Horizon divergences of fields and strings in black hole backgrounds

General arguments based on curved space-time thermodynamics show that any extensive quantity, such as the free energy or the entropy of thermal matter, always has a divergent boundary contribution in the presence of event horizons, and this boundary term comes with the Hawking-Bekenstein form. Although the coefficients depend on the particular geometry we show that intensive quantities, such as the free energy density, are universal in the vicinity of the horizon. From the point of view of the matter degrees of freedom this divergence is of infrared type rather than ultraviolet, and we use this remark to speculate about the fate of these pathologies in string theory. Finally, we interpret them as instabilities of the canonical ensemble with respect to gravitational collapse via the Jeans mechanism.