STEGR with Information Geometry

Tomonari, Kyosuke

doi:10.51094/jxiv.5821

##article.authors##

Tomonari, Kyosuke Central China Normal University (main) / University of Tokyo (Visiter)

DOI:

https://doi.org/10.51094/jxiv.5821

キーワード:

Symmetric Teleparallel Equivalent to General Relativity、 Information Geometry、 Gauge Theories of Gravity、 St\、 Jackiw--Teitelboim gravity、 Ba\~{n}ados--Teitelboim--Zanelli black hole solution

抄録

We establish Symmetric Teleparallel Equivalent to General Relativity (STEGR) in the framework of information geometry. 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 differential manifold whose geometry is likewise characterized by non-metricity. Reformulating STEGR based on information geometry, we provide a theory of gravity in which gravity acquires a stochastic interpretation while remaining equivalent to GR. First of all, we introduce three formulations of STEGR---internal STEGR, Coincident GR , and St\"{u}ckelberg STEGR---based on the internal-space formulation, each theory 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 with so-called $\theta$-coordinate system.
Within this framework, we construct the symmetric teleparallel connection in an information-geometrically dual manner and show that the coincident gauge emerges in this construction. Using the resulting dual connection, we formulate the corresponding STEGR theories and show that St\"{u}ckelberg STEGR provides a unified self-dual formulation of internal STEGR and Coincident GR. Finally, we derive the field equation of the self-dual theory and show that Jackiw--Teitelboim gravity and Ba\~{n}ados--Teitelboim--Zanelli black hole solutions are compatible with our theory as exact solutions.

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