Palatini's cousin: A New Variational Principle

A variational principle is suggested within Riemannnian geometry, in which an auxiliary metric and the Levi Civita connection are varied independently. The auxiliary metric plays the role of a Lagrange multiplier and introduces non-minimal coupling of matter to the curvature scalar. The field equations are 2nd order PDEs and easier to handle than those following from the so-called Palatini method. Moreover, in contrast to the latter method. no gradients of the matter variables appear. In cosmological modeling, the physics resulting from the new variational principle will differ from the modeling using the Palatini method.Comment: 12 page

Mission Accomplished: A Reply to Reuveny and Keshk

Reuveny and Keshk (“Reconsidering trade and conflict simultaneity: The risk of emphasizing technique over substance,” this issue, 2013) argue that the econometric techniques used by Goenner (Conflict Management and Peace Science 28(5): 459–477, 2011) to test and control for endogeneity when estimating the relationship between trade and conflict lack substance. Both sets of authors propose the use of instrumental variable methods, which are known by econometricians to be the natural remedy for estimation with potentially endogenous regressors. Where Goenner (2011) and Reuveny and Keshk (2013) agree is that theory should guide variable selection and the model’s specification. Yet they differ in that, while econometric tests cannot replace theory, one should not trust the appropriateness of the model’s specification based on theory alone – one should also verify. Otherwise, as Goenner (2011) notes, attempts to control for endogeneity may fail

Economic War and Democratic Peace

Research has shown that democracies rarely, if ever, engage each other in war and are less likely to have militarized disputes than when interacting with authoritarian regimes. Economic sanctions are an alternative to militarized conflict viewed by the masses as more acceptable. The conflict-inhibiting effects of democratic norms and institutions are thus weakened with respect to the use of sanctions. This paper examines whether a country\u27s decision to initiate sanctions is influenced by its regime type as well as that of the potential target. The results for the period 1950 to 1990 indicate that the more democratic a country is, the more likely it is to initiate sanctions. Democracies, however, are less likely to target other democratic regimes relative to nondemocratic regimes. With respect to sanctions use, pairs of democracies are not peaceful

Simultaneity between Trade and Conflict: Endogenous Instruments of Mass Destruction

The classical liberal belief is trade, which economically benefits countries, creates ties binding the interests of countries and reduces conflict. While the vast majority of the empirical literature supports this view, recent research questions these findings by also considering the reciprocal relationship between trade and conflict. If conflict also influences trade, then trade is an endogenous right hand side regressor and previous estimates which ignore this are inconsistent. This article determines when one uses appropriate instruments for the endogenous regressors that trade reduces conflict and conflict reduces trade. Failure to use such instruments results in inconsistent estimates and can lead to the spurious conclusion that trade increases conflict. The lesson is the use of inappropriate instruments can be worse than not using them at all

The tetralogy of Birkhoff theorems

We classify the existent Birkhoff-type theorems into four classes: First, in field theory, the theorem states the absence of helicity 0- and spin 0-parts of the gravitational field. Second, in relativistic astrophysics, it is the statement that the gravitational far-field of a spherically symmetric star carries, apart from its mass, no information about the star; therefore, a radially oscillating star has a static gravitational far-field. Third, in mathematical physics, Birkhoff's theorem reads: up to singular exceptions of measure zero, the spherically symmetric solutions of Einstein's vacuum field equation with Lambda = 0 can be expressed by the Schwarzschild metric; for Lambda unequal 0, it is the Schwarzschild-de Sitter metric instead. Fourth, in differential geometry, any statement of the type: every member of a family of pseudo-Riemannian space-times has more isometries than expected from the original metric ansatz, carries the name Birkhoff-type theorem. Within the fourth of these classes we present some new results with further values of dimension and signature of the related spaces; including them are some counterexamples: families of space-times where no Birkhoff-type theorem is valid. These counterexamples further confirm the conjecture, that the Birkhoff-type theorems have their origin in the property, that the two eigenvalues of the Ricci tensor of two-dimensional pseudo-Riemannian spaces always coincide, a property not having an analogy in higher dimensions. Hence, Birkhoff-type theorems exist only for those physical situations which are reducible to two dimensions.Comment: 26 pages, updated references, minor text changes, accepted by Gen. Relat. Gra