina V.N. 28-07-2003

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