Stability of asymptotically de Sitter and anti-de Sitter black holes in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e1742" altimg="si2.svg"><mml:mrow><mml:mn>4</mml:mn><mml:mi>D</mml:mi></mml:mrow></mml:math> regularized Einstein–Gauss–Bonnet theory

The regularized four-dimensional Einstein-Gauss-Bonnet model has been recently proposed in [D. Glavan and C. Lin, Phys. Rev. Lett. \textbf{124}, 081301 (2020)] whose formulation is different of the Einstein theory, allowing us to bypass Lovelock theorem. action formulated higher dimensions ($D>4$) by adding Gauss-Bonnet correction conventional Einstein-Hilbert with a cosmological constant. spacetime constructed through dimensional regularization taking limit $D\rightarrow 4$. We find explicitly parametric regions stability black holes for asymptotically flat (anti-)de Sitter spacetimes analyzing time-domain profiles gravitational perturbations both vector scalar channels. In addition known eikonal instability we due positive On contrary, anti-de have no other than one.