The first law of thermodynamics is derived for bounded, static, spherically symmetric spacetimes which include a matter distribution and either a black-hole or cosmological horizon. Heat capacities associated with horizon/matter systems are calculated. It is found that if the surface area of the boundary is held fixed, the heat capacity of a system including a black hole can always be made positive by including a matter distribution of sufficient density. The heat capacity associated with a system including a cosmological horizon and a matter distribution may be positive or negative depending on the matter configuration, but must always be negative in the limit that the boundary approaches the horizon. A discussion is given of the case in which the cosmological constant is allowed to vary. It is found that the Hawking-Coleman mechanisms for explaining the low value of the cosmological constant are not well defined.

• Received 24 July 1990

DOI:https://doi.org/10.1103/PhysRevD.43.3861