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We show that the spherically symmetric { black hole (BH)} solution of acharged (linear case) field equation of Rastall gravitational theory is notaffected by the Rastall parameter and this is consistent with the resultspresented in the literature. However, when we apply the field equation ofRastall's theory to a special form of nonlinear electrodynamics (NED) source,we derive a novel spherically symmetric BH solution that involves the Rastallparameter. The main source of the appearance of this parameter is the tracepart of the NED source, which has a non-vanishing value, unlike the linearcharged field equation. We show that the new BH solution is just Anti-de-SitterReissner-Nordstr\"om spacetime in which the Rastall parameter is absorbed intothe cosmological constant. This solution coincides with Reissner-Nordstr\"omsolution in the GR limit, i.e. when Rastall's parameter vanishing. To gain moreinsight into this BH, we study the stability using the deviation of geodesicequations to derive the stability condition. Moreover, we explain thethermodynamical properties of this BH and show that it is stable, unlike thelinear charged case that has a second-order phase transition. Finally, we provethe validity of the first law of thermodynamics.

Nonlinear charged black hole solution in Rastall gravity