https://doi.org/10.1140/epjc/s10052-025-14303-w
Regular Article - Theoretical Physics
Black holes and thermogeometric optimization
1
Department of Theoretical Physics, Sofia University, 5 J. Bourchier Blvd., 1164, Sofia, Bulgaria
2
The Bogoliubov Laboratory of Theoretical Physics, JINR, 141980, Dubna, Moscow region, Russia
3
Institute for Theoretical Physics, Vienna University of Technology, Wiedner Hauptstr. 8-10, 1040, Vienna, Austria
Received:
22
January
2025
Accepted:
12
May
2025
Published online:
28
May
2025
We suggest a finite-time geometric optimization framework to analyze thermal fluctuations and optimal processes in black holes. Our approach implement geodesics in thermodynamic space to define optimal pathways between equilibrium and non-equilibrium states. Since thermodynamic metrics need not be positive-definite, the method ensures a positive thermodynamic length by incorporating simple scale factor into the metric. We show that the thermodynamic length and the scale factor are sensitive to phase transitions in entropy representation, addressing a key gap in Hessian thermodynamic geometry. Additionally, we link the scale factor to the sign of thermodynamic curvature, connecting it to the information geometry governing optimal processes. Our results indicate that optimal fluctuations can drive the evaporation of Schwarzschild and Kerr black holes, which may significantly differ from Hawking radiation. We also explore optimal accretion-driven processes supported by an external inflow of energy.
© The Author(s) 2025
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