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says "Fortunately, the fact that the heat capacity of the cosmological horizon be positive permits to foresee the evolution of the space in absence of any external source. Taking the correct signs for the temperatures one can notice that, for a given value of M, T+ > T++. Therefore, during their interaction due to its positive heat capacity the cosmological horizon would increase its temperature, and so its radius. Conversely, the black hole horizon would become even hotter because of its negative heat capacity and shrink. In this way, there should be a net flux of energy from the black hole horizon into cosmological horizon. "

where T+, and T++ are the temperature of the black hole and cosmological horizon, respectively.

Why the fact that T+>T++ and C++>0 implies that the cosmological horizon radii increase?, and

Why the fact that T+>T++ and C+<0 implies that the black hole horizon radii shrink?,

I think in a scheme as the figure.