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Gravity, Geometry, and the Quantum

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Abstract

There are various indications that finding a quantum theory of gravity is important for a full understanding of fundamental physics. Loop quantum gravity is one possibility for such a quantum theory. In the following, we explain its origin in a gauge theoretic reformulation of gravity, and its status as a quantum theory of geometry. An overview is given over Einstein’s equations in the quantum theory. As an example for an application of loop quantum gravity, the quantum theory of certain black hole horizons is sketched. We close with an outlook on current research and future challenges.

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Abbreviations

ADM:

Arnowitt, Deser, Misner

LQG:

loop quantum gravity

QFT:

quantum field theory

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  1. Department of Physics, Friedrich-Alexander University Erlangen-Nürnberg, Staudtstr. 7, 91058, Erlangen, Germany

    Hanno Sahlmann

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Editors and Affiliations

  1. Department of Physics, Pennsylvania State University, 16802, University Park, PA, USA

    Abhay Ashtekar

  2. Institute for Foundational Studies Hermann Minkowski, Montreal, Quebec, Canada

    Vesselin Petkov

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Sahlmann, H. (2014). Gravity, Geometry, and the Quantum. In: Ashtekar, A., Petkov, V. (eds) Springer Handbook of Spacetime. Springer Handbooks. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-41992-8_37

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