https://doi.org/10.1140/epjc/s10052-023-11372-7
Regular Article - Theoretical Physics
General solutions of Einstein gravity at 
Center for Joint Quantum Studies and Department of Physics, School of Science, Tianjin University, 300350, Tianjin, China
Received:
21
November
2022
Accepted:
28
February
2023
Published online:
13
March
2023
Einstein gravity at 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 construct 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
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.
© The Author(s) 2023
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