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arXiv · 2006.01734

Schwarzschild-Tangherlini Metric from Scattering Amplitudes

Gustav Uhre Jakobsen
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Abstract

We present a general framework with which the Schwarzschild-Tangherlini metric of a point particle in arbitrary dimensions can be derived from a scattering amplitude to all orders in the gravitational constant, $G_N$, in covariant gauge (i.e. $R_\xi$-gauge) with a generalized de Donder-type gauge function, $G_\sigma$. The metric is independent of the covariant gauge parameter $\xi$ and obeys the classical gauge condition $G_\sigma=0$. We compute the metric with the generalized gauge choice explicitly to second order in $G_N$ where gravitational self-interactions become important and these results verify the general framework to one-loop order. Interestingly, after generalizing to arbitrary dimension, a logarithmic dependence on the radial coordinate appears in space-time dimension $D=5$.

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Gustav Uhre Jakobsen. 2020-06-02. Schwarzschild-Tangherlini Metric from Scattering Amplitudes. https://arxiv.org/abs/2006.01734

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