text: For the Lane-Emden equation, having a polytropic index take on this value appropriately models a stable, isothermally stratified atmosphere.
full_question: For the Lane-Emden equation, having a polytropic index take on this value appropriately models a stable, isothermally stratified atmosphere. This is the value in time at which the rate of expansion becomes zero if the density equals the critical density. When considering the Schwarzschild solution to the Field Equations, the curvature takes on this value when there is no radius. When calculating the escape velocity, this is the value that the distance takes on at the (*) final time. The luminosity of any point in a steady-state universe takes on this value according to the scenario analyzed in Olber's Paradox. As one approaches a singularity, this is the amount of force needed to maintain a particle in place. For 10 points, name this value at which things become immeasurably big.
first_sentence: For the Lane-Emden equation, having a polytropic index take on this value appropriately models a stable, isothermally stratified atmosphere.
raw_answer: infinite [or infinity]