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arXiv · 2506.15904

The Komar charge in presence of the Holst term and the gravitational Witten effect

José Luis V. Cerdeira·Tomás Ortín
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Abstract

In the first-order formalism, the Einstein--Hilbert action can be modified by the addition of a Holst term multiplied by the Barbero parameter $\alpha$. This modification breaks parity although it does not affect the equations of motion. We show that the standard Komar charge is also modified by the addition of a topological term multiplied by the Barbero parameter $\alpha$. For the Killing vector that generates time translations, the value of the Komar integral at infinity is modified by the addition of a term proportional to the NUT charge $N$ and the parity-breaking Barbero parameter. Thus, as in the standard Witten effect, a non-vanishing NUT charge $N$ induces a non-vanishing mass $\alpha N$.

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José Luis V. Cerdeira, Tomás Ortín. 2025-06-18. The Komar charge in presence of the Holst term and the gravitational Witten effect. https://arxiv.org/abs/2506.15904

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