Aguiar Alves, Níckolas de, and Bruno Arderucio Costa. 2025. “The Measure of a Mass.” Essay written for the Gravity Research Foundation 2025 Awards for Essays on Gravitation. arXiv: 2503.18963 [gr-qc].
Abstract: The concept of mass is central to any theory of gravity. Nevertheless, defining mass in general relativity is a difficult task, and even when it can be accomplished, we still need to investigate whether the typical properties of mass in Newtonian gravity are still true in Einsteinian gravity. In this essay, we discuss "the measure of a mass" in relativity by considering some of the many different definitions (Komar, ADM, and Bondi) and how they are related. Finally, we discuss when and whether the mass is positive, as is usually expected, and which physical properties of matter and gravity can ensure this result.
Tags: General Relativity and Energy Conditions
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