This paper by Sidney Coleman and Frank De Luccia explores the effects of gravitation on the decay of false vacua in classical field theories. The authors extend the semi-classical theory of false vacuum decay to include gravitational effects, which are often overlooked but can be significant, especially in the late stages of decay. They demonstrate that gravitation can stabilize the false vacuum, preventing its decay, and can also affect the growth of the bubble formed during decay. The paper discusses two special cases: decay from a space with a positive cosmological constant into a space with zero or negative cosmological constant, and decay into a space with zero cosmological constant. In the first case, gravitation stabilizes the false vacuum, while in the second, it makes decay more likely. The authors also analyze the geometry of the bubble interior, showing that it can lead to gravitational collapse. The paper concludes by discussing the implications of these findings for the cosmological constant problem and the possibility of spontaneous symmetry breakdown.This paper by Sidney Coleman and Frank De Luccia explores the effects of gravitation on the decay of false vacua in classical field theories. The authors extend the semi-classical theory of false vacuum decay to include gravitational effects, which are often overlooked but can be significant, especially in the late stages of decay. They demonstrate that gravitation can stabilize the false vacuum, preventing its decay, and can also affect the growth of the bubble formed during decay. The paper discusses two special cases: decay from a space with a positive cosmological constant into a space with zero or negative cosmological constant, and decay into a space with zero cosmological constant. In the first case, gravitation stabilizes the false vacuum, while in the second, it makes decay more likely. The authors also analyze the geometry of the bubble interior, showing that it can lead to gravitational collapse. The paper concludes by discussing the implications of these findings for the cosmological constant problem and the possibility of spontaneous symmetry breakdown.