Confinement and focusing of geodesics in warped spacetimes

7th International Conference on Gravitation and Cosmology

Kar, S.^1 ; Gupta, A. Das^2 ; Ghosh, S.^3 ; Nandan, H.^4

Department of Physics and Centre for Theoretical Studies, Indian Institute of Technology, Kharagpur 721302, India^1

Department of Mechanical Engineering, Centre for Theoretical Studies, Indian Institute of Technology, Kharagpur 721302, India^2

School of Physics, Indian Institute of Science Education and Research, Thiruvananthapuram 695016, India^3

Department of Physics, Gurukula Kangri Vishwavidyalaya, Haridwar 249404, Uttarakhand, India^4

关键词: Analytical and numerical methods;    Autonomous dynamical systems;    Extra dimensions;    Geodesic equations;    Numerical approaches;    Test particles;    Time dependent;    Time-like geodesics;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/484/1/012019/pdf
DOI  :  10.1088/1742-6596/484/1/012019

来源: IOP

【 摘 要 】

We have explored certain characteristic features of test particle trajectories in five dimensional, warped bulk geometries with a single thick brane. After a brief introduction on such spacetimes, we have first discussed timelike geodesic motion. The geodesic equations, which reduce to a first order autonomous dynamical system, have been solved using analytical and numerical methods. We have demonstrated how a growing (decaying) warp factor leads to oscillatory (runaway) trajectories, suggesting confinement (deconfinement). Further, we have pointed out differences that arise when we have a cosmological brane and/or a time-dependent extra dimension. Next, we have moved on to the kinematics of geodesic congruences. The evolution of the kinematical variables (expansion, rotation and shear) along geodesic flows have been obtained using analytical and numerical approaches, with particular emphasis on the required conditions and occurence of geodesic focusing.