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Spacetime Engineering: Time-Slowing Space-Expanding **Lunchbox**

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Haidar Esseili

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2019

We propose a method of modifying spacetime to control the extent to which proper time and proper distance are contracted or expanded. This is done by solving Einstein’s field equations backwards starting from a metric we create to arrive at a recipe of Stress-Energy-Momentum (SEM) that curves spacetime in accordance with our metric. The metric we propose connects Minkowski flat space metric characterized by diagonal elements [−1 1 1 1] with a scaled version of said metric with diagonal elements [−*a* *b*_{1} *b*_{2} *b*_{3}] using polynomial join function of rank *C*^{2} or higher. This metric partitions spacetime into Minkowski flat spacetime, curved spacetime dictated by the join function, and a scaled version of Minkowski flat spacetime.

We adopt this metric to design the spacetime where proper distance and proper time are contracted or expanded only in the confines of a finite box. Using this formalism, we can vary a and b to, loosely speaking, slow time and expand the interior volume of the box. We call this box the lunchbox, because it can be used to preserve large volumes of food over long periods of time. The spacetime curvature, and corresponding SEM, responsible for contracting or expanding proper distance and time is confined to the thickness in the faces of the lunchbox. We investigate three potential shapes for the **lunchbox**, namely a cuboid, a cylinder, and a sphere. The design of the lunchbox will be difficult to implement practically, but it elucidates the nature of general relativity and Einstein field equations.