Entanglement Entropy and Quantum Energy Conditions in Dilaton Black Holes with Geometric Deformation

We investigate the entanglement entropy and quantum energy conditions in a four-dimensional dilaton black hole with a deformed angular geometry [Formula: see text], where [Formula: see text]. Using the replica method and holographic techniques, we compute the entanglement entropy for a boundary region and show that it depends explicitly on the geometric parameter [Formula: see text] and the dilaton coupling [Formula: see text]. The deformation modifies the scaling of entanglement with radius and influences the structure of quantum correlations in the boundary theory. We further analyze the Quantum Null Energy Condition (QNEC) and the Quantum Focussing Conjecture (QFC), demonstrating that they are satisfied for [Formula: see text] but may be violated for negative [Formula: see text], indicating enhanced quantum fluctuations and potential instability in the semiclassical regime. Crucially, we verify that in the limit [Formula: see text], [Formula: see text], the solution reduces exactly to the Reissner–Nordström–AdS black hole, with all quantum information measures recovering their standard forms. This confirms the model as a consistent generalization of classical black holes, where the geometric deformation and dilaton field act as physical parameters that smoothly modify the spacetime structure and its quantum properties.