The thermodynamic stability and phase structureof the Einstein-Euler-Heisenberg-AdS black holes

Abstract In both canonical ensemble and grand canonical ensemble, the
thermodynamic stability and phase structure of
Einstein-Euler-Heisenberg-AdS black hole are studied. We derive
the Hawking temperature, Helmholtz free energy, Gibbs potential,
entropy and heat capacity of the black holes. We compute the
minimum temperature to find that the phase transition may happen
at the lowest point. The entropy-temperature diagram consists of
two parts. The upper part belonging to the large black holes under
the influence from the electromagnetic self-interactions keeps the
positive heat capacity, leading the huge compact objects to
survive. The lower curves corresponding to the small ones show
that the heat capacity of the tiny black holes is negative, which
means that the nonlinear-effect-corrected smaller sources will
evaporate. The further discussions show that the nonlinear effect
modifies the thermodynamic quantities, but the corrections limited
by the nonlinear factor $\mu$ with allowed values can not change
the properties and the phase structure fundamentally and
thoroughly. We argue that the influence from self-interaction can
not make the Einstein-Euler-Heisenberg-AdS black holes to split
under the second law of thermodynamics.