End of the World Perspective to BCFT

In this work, we study the end-of-the-world (EOW) branes anchored to the boundaries of BCFT${}_2$ dual to the BTZ black hole. First, we explore the thermodynamics of the boundary system consisting of the conformal boundary and two EOW branes. This thermodynamics is extended by the tension appearing as the effective cosmological constant of JT black holes on the EOW branes. The tension contribution is identified with the shadow entropy equivalent to the boundary entropy of the BCFT${}_2$. The thermodynamics of the JT black holes and the bulk of BCFT${}_2$ can be combined into a novel grafted thermodynamics based on the first law. Second, we focus on the observer's view of the EOW branes by lowering the temperature. We show that the EOW branes generate a scale called ``reefs" inside the horizon. This scale also appears in the grafted thermodynamics. At high temperatures, observers on the EOW branes see their respective event horizons. The reef starts to grow relatively to the horizon size at the temperature, $T_{grow}$. As the temperature cools down the reef area fills the entire interior of the JT black holes at the temperature $T_{out}$. Then, the observers recognize their horizons disappear and see the large density of the energy flux. At this temperature, the two JT regions become causally connected. This connected spacetime has two asymptotic $AdS_2$ boundaries with a conformal matter. Also, we comment on the grafted thermodynamics to higher dimensions in Appendix B.