Chaotic Solutions and Black Hole Shadow in $f(R)$ gravity

Andrea Addazi; Salvatore Capozziello; Sergei D. Odintsov

doi:10.1016/j.physletb.2021.136257

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arXiv · 2103.16856

Chaotic Solutions and Black Hole Shadow in $f(R)$ gravity

Andrea Addazi·Salvatore Capozziello·Sergei D. Odintsov

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Abstract

We discuss the emergence of black hole shadow and photon-sphere in the context of $f(R)$ gravity. It is shown that the shadow is exponentially sensitive to linear instabilities of metric coming from some $f(R)$ solutions. Thus, the instabilities of photon circular trajectories, delimiting the black hole photon-sphere, are double exponentialized. Specifically we individuate two Lyapunov exponents, rather than only one, related to two different sources of chaos in geodesic orbits as a sort of butterfly effect. Such a result violates the black hole chaos bound proposed by Maldacena, Shenker and Stanford for General Relativity. We also explore the impact of the black hole metric instabilities in $f(R)$ gravity on the quasi-normal modes. In the framework of Extended Theories of Gravity, our analysis suggests a new paradigm to deal with black hole shadow and gravitational waves observations coming from black hole merging in the ringdown phase.

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Andrea Addazi, Salvatore Capozziello, Sergei D. Odintsov. 2021-03-31. Chaotic Solutions and Black Hole Shadow in $f(R)$ gravity. https://doi.org/10.1016/j.physletb.2021.136257

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