arXiv subjects
Publications and source records attributed to J. Katz.
A relative mechanics with no absolute space is shown to be equivalent to Newtonian mechanics applied in a universe of zero net angular momentum. Closed spaces in General Relativity have no angular momentum and shrivel to one point as the mass-energy contained tends to zero, so obeying Mach's principle on the origin of inertia.
We point out that, contrary to signs of heat capacities, thermodynamic fluctuations are simply and unequivocally related to onset of instabilities that show up near critical points. Fluctuation theory is then applied to \Schw\ \bh s surrounded by radiation. This shows that slowly evolving \bh s along quasi-equilibrium states in cavities greater than $10^6$ Planck length will not evaporate below the critical Hawking limit temperature despite the fact that pure radiation has a much higher entropy. (CQG in press, figure request to okamoto@gprx.miz.nao.ac.jp)
This comment contains a suggestion for a slight modification of Israel's covariant formulation of junction conditions between two spacetimes, placing both sides on equal footing with normals having uniquely defined orientations. The signs of mass energy densities in thin shells at the junction depend not only on the orientations of the normals and it is useful therefore to discuss the sign separately. Calculations gain in clarity by not choosing the orientations in advance. Simple examples illustrate our point and complete previous classifications of spherical thin shells in spherically symmetric spacetimes relevant to cosmology.