Extended-phase-space thermodynamics of κ-deformed black strings

Investigate phase transitions, criticality, and the systematic derivation of the first law of thermodynamics in the extended phase space of κ-deformed black holes and black strings.

Background

The paper motivates κ-deformed spacetime as a noncommutative framework for incorporating quantum-gravitational corrections into black-hole physics. Although previous studies examined quantities such as corrected entropy and Hawking radiation, the introduction states that a comprehensive thermodynamic treatment of κ-deformed objects is lacking.

The explicitly identified unresolved agenda concerns detailed analyses of phase transitions and critical behavior, together with a systematic derivation of the thermodynamic first law when the cosmological constant is treated as a pressure in an extended phase space. These issues are presented as open problems for future study in the paper's discussion of the existing literature.