General Solutions of Einstein Gravity at $D\to 2$

Abstract

Einstein gravity at $D\to 2$ limit can be obtained from the Kaluza-Klein procedure by taking the dimensions of the internal space to zero while keeping only the breathing mode. The resulting scalar-tensor theory can be further reduced to JT gravity or the Liouville CFT at the large central charge limit, bridging the two important 2d models. We study the general solutions of the theory, including black holes and wormholes for both positive and negative cosmological constants. We obtain the on-shell action of the nearly AdS${}_2$ and show that for suitable boundary slices, the Schwarzian action governs the leading-order dynamics at the finite boundary cutoff in later time. For positive cosmological constant, we find that the scalar is well defined on the 2-sphere.

Latex, 23 pages

References in corpus (3)

• Holography of Gravitational Action Functionals
• Novel cosmological and black hole solutions in Einstein and higher-derivative gravity in two dimensions
• On the Lagrangian Holographic Relation at $D\to 2$ and $4$ Limits of Gravity

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