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arXiv · 2602.11900

The total geodesic curvature and the $(2+1)$-dimensional hyperbolic mass

Xiaokai He·Xiaoning Wu·Naqing Xie
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Abstract

In this paper, we derive a novel geometric inequality involving the total geodesic curvature, serving as an analogue of the Brown-York mass in the setting of $(2+1)$-dimensional gravity. The asymptotic behaviour of this newly defined quasi-local mass is examined for large ellipses in the time-symmetric slices of the Ba\~{n}ados-Teitelboim-Zanelli black hole solutions. Moreover, we establish an improved upper bound for the $(2+1)$-dimensional hyperbolic Bartnik mass.

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Xiaokai He, Xiaoning Wu, Naqing Xie. 2026-02-12. The total geodesic curvature and the $(2+1)$-dimensional hyperbolic mass. https://doi.org/10.1007/s00209-026-04131-3

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