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arXiv · 0812.3554

Quasi-Local Energy in Loop Quantum Gravity

Jinsong Yang·Yongge Ma
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Abstract

Although there is no known meaningful notion of the energy density of the gravitational field in general relativity, a few notions of quasi-local energy of gravity associated to extended but finite domains have been proposed. In this paper, the notions of quasi-local energy are studied in the framework of loop quantum gravity, in order to see whether these notions can be carried out at quantum level. Two basic quasi-local geometric quantities are quantized, which lead to well-defined operators in the kinematical Hilbert space of loop quantum gravity. We then use them as basic building blocks to construct different versions of quasi-local energy operators. The operators corresponding to Brown-York energy, Liu-Yau energy, Hawking energy, and Geroch energy are obtained respectively. The virtue of the Geroch energy operator is beneficial for us to derive a rather general entropy-area relation and thus a holographic principle from loop quantum gravity.

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Jinsong Yang, Yongge Ma. 2009-11-01. Quasi-Local Energy in Loop Quantum Gravity. https://doi.org/10.1103/physrevd.80.084027

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