Evolution of interior entropy of a loop quantum-corrected black hole pierced by a cosmic string

The concept of interior entropy of black hole provides a possible way to deal with information problem. We derive evolution relation between interior entropy and Bekenstein-Hawking entropy for a loop quantum-corrected black hole with large mass pierced by an infinitely straight cosmic string during Hawking radiation. We find that the present cosmic string can influence the evolution relation between these two types of entropy under black hole evaporation and the second law of thermodynamics is satisfied for the total variation of these two types of entropy.