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Black Holes in Asymptotically Safe Gravity

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Handbook of Quantum Gravity

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Abstract

In this chapter, we review the state-of-the-art of black holes in asymptotically safe gravity. After a brief recap of the asymptotic safety program, we shall summarize derivations and features of the main asymptotic safety-inspired models that have been constructed in the past by the so-called renormalization group improvement. Specifically, we will discuss static configurations, both in spherically and axially symmetric settings, the role played by the cosmological constant, and the impact of the collapse dynamics in determining black hole configurations realized in nature. In particular, we will review how quantum gravity could modify the Buchdahl limit and the corresponding conditions to form ultra-compact objects and Planckian black holes. We will then proceed by describing the most recent developments, particularly those aiming at making model building in asymptotic safety more rigorous and free from ambiguities. These include self-consistent and coordinate-independent versions of the renormalization group improvement and next steps to fill the gap between model building and renormalization group computations in asymptotic safety. Finally, we will focus on a selection of results that have been obtained from first-principle calculations or arguments, within and beyond asymptotic safety. Concretely, we will review the state-of-the-art in determining black hole entropy in asymptotic safety from a microstate counting and progress in deriving the quantum-corrected Newtonian potential. We will discuss how in quantum gravity theories linked to a gravitational path integral singularity resolution could be achieved by a dynamical suppression of singular configurations and how this is related to the form of the bare action. Finally, we will show that – independent of the specific ultraviolet completion of gravity – asymptotic modifications to Schwarzschild black holes are strongly constrained by the principle of least action at large-distance scales.

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Notes

  1. 1.

    FRG computations are typically performed in Euclidean. First steps toward Lorentzian calculations have been taken in [15,16,17,18,19,20,21,22,23,24], while Lorentzian computations based on the spectral FRG have been developed and applied in [25,26,27].

  2. 2.

    The value originally used in [49] was \(g_{\ast }^{-1}\xi ^{2}={118}/{(15\pi )}\) and was based on the corrections to the Newtonian potential computed in [60].

  3. 3.

    Such an identification is however a stretch, as we will discuss in section “Toward a Dressed Newtonian Potential Within Asymptotic Safety”.

  4. 4.

    In a unimodular approach to quantum gravity, the cosmological constant emerges as an integration constant instead of a coupling, and thus it does not reintroduce the Schwarzschild singularity [77].

  5. 5.

    The dent introduced in [91,92,93,94,95] and the one discussed in [85, 89, 90] are however structurally different, since in the case of [85, 89, 90] the scale identification introduces an angular dependence in all metric components that breaks a mathematical property known as “circularity.” The non-circularity yields a dent whose boundary has a concave piece, as opposed to the one in [91,92,93,94,95] which is fully convex.

  6. 6.

    It is worth mentioning that the one-loop results in [61] have not been reproduced yet via full-fledged FRG computations. See however [150] for first steps in this direction.

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Acknowledgements

The author thanks J. Borissova, A. Held, and B. Knorr for comments on various sections of the book chapter, A. Held for many fruitful discussions on the derivations in [135], and B. Knorr for providing the numerical data of [34] to generate the plots in Fig. 13. A.P. acknowledges support by Perimeter Institute for Theoretical Physics. Research at Perimeter Institute is supported in part by the Government of Canada through the Department of Innovation, Science and Economic Development and by the Province of Ontario through the Ministry of Colleges and Universities. A.P. also acknowledges Nordita for support within the “Nordita Distinguished Visitors” program and for hospitality during the last stages of development of this work. Nordita is supported in part by NordForsk.

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  1. Perimeter Institute for Theoretical Physics, Waterloo, ON, Canada

    Alessia Platania

  2. Nordita, KTH Royal Institute of Technology and Stockholm University, Stockholm, Sweden

    Alessia Platania

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  1. Department of Physics, Fudan University, Shanghai, China

    Cosimo Bambi

  2. Department of Physics, Southern University of Science and Techn, Shenzhen, China

    Leonardo Modesto

  3. Departamento de Física, Universidade Federal de Juiz de Fora, Juiz de Fora, Minas Gerais, Brazil

    Ilya Shapiro

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  1. SISSA, Trieste, Italy

    Roberto Percacci

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Platania, A. (2023). Black Holes in Asymptotically Safe Gravity. In: Bambi, C., Modesto, L., Shapiro, I. (eds) Handbook of Quantum Gravity. Springer, Singapore. https://doi.org/10.1007/978-981-19-3079-9_24-1

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