Curvature Invariants for the Alcubierre and Nat\'ario Warp Drives

A process for using curvature invariants is applied to evaluate the metrics for the Alcubierre and the Natario warp drives at a constant velocity.Curvature invariants are independent of coordinate bases, so plotting these invariants will be free of coordinate mapping distortions. As a consequence, they provide a novel perspective into complex spacetimes such as warp drives. Warp drives are the theoretical solutions to Einstein's field equations that allow the possibility for faster-than-light (FTL) travel. While their mathematics is well established, the visualisation of such spacetimes is unexplored. This paper uses the methods of computing and plotting the warp drive curvature invariants to reveal these spacetimes. The warp drive parameters of velocity, skin depth and radius are varied individually and then plotted to see each parameter's unique effect on the surrounding curvature. For each warp drive, this research shows a safe harbor and how the shape function forms the warp bubble. The curvature plots for the constant velocity Natario warp drive do not contain a wake or a constant curvature indicating that these are unique features of the accelerating Natario warp drive.Comment: 41 Pages, 15 figure

IR-improved DGLAP-CS parton shower effects in W + jets at √ s = 7, 8, and 13 TeV.

The invention and development of collider physics in the twentieth century provides us with opportunities to determine which particles exist in nature, their properties, and the ways they interact with each other. The discovery of the Higgs boson, the last undetected particle predicted in the Standard Model (SM) of Particle Physics, brought a lot of excitement to the international physics community. The SM is based on the gauge group SU(3)QCD ×SU(2)weak ×U(1)hypercharge. Through a process called Spontaneous Symmetry Breaking (SSB), it is broken down to SU(3)QCD × U(1)EM at a scale around 247 GeV [1]. Since the SM is a renormalizable theory with 27 parameters, we can test it by performing enough experiments with enough precision. It is possible to improve the infrared aspects of the standard treatment of the DGLAP-CS evolution theory to take into account a large class of higher-order corrections that significantly improve the precision of the theory for any given level of fixed-order calculation of its respective kernels [2]. We use recently introduced MC realizations of IR-improved DGLAP-CS parton showers to study the attendant improvement effects in W + jets at the LHC in the MG5 aMC@NLO framework for exact O(αs) corrections. Implementation of the new IR-improved kernels in the framework of HERWIG6.5 yields the new IR-improved parton shower MC HERWIRI1.031 [3]. Events are showered by HERWIG6.5 and HERWIRI1.031 with PTRMS = 2.2 GeV and PTRMS = 0 GeV, respectively. We compare our results with the available LHC data and discuss the corresponding phenomenological implications. In Chapter Four we have used the latest results provided by CMS and ATLAS for 7 TeV. In Chapter Five we have used the CMS results published in 2017 for 8 TeV