A Derivation of the Kerr–Newman Metric Using Ellipsoid Coordinate Transformation | Chapter 06 | Theory and Applications of Physical Science Vol. 1

The Kerr–Newman metric describes a special rotating charged mass and is the most general solution for the asymptotically stable “black-hole” solution in the Einstein–Maxwell equations in general relativity. Because these are nonlinear partial differential equations, it is difficult to find an exact analytical solution other than spherical symmetry. This study presented a new derivation of the Kerr–Newman metric which is an extension of the authors’ previous research. Using the ellipsoid symmetry of space-time in the Kerr metric, an ellipsoidal coordinate transformation method was performed and the Kerr–Newman metric was more intuitively obtained. The relation with this method and Newman–Janis algorithm was discussed.

Author(s) Details

Dr. Yu-Ching, Chou
Health 101 Clinic, 1F., No.97, Guling St., Zhongzheng District, Taipei City 100, Taiwan and Archilife Research Foundation, 2F.-1, No.3, Ln. 137, Changchun Rd., Zhongshan District, Taipei City 104, Taiwan.

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Analytical Approach to Obtain Some New Traveling Wave Solutions of Coupled Systems of Nonlinear Equations | Chapter 11 | Advances in Mathematics and Computer Science Vol. 2

The second order nonlinear ordinary differential equation is executed as an auxiliary equation. For illustration, a new extension of so called (G’/G) method is considered to investigate the generalized Hirota-Satsuma coupled KdV equations for producing some new analytical solutions. The obtained solutions belong to hyperbolic functions, trigonometric functions and rational forms which show the wider applicability of this new extended method for handling other nonlinear evolution equations. The numerical results are also described in the figures.

Author(s) Details

Dr. Hasibun Naher
Department of Mathematics and Natural Sciences, BRAC University, 66 Mohakhali, Dhaka 1212, Bangladesh.

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