Equality of ADM mass and generalized Komar energy in asymptotically-flat dynamical spacetimes

2025/09/07 by Wang, Zhi-Wei, Braunstein, Samuel L.
#Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #Instrumentation and Methods for Astrophysics (astro-ph.IM) #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2509.05928

Abstract

We find a relation between the ADM mass and a generalized Komar energy in asymptotically-flat spacetime. We do not need to assume the existence of either a Killing or even asymptotically-Killing vector field. Instead, our generalized Komar energy is constructed from the normal evolution vector (the lapse function times the future-directed unit normal to the spacelike hypersurfaces on which the ADM mass is measured). We find equality between the ADM mass and this generalized Komar energy even for dynamical asymptotically-flat spacetimes provided the 3-dimensional Einstein tensor drops off quickly enough at spatial infinity, in particular, whenever ⁽³⁾G_ij=o(r^-3). No additional assumptions are required for equality. As this generalized energy is fully covariant, it may provide a powerful tool for analyzing energy content in dynamical spacetimes containing compact objects.

Citations

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