Phys. Rev. D, 103, 084043 (2021)

Black hole scalarization in Gauss-Bonnet extended Starobinsky gravity

Hai-Shan Liu¹, Hong Lü¹, Zi-Yu Tang² and Bin Wang^3,2

1 Center for Joint Quantum Studies and Department of Physics, School of Science, Tianjin University, 135 Yaguan Road, Tianjin 300350, China.

2 School of Aeronautics and Astronautics, Shanghai Jiao Tong University, Shanghai 200240, China.

3 Center for Gravitation and Cosmology, Yangzhou University, Yangzhou 225009, China.

* hsliu.zju@gmail.com, mrhonglu@gmail.com, tangziyu@sjtu.edu.cn, wang_b@sjtu.edu.cn

Abstract

We propose a class of higher-derivative gravities that can be viewed as the Gauss-Bonnet extension of the Starobinsky model. The theory admits the Minkowski spacetime vacuum whose linear spectrum consists of the graviton and a massive scalar mode. In addition to the usual Schwarzschild black hole, we use numerical analysis to establish that in some suitable mass range, new black holes carrying the massive scalar hair can emerge. The new black hole serves as a “wall” separating the naked spacetime singularity and wormholes in the parameter space of the scalar hair. Our numerical results also indicate that although the new hairy black hole and the Schwarzschild black hole have different spacetime geometry, their entropy and temperature are the same for the same mass.