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arXiv · 1907.09521

On the link between the Maxwell and linearised Einstein equations on Schwarzschild

Thomas Johnson
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Abstract

In this short note we shall demonstrate that given a smooth solution $\gamma$ to the linearised Einstein equations on Schwarzschild which is supported on the $l\geq 2$ spherical harmonics and expressed relative to a transverse and traceless gauge then one can construct from it a smooth solution to the sourced Maxwell equations expressed relative to a generalised Lorentz gauge. Here the Maxwell current is constructed from those gauge-invariant combinations of the components of $\gamma$ which are determined by solutions to the Regge--Wheeler and Zerilli equations. The result thus provides an elegant link between the spin 1 and spin 2 equations on Schwarzschild.

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Thomas Johnson. 2019-07-22. On the link between the Maxwell and linearised Einstein equations on Schwarzschild. https://doi.org/10.1088/1361-6382%2Fab6caa

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