Astronomical observations have established that extremely compact, massive objects are common in the universe. It is generally accepted that these objects are, in all likelihood, black holes. As observational technology has improved, it has become possible to test this hypothesis in ever greater detail. In particular, it is or will be possible to measure the properties of orbits deep in the strong field of a black hole candidate (using x-ray timing or future gravitational-wave measurements) and to test whether they have the characteristics of black hole orbits in general relativity. Past work has shown that, in principle, such measurements can be used to map the spacetime of a massive compact object, testing in particular whether the object's multipolar structure satisfies the rather strict constraints imposed by the black hole hypothesis. Performing such a test in practice requires that we be able to compare against objects with the "wrong" multipole structure. In this paper, we present tools for constructing the spacetimes of bumpy black holes: objects that are almost black holes, but that have some multipoles with the wrong value. In this first analysis, we focus on objects with no angular momentum. Generalization to bumpy Kerr black holes should be straightforward, albeit labor intensive. Our construction has two particularly desirable properties. First, the spacetimes which we present are good deep into the strong field of the object -we do not use a "large r" expansion (except to make contact with weak field intuition). Second, our spacetimes reduce to the exact black hole spacetimes of general relativity in a natural way, by dialing the "bumpiness" of the black hole to zero. We propose that bumpy black holes can be used as the foundation for a null experiment: if black hole candidates are indeed the black holes of general relativity, their bumpiness should be zero. By comparing the properties of orbits in a bumpy spacetime with those measured by an astrophysical source, observations should be able to test this hypothesis, stringently testing whether they are in fact the black holes of general relativity.
Social science research demonstrates that people are drawn to others perceived as similar. We extend this finding to political candidates by comparing the relative effects of candidate familiarity as well as partisan, issue, gender, and facial similarity on voters' evaluations of candidates. In Experiment 1, during the week of the 2006 Florida gubernatorial race, a national representative sample of voters viewed images of two unfamiliar candidates (Crist and Davis) morphed with either themselves or other voters. Results demonstrated a strong preference for facially similar candidates, despite no conscious awareness of the similarity manipulation. In Experiment 2, one week before the 2004 presidential election, a national representative sample of voters evaluated familiar candidates (Bush and Kerry). Strong partisans were unmoved by the facial similarity manipulation, but weak partisans and independents preferred the candidate with whom their own face had been morphed over the candidate morphed with another voter. In Experiment 3, we compared the effects of policy similarity and facial similarity using a set of prospective 2008 presidential candidates. Even though the effects of party and policy similarity dominated, facial similarity proved a significant cue for unfamiliar candidates. Thus, the evidence across the three studies suggests that even in high-profile elections, voters prefer candidates high in facial similarity, but most strongly with unfamiliar candidates.
We present a dynamic model of turnout in which voters behavior in one election depends only on whether they voted in the last election and whether their party won. This assumption may be justified by assuming citizens satisfice or by assuming they adjust subjective beliefs about being pivotal in ways that depend on whether they voted and on the outcome of the election. Regardless of the individual-level mechanism, this assumption (prior participation and prior electoral outcome affect current turnout) has empirical support, and we show that it implies turnout dynamics that are in accord with observed dynamics in several countries. Thus, this assumption or something very much like it is a necessary feature of any model of turnout. The ensuing model meets a basic requirement of any turnout model, substantial steady-state turnout, and correctly predicts some counterintuitive dynamical features of aggregate turnout-including declining turnout despite close elections and nonmonotonic changes-following significant political events such as the (re)establishment of democracy or major wars.
We give analytic expressions for the gravitational inner spherical multipole moments, q lm with l ≤ 5, for eleven elementary solid shapes. These moments, in conjunction with their known rotational and translational properties, can be used to calculate precisely the moments of complex objects that may be assembled from the elementary shapes. We also give an analytic expression for the gravitational force between two rectangular solids at arbitrary separations. These expressions are useful for computing the gravitational properties of complex instruments, such as those used in equivalence principle tests, and in the gravitational balancing of drag-free spacecraft.
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