In this work, a new class of black hole solutions in dilaton gravity has been obtained where the dilaton field is coupled with nonlinear Maxwell invariant as a source. The background space–time in this works is considered as the [Formula: see text]-dimensional toroidal metric. In the presence of the dilaton field (for some unique values of [Formula: see text][Formula: see text] a ), the electric field increases as we got farther away from the origin. In the absence of the dilaton field [Formula: see text], the electric field always decreases as one goes farther away from the origin. In the thermodynamical analysis, we obtain the Smarr formula for our solution. We find that the presence of the dilaton field makes the solutions to be locally stable near the origin. Also, this field vanishes the global stability near the origin compared to the no dilaton field case [Formula: see text]. We can say that the dilaton field has a crucial impact on the thermodynamical stability and it is a key factor in stability analysis. We study the quasinormal modes (QNMs) of black hole solutions in dilaton gravity. For this purpose, we use the WKB approximation method upto first order corrections. We have shown the perturbations decay in corresponding diagrams when the dilaton parameter [Formula: see text] and coupling constant [Formula: see text] change. Motivated by the thermodynamical analogy of black holes and Van der Waals liquid/gas systems, in this work, we investigate PV criticality of the obtained solution. We extend the phase space by considering the cosmological constant as thermodynamic pressure. We obtain the equation of state (EOS) and plot the relevant PV [Formula: see text] diagrams. We also present a class of interior solutions corresponding to the exterior solution in dilaton gravity. The solution which is obtained for a linear equation of state is regular and well-behaved at the stellar interior. a Dilaton field representation.
QUANTUM DILATON GRAVITY IN THE LIGHT-CONE GAUGE
