Sigma Club Seminar by Shelly Yiran Shi (University of California)

Title: Why Not a Gravitational Perpetual Motion Machine?

Abstract: This paper examines longstanding concerns about gravitational energy and asks what it takes to rule out perpetual motion machines in General Relativity (GR). The answer is subtle. GR resists familiar assumptions behind conservation: there is no gravitational insulator, and defining an isolated system typically relies on asymptotic flatness. While the covariant conservation of stress–energy always holds, it offers little dynamical insight. Generic spacetimes lack Killing vectors, and stress–energy pseudotensors are non-tensorial and non-unique. To clarify these difficulties, I distinguish energy conservation (a closed-system notion) from energy balance (an open-system relation). I then argue that gravitational-energy eliminativism associated with Hoefer (2000) and Duerr (2019, 2021) faces a pressure often missed: if energy balance is abandoned altogether, one loses any upper bound on extractable work in gravitational-wave processes, leaving room—in principle—for gravitational perpetual motion machines. Drawing on the asymptotic balance between ADM energy, Bondi energy, and radiative energy (Ashtekar and Magnon-Ashtekar 1979), I propose an account of energy balance as a constraint on maximal extractable work, compatible with gravitational-energy skepticism.

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