摘要: We present an analytic, perturbative solution to the Einstein equations with a scalar field that describes dynamical black holes in slow-roll inflationary cosmology. show metric evolves quasi-statically through sequence of Schwarzschild–de Sitter like metrics time dependent cosmological constant and mass parameters, such is instantaneously equal value potential. The areas hole horizons each increase as effective decreases, fractional area proportional change constant, times geometrical factor. For ranging size from much smaller than comparable horizon, pre-factor varies very small order one. 'mass first law' 'Schwarzchild–de patch thermodynamics are satisfied throughout evolution.