Exact solutions of (deformed) Jackiw–Teitelboim gravity

It is well known that Jackiw-Teitelboim (JT) gravity posses the simplest theory on 2-dimensional gravity. The model has been fruitfully studied in recent years. In present work, we investigate exact solutions for both JT and deformed recently proposed literature. We revisit Euclidean using all non-zero components of dilatonic equations motion proper integral transformation over time coordinate. More precisely, study hyperbolic coverage, cusp geometry another compact sector AdS$_2$ spacetime manifold.