Nonsingular black hole in two-dimensional asymptotically flat spacetime

We study a special two-dimensional dilaton gravity with Lagrangian $\mathcal{L}=\frac{1}{2}\sqrt{\ensuremath{-}g}(\ensuremath{\phi}R+{\ensuremath{\lambda}}^{2}{\mathrm{sech}}^{2}\ensuremath{\phi})$ where $\ensuremath{\lambda}$ is parameter of dimension mass. This theory describes spacetimes that are asymptotically flat. Very interestingly, it has an exact solution for the metric, $\mathrm{d}{s}^{2}=\ensuremath{-}(c+\mathrm{tanh}\ensuremath{\lambda}x)\mathrm{d}{t}^{2}+\phantom{\rule{0ex}{0ex}}\mathrm{d}{x}^{2}/(c+\mathrm{tanh}\ensuremath{\lambda}x)$, parametrized by $c$. For $c\ensuremath{\in}(\ensuremath{-}1,1)$, presents event horizon but no singularity. Because kink profile metric components appearing in solution, we refer to spacetime described as gravitational domain wall simply being and separating two Minkowskian spacetimes. The global causal structure such object studied via coordinate extension thermodynamical quantities computed. Only when $c\ensuremath{\in}(\ensuremath{-}1,0]$ entropy energy non-negative.