Matched Asymptotic Expansions

Holmes, Mark H.

doi:10.1007/978-1-4614-5477-9_2

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Justine Tarrant1

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2023

2024

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Cited by 2 publications

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“…The sub-divided regions are described by the best suited approximate solution to the linearised Einstein equation in that region. To find the single, global metric we desire, a mathematical technique called matched asymptotic expansions [10] is used. In matching, one attempts to join two metrics along a boundary between them.…”

Section: Justine Tarrantmentioning

confidence: 99%

Geodesics on approximately analytic spacetimes

Tarrant,

Beck

2023

Proceedings of High Energy Astrophysics in Southern Africa 2022 — PoS(HEASA2022)

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In order to derive models that realistically describe the dynamics of photons around black holes, the use of a geodesic integrator is required. Using such an integrator, we may track null geodesics in curved spacetimes surrounding black holes. Since the binary black hole solution to the Einstein equations is not analytic, one requires the use of computationally intensive 3 + 1 numerical relativity. Instead, we consider a different route, by defining a novel metric created from analytic space-like hyper-surfaces. With this in hand, applying a ray-tracing algorithm requires minimal computational resources. Critically, we present a preliminary step to finding black hole shadows for general binaries.

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Section: Justine Tarrantmentioning

confidence: 99%