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arXiv · 2407.17528

Interacting Null Sources in Different Geometries

Chia-Li Hsieh
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Abstract

We introduce basic mathematical techniques, followed by an exploration of three distinct topics: the Callan-Giddings-Harvey-Strominger (CGHS) model in 1+1-dimensional spacetime, the formation of astrophysical jets in Schwarzschild-like black holes, and collisions and confinement phenomena in the third-order Lovelock gravity. In the CGHS model, we investigate the collision of ghost fields within the dilaton background geometry, observing the formation and dissolution of wormholes by inserting and removing the ghost fields, respectively. This process mimics a cosmological-scale analogue of Feynman diagrams. Next, we study the non-zero expectation values of bumblebee fields due to Lorentz symmetry breaking. This alteration in the energy-momentum tensor necessitates the inclusion of a potential vacuum, resulting in a shift of the vacuum solution towards Schwarzchild-like black holes with a scaling factor $l$. This scaling factor facilitates discussions on the collision of null sources, leading to the formation of impulsive null shells and satisfying the type-D condition. When $l$ approaches zero, jet-like formations vanish, transforming the problem into one involving colliding gravitational waves, which is isometric to the Schwarzschild geometry. Moreover, our method can be applied to any resembling Schwarzschild-like metrics. We aim to enhance our model by incorporating additional physical factors such as extra polarizations or EM fields. Finally, our examination extends to the 4-dimensional third-order Lovelock gravity, observing that particles possess finite energy and be confined within the metric time interval extending from - to + infinity. Moreover, this finding does not admit flat rotation curves. Additionally, when collisions occur within the background of this metric, intriguingly, we observe impulsive Weyl curvatures along the null boundaries subsequent to the collision.

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Chia-Li Hsieh. 2024-07-23. Interacting Null Sources in Different Geometries. https://arxiv.org/abs/2407.17528

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