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arXiv · 2105.07521

Covariance Group for Null Geodesic Expansion Calculations, and its Application to the Apparent Horizon

Stephen L. Adler
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Abstract

We show that the recipe for computing the expansions $\theta_\ell$ and $\theta_n$ of outgoing and ingoing null geodesics normal to a surface admits a covariance group with nonconstant scalar $\kappa(x)$, corresponding to the mapping $\theta_\ell \to \kappa \theta_\ell$, $\theta_n \to \kappa^{-1} \theta_n$. Under this mapping, the product $\theta_\ell \theta_n$ is invariant, and thus the marginal surface computed from the vanishing of $\theta_\ell$, which is used to define the apparent horizon, is invariant. This covariance group naturally appears in comparing the expansions computed with different choices of coordinate system.

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Stephen L. Adler. 2021-05-16. Covariance Group for Null Geodesic Expansion Calculations, and its Application to the Apparent Horizon. https://doi.org/10.1142/s0218271821420232

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