Generalized Jackiw-Teitelboim gravity in presence of Block brane-like models*DB and RM would like to thank CNPq (Brazil), grants No. 303469/2019-6 (DB) and No. 310994/2021-7 (RM). They also thank Paraiba State Research Foundation, FAPESQ-PB, grants No. 0003/2019 (RM) and No. 0015/2019 (DB), for partial financial support. (1st December 2022)