Bulk-Boundary interaction and the second law in Ho\v{r}ava-Lifshitz cosmology

TL;DR

This paper investigates the validity of the second law of thermodynamics in Hořava-Lifshitz cosmology by analyzing energy transfer between bulk and boundary, including phase transitions and thermal equilibrium considerations.

Contribution

It introduces a framework for understanding bulk-boundary energy transfer in HL cosmology and explores the implications for thermodynamic laws and phase transitions.

Findings

Sign changes in energy transfer affect thermodynamic consistency.

Possible phase transitions indicated by heat capacity sign changes.

Thermal equilibrium between bulk and boundary may not be achieved.

Abstract

By defining $Q$ as a function which realizes the energy transference between the bulk and the boundary of spacetime, as we interprete it here in the framework of Ho\v{r}ava-Lifshitz (HL) cosmology, flat case, we discuss the validity of the second law of thermodynamics in the light of the sign changes of $Q$ (changes in the direction of energy transference) and its consequences through the cosmic evolution, in particular, whether the thermal equilibrium between bulk and boundary is reached or not. Additionally, we discuss possible phase transitions experienced by the bulk and the boundary (seen as sign changes in their heat capacities) through the cosmic evolution. The energy density in the bulk is modeled under an holographic perspective. As far as we know, currently there is not observational data on bulk-boundary interaction.