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

TL;DR

This paper explores the shadows of four-dimensional rotating Gauss-Bonnet black holes to test the gravity theory, finding that the metric parameter significantly affects shadow size and distortion, with implications for astronomical observations like M87*.

Contribution

The authors derive a rotating black hole solution in four-dimensional Gauss-Bonnet gravity and analyze its shadow, extending previous static solutions and providing observationally relevant predictions.

Findings

Positive metric parameter shrinks the shadow

Negative metric parameter enlarges the shadow

Negative alpha (-4.5, 0) is favored by M87* observations

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.