Selected Honorable Mention EssayNo Access

Covariance group for null geodesic expansion calculations, and its application to the apparent horizon

Institute for Advanced Study, 1 Einstein Drive, Princeton, NJ 08540, USA

https://doi.org/10.1142/S0218271821420232Cited by:5 (Source: Crossref)

This article is part of the issue:

SPECIAL ISSUE: Selected Essays from the Annual Essay Competition of the Gravity Research Foundation 2021
Editor: D. V. Ahluwalia

Abstract

We show that the recipe for computing the expansions $𝜃_{ℓ}$ and $𝜃_{n}$ of outgoing and ingoing null geodesics normal to a surface admits a covariance group with nonconstant scalar $κ (x)$ , corresponding to the mapping $𝜃_{ℓ} \to κ 𝜃_{ℓ}$ , $𝜃_{n} \to κ^{- 1} 𝜃_{n}$ . Under this mapping, the product $𝜃_{ℓ} 𝜃_{n}$ is invariant, and thus the marginal surface computed from the vanishing of $𝜃_{ℓ}$ , 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.

This essay received an Honorable Mention in the 2021 Essay Competition of the Gravity Research Foundation.

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