标题： 曲速引擎：广义相对论内的超光速旅行 显示英文标题

标题： The Warp Drive: Superluminal Travel within General Relativity

摘要： 1994年，Miguel Alcubierre提出，当在特定的广义相对论框架内整体考虑这样的旅程时，可以绕过众所周知的特殊相对论限制，即粒子不能以超过光速的速度旅行，方法是使用一个形状像气泡的时空扭曲区域，该区域通过时空传输具有质量的粒子以超光速运动。 尽管最初的结果表明这种情景是非物理的，因为它似乎需要负质量-能量密度，但最近的理论分析表明，这种非物理的情况可能并不总是成立。 本论文提出了爱因斯坦场方程的新解，考虑了Alcubierre曲速驱动时空度规。 核心前提是研究流体物质作为引力源，而不是更常见的真空或负能源，以探索通过时空中扭曲区域产生超光速速度，或\textit{曲速速度}的可能性。 这些解有各种物质-能量来源：尘埃粒子、理想流体、具有各向异性压力的准理想流体、带电尘埃，以及在宇宙常数时空中的理想流体。 还展示了某些涉及由Burgers型方程描述的冲击波的解之间的联系，该方程右边的项仅依赖于时间。 这可能意味着曲速驱动与真空能量密切相关，并可能具有拓扑效应，如冲击波。 显示英文摘要

摘要： In 1994, Miguel Alcubierre proposed that the well-known special relativistic limitation that particles cannot travel with velocities higher than light speed can be bypassed when such trips are considered globally within specific general relativistic frameworks, using a warped region of spacetime in the shape of a bubble that transports particles with mass traveling through spacetime with superluminal speed. Although initial results indicated this scenario as nonphysical, since it would seem to require negative mass-energy density, recent theoretical analyses suggest that such a nonphysical situation may not always be true. This thesis presents newfound solutions for the Einstein field equations, considering the Alcubierre warp drive spacetime metrics. The central premise is to study the fluid matter as the gravity source, rather than the more common vacuum or negative energy sources, to explore the potential for generating superluminal velocities, or \textit{warp speeds}, through a warped region in the spacetime. Such solutions have various matter-energy sources: dust particles, perfect fluid, quasi-perfect fluid with anisotropic pressures, charged dust, and a perfect fluid within a cosmological constant spacetime. A connection between some of these solutions featuring shock waves described by a Burgers-type equation with a term on the right-hand side of the equation purely dependent on time is also shown. This could mean warp drives are closely related to vacuum energy and possibly have topological effects such as shock waves.