@phdthesis{discovery10190164,
          school = {UCL (University College London)},
            note = {Copyright {\copyright} The Author 2024.  Original content in this thesis is licensed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0) Licence (https://creativecommons.org/licenses/by-nc/4.0/).  Any third-party copyright material present remains the property of its respective owner(s) and is licensed under its existing terms.  Access may initially be restricted at the author's request.},
            year = {2024},
           title = {Covariant Radiative Transfer in Dynamical Spacetime: a 5 Dimensional Formulation},
           month = {March},
        keywords = {General Relativity, Geometry, Black Hole},
        abstract = {We propose a novel approach for constructing a covariant formulation of radiative transfer in dynamical spacetimes, which overcomes limitations of previous methods when they are applied in the strong-field
regime, by promoting the 3+1 numerical relativity (NR) decomposition via an embedding of a 4 dimensional spacetime into a 5 dimensional non-flat pseudo-Riemannian manifold. This new formulation uses a 4+1
approach: one is able to calculate, in a physically-consistent way, the null geodesics emitted from gravitational wave (GW) sources, e.g., from black hole and neutron star coalescence. Chapters 1-3 introduce the fundamental knowledge for this work and review previous studies of the general relativistic radiative transfer formulation in stationary spacetimes (e.g., Kerr). Chapter 4 introduces the level set method, which is applied to evolving the 4 dimensional spacetime (and null geodesics) in higher dimensional manifolds. Chapter 5 discusses the causal structure of a generic spacetime and studies the embedding of a 4 dimensional spacetime in a 5 dimensional flat and a non-flat manifold. We recover the Lorentz structure by choosing a specific isometric embedding and by defining an appropriately-chosen form of the 5 dimensional metric (e.g., the Schwarzschild and Oppenheimer-Snyder metrics). Chapter 6 discusses
the embedding of the 3+1 numerical representation of the Kerr black hole and a 4 dimensional Brill-Lindquist spacetime. In Chapter 7, we present the proof that the isometric embedding of a 4 dimensional Lorentzian manifold in a 5 dimensional manifold with chosen metric, where the Lorentz structure is enforced, exists and is non-unique. Chapter 8 looks at the construction of a covariant radiative transfer formulation for a binary black hole system. We apply the embedding method for an equal mass non-spinning black hole merger using 3+1 numerical relativity and find the evolution equation of the geometric flow (spacetime
flow). A summary of the work presented in this thesis, together with discussions and additional remarks, is presented in Chapter 9. Finally, directions for future work are presented in Chapter 10.},
             url = {https://discovery.ucl.ac.uk/id/eprint/10190164/},
          author = {Hu, Yichao}
}