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Curvature Invariants and Black Hole Horizons

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Abstract

Black hole horizons are teleological in nature, that is, for locating them in a given spacetime it is necessary to know the entire evolution of the universe. Thus, it has been argued that black hole horizons cannot be observed by any astrophysical measurement. Furthermore, this nonlocal feature of the horizon seems to contradict the very basic foundation of general relativity, which is a local field theory. In this report, we will review two recently formulated local methods for detecting the black hole horizon based on the scalar polynomial curvature invariants and the Cartan curvature invariants, respectively. Then, we will enlighten both the conceptual and computational improvements with respect to the standard techniques which have been adopted so far for tackling this task. Finally, we will discuss the most relevant applications of our methods in numerical relativity both for gravitational-waves simulations in astrophysics, and in the study of the quark-gluon plasma in light of the AdS/CFT correspondence.

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ACKNOWLEDGMENTS

The author thanks the organizers of the fourth (virtual) Zel’dovich conference.

Funding

D.G. acknowledges support from China Postdoctoral Science Foundation (grant no. 2019M661944), and from the 2020 Galaxies travel award (Galaxies is an open access journal by MDPI).

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Authors and Affiliations

  1. School of Science, Jiangsu University of Science and Technology, 212003, Zhenjiang, China

    D. Gregoris

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  1. D. Gregoris
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Correspondence to D. Gregoris.

Additional information

Paper presented at the Fourth Zeldovich meeting, an international conference in honor of Ya.B. Zeldovich held in Minsk, Belarus, on September 7–11, 2020. Published by the recommendation of the special editors: S.Ya. Kilin, R. Ruffini, and G.V. Vereshchagin.

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Gregoris, D. Curvature Invariants and Black Hole Horizons. Astron. Rep. 65, 947–951 (2021). https://doi.org/10.1134/S1063772921100127

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