https://doi.org/10.1140/epjc/s10052-025-13809-7
Regular Article - Theoretical Physics
Phase structure and optical properties of the de Sitter Spacetime with KR field based on the Lyapunov exponent
1
Department of Physics, Shanxi Datong University, 037009, Datong, China
2
Institute of Theoretical Physics, Shanxi Datong University, 037009, Datong, China
3
College of General Education, Shanxi college of technology, 036000, Shuozhou, China
Received:
15
April
2024
Accepted:
13
January
2025
Published online:
25
January
2025
Since the spontaneously broken of the Lorentz symmetry in the gravity theory with the non-minimally coupling between the Kalb–Ramond (KR) field (that acquires a nonzero vacuum expectation value) and the Einstein gravity, there exists the exactly static and spherically symmetric black holes solutions related with the Lorentz violating parameter. Based on this, we consider the corresponding black hole solution in the de-Sitter (dS) spacetime with the KR field and investigate the thermodynamic properties in the expanded phase space through introducing the interplay entropy between the black hole and cosmological horizons. Especially we analyze the effect of the Lorentz-violating parameter on the thermodynamic properties. Furthermore, the Lyapunov exponent and the shadow of these static and spherically symmetric black holes in this Lorentz-violating gravity theory are also investigated. These study will open a new perspective to probe the thermodynamics of black holes.
© The Author(s) 2025
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