Abstract Observable signatures of black hole thermodynamics remain far from fully explored. Previous works have suggested that thermodynamic phase transitions of black holes could leave imprints on their images. In this work, we demonstrate that richer black hole thermodynamic information can also leave imprints on the resulting images. Using the charged anti-de Sitter black hole as an example, we study the evolution of its images (shadow and accretion-disk images) along isobaric and isothermal processes. We find that the image size evolves monotonically along isobars but becomes nonmonotonic along isotherms. After further considering phase transitions, the image size exhibits a sudden increase in both thermodynamic processes. More importantly, in the isothermal process, the phase transition further results in the emergence of a critical reduced temperature that separates two qualitatively distinct image evolutions. These results show that black hole images can probe not only phase transitions, but also thermodynamic process and temperature.
You et al. (Tue,) studied this question.