Disturbing the Black Hole

I describe some examples in support of the conjecture that the horizon area of a near equilibrium black hole is an adiabatic invariant. These include a Schwarzschild black hole perturbed by quasistatic scalar fields (which may be minimally or nonminimally coupled to curvature), a Kerr black under the influence of scalar radiation at the superradiance treshold, and a Reissner--Nordstr\"om black hole absorbing a charge marginally. These clarify somewhat the conditions under which the conjecture would be true. The desired ``adiabatic theorem'' provides an important motivation for a scheme for black hole quantization.Comment: 15 pages, LaTeX with crckapb style, to appear in ``The Black Hole Trail'', eds. B. Bhawal and B. Iyer (Kluwer, Dordrecht 1998

Optimizing entropy bounds for macroscopic systems

The universal bound on specific entropy was originally inferred from black hole thermodynamics. We here show from classical thermodynamics alone that for a system at fixed volume or fixed pressure, the ratio of entropy to nonrelativistic energy has a unique maximum $(S/E)_\mathrm{max}$. A simple argument from quantum dynamics allows one to set a model--independent upper bound on $(S/E)_\mathrm{max}$ which is usually much tighter than the universal bound. We illustrate with two examples.Comment: 13 pages, 2 figures, LaTe

The Debt Limit and the Constitution: How the Fourteenth Amendment Forbids Fiscal Obstructionism

The statutory debt limit restricts the funds that can be borrowed to meet the government\u27s financial obligations. On the other hand, the Fourteenth Amendment\u27s Public Debt Clause mandates that all the government\u27s financial obligations be met. This Note argues that the Public Debt Clause is violated when government actions create substantial doubt about the validity of the public debt, a standard that encompasses government actions that fall short of defaulting on or directly repudiating the public debt. The Note proposes a test to determine when substantial doubt is created. This substantial doubt test analyzes the political and economic environment at the time of the government\u27s actions and the subjective apprehension exhibited by debt holders. Applying this test, this Note concludes that Congress\u27s actions during the 1995–96 and 2011 debt-limit debates violated the Public Debt Clause, though Congress\u27s conduct during the debate over the debt limit in 2002 did not. And under a departmentalist understanding of executive power, a conclusion of this nature would be the basis for the president to ignore the debt limit when congressional actions create unconstitutional doubt about the validity of the public debt