https://doi.org/10.1140/epjp/s13360-021-01398-9
Regular Article
Testing the nature of Gauss–Bonnet gravity by four-dimensional rotating black hole shadow
1
Institute of Theoretical Physics & Research Center of Gravitation, Lanzhou University, 730000, Lanzhou, China
2
Key Laboratory of Theoretical Physics of Gansu Province, Lanzhou Center for Theoretical Physics, Lanzhou University, 730000, Lanzhou, China
3
Joint Research Center for Physics, Lanzhou University, 730000, Lanzhou, China
4
Qinghai Normal University, 810000, Xining, China
Received:
27
June
2020
Accepted:
5
April
2021
Published online:
23
April
2021
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 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
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
in (−4.5, 0) is more favored. Since the negative energy appears for negative
, 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.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2021