Radiation from a D-dimensional collision of shock waves: two-dimensional reduction and Carter–Penrose diagram
| Autor: | Flávio S. Coelho, Marco O. P. Sampaio |
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| Jazyk: | angličtina |
| Rok vydání: | 2016 |
| Předmět: |
High Energy Physics - Theory
Physics 010308 nuclear & particles physics Gravitational wave FOS: Physical sciences Astronomy and Astrophysics Conformal map Penrose diagram General Relativity and Quantum Cosmology (gr-qc) 01 natural sciences General Relativity and Quantum Cosmology Singularity High Energy Physics - Theory (hep-th) Space and Planetary Science Dimensional reduction Light cone 0103 physical sciences Large extra dimensions Gravitational singularity Gravitational radiation D'Alembert operator 010306 general physics Trans-Planckian collisions Mathematical Physics Mathematical physics |
| Zdroj: | Repositório Científico de Acesso Aberto de Portugal Repositório Científico de Acesso Aberto de Portugal (RCAAP) instacron:RCAAP |
| Popis: | We analyse the causal structure of the two dimensional (2D) reduced background used in the perturbative treatment of a head-on collision of two $D$-dimensional Aichelburg-Sexl gravitational shock waves. After defining all causal boundaries, namely the future light-cone of the collision and the past light-cone of a future observer, we obtain characteristic coordinates using two independent methods. The first is a geometrical construction of the null rays which define the various light cones, using a parametric representation. The second is a transformation of the 2D reduced wave operator for the problem into a hyperbolic form. The characteristic coordinates are then compactified allowing us to represent all causal light rays in a conformal Carter-Penrose diagram. Our construction holds to all orders in perturbation theory. In particular, we can easily identify the singularities of the source functions and of the Green's functions appearing in the perturbative expansion, at each order, which is crucial for a successful numerical evaluation of any higher order corrections using this method. Comment: 20 pages, 3 figures. To appear in a Special Issue of the IJMPD on Selected Papers of the III Amazonian Symposium on Physics (Eds. C. Herdeiro, E. Berti, V. Cardoso, L. C. Crispino, L. Gualtieri and U. Sperhake) |
| Databáze: | OpenAIRE |
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