Nonlinearly charged black holes surrounded by cloud of strings and quintessence in Einstein-Massive gravity

In this work, a new model of double-Logarithmic electrodynamics has been minimally coupled to Einstein-massive gravity and the nonlinearly charged black holes in the presence of quintessential cosmic dark energy and string cloud background are investigated. In this set up, new magnetically charged black hole solution has been derived. Thermodynamics of these black holes are also analyzed and different thermodynamic quantities are computed. Basic thermodynamic quantities such as heat capacity and Hawking temperature have been plotted and the regions corresponding to thermodynamic stability and instability are pointed out. The generalized first law of thermodynamics and the associated Smarr's relation have also been written down in this context of massive gravity and matter sources. At last, the nonlinearly electrically charged black holes are also briefly studied.