Black Hole Thermodynamics with Dynamical Lambda
  We study evolution and thermodynamics of a slow-roll transition between early
and late time de Sitter phases, both in the homogeneous case and in the
presence of a black hole, in a scalar field model with a generic potential
having both a maximum and a positive minimum. Asymptotically future de Sitter
spacetimes are characterized by ADM charges known as cosmological tensions. We
show that the late time de Sitter phase has finite cosmological tension when
the scalar field oscillation around its minimum is underdamped, while the
cosmological tension in the overdamped case diverges. We compute the variation
in the cosmological and black hole horizon areas between the early and late
time phases, finding that the fractional change in horizon area is proportional
to the corresponding fractional change in the effective cosmological constant.
We show that the extended first law of thermodynamics, including variation in
the effective cosmological constant, is satisfied between the initial and final
states, and discuss the dynamical evolution of the black hole temperature.
