STEGR with Information Geometry
DOI:
https://doi.org/10.51094/jxiv.5821キーワード:
（一般相対論に等価な）対称遠隔平行重力理論、 情報幾何学、 ゲージ重力理論、 シュトゥックルベルグ場、 Jackiw--Teitelboim重力、 Banados--Teitelboim--Zanneliブラックホール解抄録
We develop an information-geometric formulation of Symmetric Teleparallel Equivalent to General Relativity (STEGR). STEGR describes gravity in terms of the non-metricity of spacetime and is physically equivalent to General Relativity (GR). Information geometry represents a family of probability distributions as a differentiable manifold whose geometry is likewise characterized by non-metricity. Reformulating STEGR within information geometry, we provide a framework that endows gravity with a probabilistic interpretation while maintaining a direct correspondence with GR. We first introduce three formulations of STEGR---internal STEGR, Coincident GR, and St\"{u}ckelberg STEGR---based on the internal-space formulation, each characterized by a different realization of non-metricity. We show that these theories are related through appropriate gauge fixing. We then review $\alpha$-geometry and focus on the case $\alpha=1$, corresponding to information geometry in the so-called $\theta$-coordinate system. Within this framework, we construct the symmetric teleparallel connection in a manner compatible with the dual structure of information geometry and show that the coincident gauge emerges naturally.Using the resulting dual connection, we show that St\"{u}ckelberg STEGR provides a self-dual formulation of Coincident GR. Finally, we derive the field equations of the self-dual theory and show that the theory admits Jackiw--Teitelboim gravity and the Ba\~{n}ados--Teitelboim--Zanelli black hole as exact solutions.
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