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arXiv · 2406.08452

Einstein gravity from the Einstein action: Counterterms and covariance

Martin Krššák
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Abstract

The field equations of general relativity can be derived from the Einstein action, which is quadratic in connection coefficients, rather than the standard action involving the Gibbons-Hawking-York term and counterterm. We show that it is possible to construct a new counterterm directly for the Einstein action, which removes divergences and naturally introduces a flat reference spacetime. The total action is then covariant under simultaneous transformation of both the spacetime and reference tetrads, and argue that this is analogous to the Gibbons-Hawking action. We then explore different perspectives arising naturally from different uses of the reference tetrad, and explore implications of viewing gravity as fundamentally described in terms of non-covariant connection coefficients.

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Martin Krššák. 2024-06-12. Einstein gravity from the Einstein action: Counterterms and covariance. https://doi.org/10.1103/physrevd.110.104061

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