Testing the nature of Gauss-Bonnet gravity by four-dimensional rotating black hole shadow

Abstract: The recent discovery of the novel four-dimensional static and spherically symmetric Gauss-Bonnet black hole provides a promising bed to test Gauss-Bonnet gravity by using astronomical observations [Phys. Rev. Lett. 124, 081301 (2020)]. In this paper, we first obtain the rotating Gauss-Bonnet black hole solution by using the Newman-Janis algorithm, and then study the shadow cast by the nonrotating and rotating candidate Gauss-Bonnet black holes. The result indicates that positive metric parameter $\alpha$ shrinks the shadow, while negative one enlarges it. Meanwhile, both the distortion and ratio of two diameters of the shadow are found to increase with the metric parameter for certain spin. Comparing with the Kerr black hole, the shadow gets more distorted for $\alpha$, and less distorted for negative one. Furthermore, we calculate the angular diameter of the shadow by making use of the observation of M87*. The result indicates that negative metric parameter $\alpha$ in (-4.5, 0) is more favored. Since the negative energy appears for negative $\alpha$, our results extends the study of Gauss-Bonnet gravity. We believe further study on the four-dimensional rotating black hole may shed new light on Gauss-Bonnet gravity.

Analysis of Shadows Cast by Rotating Gauss-Bonnet Black Holes in Four-Dimensional Spacetime

This study presents a detailed examination of Gauss-Bonnet gravity's implications in four-dimensional spacetime, specifically focusing on the solution for rotating black holes and the resulting observational phenomena, notably the black hole shadow. The significance of this research lies in its endeavor to test and extend Gauss-Bonnet gravity through astronomical observations, contributing to the understanding of modified gravity theories.

The authors begin by deriving the rotating Gauss-Bonnet black hole metric using the Newman-Janis algorithm, from a newly discovered four-dimensional static and spherically symmetric Gauss-Bonnet black hole solution. This extension to rotating black holes is significant as most astrophysical black holes are expected to possess spin. The study reveals that the additional metric parameter, (\alpha), influences the shadow's size and shape: a positive (\alpha) reduces the shadow size compared to the Kerr black hole, while a negative (\alpha) enlarges it. This outcome implies that the Gauss-Bonnet coupling does have a non-negligible effect even in a four-dimensional setting, where traditionally it had been considered trivial.

Alongside numerical simulations of black hole shadows, the authors utilize the recent observational data of M87* from the Event Horizon Telescope (EHT) to constrain the Gauss-Bonnet coupling constant (\alpha). The study finds that (\alpha) within the range ((-4.5, 0)) is more compatible with the observed angular diameter of M87*, thereby favoring a negative (\alpha). This conclusion is intriguing as it suggests the potential for negative-energy properties within certain configurations of Gauss-Bonnet gravity, extending previous understandings of the theory.

The analysis has practical observational implications; distinguishing between various modified gravity theories will increasingly depend on the precise measurement of black hole shadows. This research advocates for the utility of high-resolution astronomical observations to not only test, but potentially confirm or refute, modified theories of gravity such as Gauss-Bonnet gravity. Furthermore, the conclusions drawn about the shadow and constraints on (\alpha) highlight the role of black hole observations in parameterizing deviations from general relativity.

Theoretically, this research opens discussions on the limitations and viability of certain extensions to Einstein’s theory, particularly in low-dimensional regimes where conventional Gauss-Bonnet terms traditionally offer no dynamic contribution. This lines up with recent efforts to regularize the theory in four dimensions to allow for meaningful contributions from higher-dimensional terms.

Future research could focus on refining these models with up-and-coming observational platforms promising higher accuracy. Moreover, expanding this framework to include other modified gravity models will provide a more comprehensive phase space for understanding strong gravitational regimes. This paper's findings underscore the critical interplay between theoretical physics and observational astrophysics, paving the way for novel tests of gravity with real-world data.