# Finding and using exact solutions of the Einstein equations

@article{MacCallum2006FindingAU, title={Finding and using exact solutions of the Einstein equations}, author={Malcolm A. H. MacCallum}, journal={arXiv: General Relativity and Quantum Cosmology}, year={2006}, volume={841}, pages={129-143} }

The evolution of the methods used to find solutions of Einstein’s field equations during the last 100 years is described. Early papers used assumptions on the coordinate forms of the metrics. Since the 1950s more invariant methods have been deployed in most new papers. The uses to which the solutions found have been put are discussed, and it is shown that they have played an important role in the development of many aspects, both mathematical and physical, of general relativity.

## 10 Citations

### An Exact Solution of the Einstein's Equation

- Physics
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In this short letter we present a rigorous vacuum solution of the Einstein’s equation with a few singular surfaces. In contrast with the well known solutions, this solution looks somewhat exotic and…

### Exact Vacuum Solutions to the Einstein Equation

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AbstractIn this paper, the author presents a framework for getting a series of exact
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We find new exact solutions of the Einstein field equations for a perfect fluid metric conformal to a spacetime of type D in the Petrov classification scheme. We analyse the complete system of…

### Static axisymmetric Einstein equations in vacuum: Symmetry, new solutions, and Ricci solitons

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- 2015

An explicit one-parameter Lie point symmetry of the four-dimensional vacuum Einstein equations with two commuting hypersurface-orthogonal Killing vector fields is presented. The parameter takes…

### A Canonical Form of the Metric in General Relativity

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- 2007

If there is a null gradient field in a 1+3 dimensional Lorentzian manifold, we can establish a kind of light-cone coordinate system for the manifold from the null gradient field. In such coordinate…

### A Derivation of the Kerr–Newman Metric Using Ellipsoid Coordinate Transformation

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- 2018

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…

### Astrophysically Satisfactory Solutions to Einstein's R-33 Gravitational Field Equations Exterior/Interior to Static Homogeneous Oblate Spheroidal Masses

- Physics, Geology
- 2009

In this article, we formulate solutions to Einstein’s geometrical field equations derived using our new approach. Our field equations exterior and interior to the mass distribution have only one…

### Algebraic computing Tools in General Relativity: Energy-Momentum Tensors and Exact Solutions to the Einstein Field Equations

- Computer Science
- 2009

Applications of the new tools in the Tensor package are extensive, and will provide researchers with a more useful interface for investigating problems in theoretical physics and mathematics.

### Relativistic Mechanics in Gravitational Fields Exterior to Rotating Homogeneous Mass Distributions within Regions of Spherical Geometry

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- 2009

General Relativistic metric tensors for gravitational fields exterior to homogeneous spherical mass distributions rotating with constant angular velocity about a fixed diameter are constructed. The…

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