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

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 (Glavan et al. in PRL 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.