Hawking–Page phase transition of four-dimensional de-Sitter spacetime with nonlinear source Yun-Zhi Du, Huai-Fan Li and Li-Chun Zhang Eur. Phys. J. Plus, 137 5 (2022) 574 Published online: 12 May 2022 DOI: 10.1140/epjp/s13360-022-02664-0