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AdS₃ Action in the Dreibein Formalism

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  • Kazuyasu Shigemoto

Abstract

We examine how to rewrite the (2 + 1)-dimensional AdS3 action with gravitational field into action with dreibein. We obtained the non-trivial Einstein equation with dreibein. While Brown-Henneaux rewrite the AdS3 action by using i) torsionless condition, ii) Einstein equation with dreibein. But we cannot use torsionless condition because the torsionless condition is automatically satisfied by imposing the dreibein hypothesis. Furthermore, we cannot use the Einstein equation with the dreibein to rewrite the AdS3 action. If the AdS3 action becomes in the Chern-Simons form, the equation of motion becomes trivial and there is no equation of motion, which contradicts with the non-trivial Einstein equation with dreibein. Therefore, the Brown-Henneaux’s procedure is not allowed, and we cannot obtain the Chern-Simons type action.

Suggested Citation

  • Kazuyasu Shigemoto, 2024. "AdS₃ Action in the Dreibein Formalism," European Journal of Applied Physics, European Open Science, vol. 6(3), pages 14-18, May.
    • Handle: RePEc:epw:physic:v:6:y:2024:i:3:id:11316
    DOI: 10.24018/ejphysics.2024.6.3.316
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    References listed on IDEAS

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    1. Kazuyasu Shigemoto, 2024. "Back Reaction of the Electromagnetic Radiation and the Local Inertial Frame," European Journal of Applied Physics, European Open Science, vol. 6(3), pages 1-6, May.
    2. Kazuyasu Shigemoto, 2024. "Comments on the Black Hole War," European Journal of Applied Physics, European Open Science, vol. 6(2), pages 10-18, March.
    3. Kazuyasu Shigemoto, 2024. "The Ergo Region of the Kerr Black Hole in the Isotropic Coordinate," European Journal of Applied Physics, European Open Science, vol. 6(2), pages 26-30, March.
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