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Schwarzschild and Kerr Solutions of Einstein’s Field Equation

Schwarzschild and Kerr Solutions of Einstein’s Field Equation

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Schwarzschild and Kerr Solutions of Einstein’s Field Equation

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Year:2015
Publisher:Autoedición
Pages:96 pages
Language:english
Since:20/04/2015
Size:2.47 MB
License:Pending review

Content:

Starting from Newton’s gravitational theory, we give a general introduction into the spherically symmetric solution of Einstein’s vacuum field equation, the Schwarzschild(-Droste) solution, and into one specific stationary axially symmetric solution, the Kerr solution. The Schwarzschild solution is unique and its metric can be interpreted as the exterior gravitational field of a spherically symmetric mass. The Kerr solution is only unique if the multipole moments of its mass and its angular momentum take on prescribed values. Its metric can be interpreted as the exterior gravitational field of a suitably rotating mass distribution. Both solutions describe objects exhibiting an event horizon, a frontier of no return. The corresponding notion of a black hole is explained to some extent. Eventually, we present some generalizations of the Kerr solution.

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