And. what is the relation between the metabolic efficiency and slavery...

The painful truth is that slavery, in terms of biological efficiency of energy resources, made perfect sense*.

It's the simple reason it appeared in every single civilization across the globe. Until we started using fossil fuels…:)

*As the authors of In the Servitude of Power: Energy and Civilization Through the Ages, Jean-Claude Débeir, Jean-Paul Deléage and Daniel Hémery have pointed out:

“Nevertheless, and this is a very important point, the efficiency of the human-machine [20%] is the highest of the animal kingdom. That of the horse, for example, which had a major role in past energy systems, scarcely rises above ten per cent and that of the ox is still lower. From the standpoint of energy, the use of draught animals is, therefore, a luxury. It will now be understood why, for centuries, the human converter was the most desirable. In historical circumstances where exosomatic organs are underdeveloped, slavery is a more rational energy system."