Axisymmetric gravitational solutions as possible classical backgrounds around closed string mass distributions

By studying singularities in stationary axisymmetric Kerr and Tomimatsu–Sato solutions with distortion parameter δ = 2, 3, … in general relativity, we conclude that these singularities can be regarded as nothing other than closed string-like circular mass distributions. We use two different regularizations to identify δ-function type singularities in the energy–momentum tensor for these solutions, realizing a regulator independent result. This result gives supporting evidence that these axisymmetric exact solutions may well be the classical solutions around closed string-like mass distributions, just like Schwarzschild solution corresponding to a point mass distribution. In other words, these axisymmetric exact solutions may well provide the classical backgrounds around closed strings.