We present a D-dimensional Bardeen like Anti-de Sitter (AdS) black hole solution in Einstein-Gauss-Bonnet (EGB) gravity, viz., Bardeen-EGB-AdS black holes. The Bardeen-EGB-AdS black hole has an additional parameter due to charge (e), apart from mass (M ) and Gauss-Bonnet parameter (α). Interestingly, for each value of α, there exist a critical e = e E which corresponds to an extremal regular black hole with degenerate horizons, while for e < e E , it describes non-extremal black hole with two horizons.Despite the complicated solution, the thermodynamical quantities, like temperature (T ), specific heat(C) and entropy (S) associated with the black hole are obtained exactly. It turns out that the heat capacity diverges at critical horizon radius r + = r C , where the temperature attains maximum value and the Hawking-Page transition is achievable. Thus, we have an exact D-dimensional regular black holes, when evaporates lead to a thermodynamical stable remnant. * Electronic address:

We study the nonsingular black hole in Anti de-Sitter background taking the negative cosmological constant as the pressure of the system. We investigate the horizon structure, and find the critical values m0 andk0, such that m > m0 (ork k0), no black hole solution exists. In turn, we calculate the thermodynamical properties and by observing the behaviour of Gibb's free energy and specific heat, we find that this black hole solution exhibits first order (small to large black hole) and second order phase transition. Further, we study the P − V criticality of system and then calculate the critical exponents showing that they are the same as those of the Van der Waals fluid.

No abstract

No abstract

We obtain exact Bardeen black holes to the regularized 4D Einstein–Gauss–Bonnet (EGB) gravity minimally coupled with the nonlinear electrodynamics (NED). In turn, we analyze the horizon structure to determine the effect of GB parameter α on the minimum cutoff values of mass, M0, and magnetic monopole charge, g0, for the existence of a black hole horizon. We obtain an exact expression for thermodynamic quantities, namely, Hawking temperature T+, entropy S+, Helmholtz free energy F+, and specific heat C+ associated with the black hole horizon, and they show significant deviations from the 4D EGB case owing to NED. Interestingly, there exists a critical value of horizon radius, r+c, corresponding to the local maximum of Hawking temperature, at which heat capacity diverges, confirming the second-order phase transition. A discussion on the black holes of alternate regularized 4D EGB gravity belonging to the scalar-tensor theory is appended.