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arXiv 2103.14725gr-qc
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虫洞和弯曲时空的曲率不变量

Curvature Invariants for Wormholes and Warped Spacetimes

Brandon Mattingly

摘要:

Carminati和McLenaghan(CM)曲率不变量是探测时空的有力工具。Henry等人制定了一种绘制CM曲率不变量的方法来研究黑洞。CM曲率不变量是底层时空的标量函数。因此,它们独立于所选择的坐标,并表征时空。对于B1类时空,有四个独立的CM曲率不变量:R、r1、r2和w2。洛伦兹可穿越虫洞和曲速驱动器是爱因斯坦场方程的两种理论解,它们允许超光速(FTL)传输。CM曲率不变量的绘制和分析这些特定的FTL时空:(i)薄壳平面虫洞,(ii)莫里斯-索恩虫洞,(iii)薄壳史瓦西虫洞,(iv)指数度规,(v)Alcubierre度规在恒定速度,(vi)Natário度规在恒定速度,和(vii)Natário度规在加速。虫洞CM不变量的图证实了它们的可穿越性,并显示了如何区分虫洞。翘曲驱动CM不变量揭示了一些关键特征,例如每个翘曲气泡中心的平坦港口,每个翘曲气泡的动态尾流,以及每个翘曲气泡丰富的内部结构。

英文摘要:

The Carminati and McLenaghan (CM) curvature invariants are powerful tools for probing spacetimes. Henry et al. formulated a method of plotting the CM curvature invariants to study black holes. The CM curvature invariants are scalar functions of the underlying spacetime. Consequently, they are independent of the chosen coordinates and characterize the spacetime. For Class B1 spacetimes, there are four independent CM curvature invariants: R, r1, r2, and w2. Lorentzian traversable wormholes and warp drives are two theoretical solutions to Einstein's field equations, which allow faster-than-light (FTL) transport. The CM curvature invariants are plotted and analyzed for these specific FTL spacetimes: (i) the Thin-Shell Flat-Face wormhole, (ii) the Morris-Thorne wormhole, (iii) the Thin-Shell Schwarzschild wormhole, (iv) the exponential metric, (v) the Alcubierre metric at constant velocity, (vi) the Natário metric at constant velocity, and (vii) the Natário metric at an accelerating velocity. Plots of the wormhole CM invariants confirm their traversability and show how to distinguish the wormholes. The warp drive CM invariants reveal key features such as a flat harbor in the center of each warp bubble, a dynamic wake for each warp bubble, and rich internal structure(s) of each warp bubble.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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