Sufficient Conditions for Apparent Horizons in Spherically Symmetric Initial Data

We establish sufficient conditions for the appearance of apparent horizons in spherically symmetric initial data when spacetime is foliated extrinsically. Let $M$ and $P$ be respectively the total material energy and the total material current contained in some ball of radius $\ell$. Suppose that the dominant energy condition is satisfied. We show that if $M- P \ge \ell$ then the region must possess a future apparent horizon for some non -trivial closed subset of such gauges. The same inequality holds on a larger subset of gauges but with a larger constant of proportionality which depends weakly on the gauge. This work extends substantially both our joint work on moment of time symmetry initial data as well as the work of Bizon, Malec and \'O Murchadha on a maximal slice.Comment: 16 pages, revtex, to appear in Phys. Rev.

Geometric Bounds in Spherically Symmetric General Relativity

We exploit an arbitrary extrinsic time foliation of spacetime to solve the constraints in spherically symmetric general relativity. Among such foliations there is a one parameter family, linear and homogeneous in the extrinsic curvature, which permit the momentum constraint to be solved exactly. This family includes, as special cases, the extrinsic time gauges that have been exploited in the past. These foliations have the property that the extrinsic curvature is spacelike with respect to the the spherically symmetric superspace metric. What is remarkable is that the linearity can be relaxed at no essential extra cost which permits us to isolate a large non - pathological dense subset of all extrinsic time foliations. We identify properties of solutions which are independent of the particular foliation within this subset. When the geometry is regular, we can place spatially invariant numerical bounds on the values of both the spatial and the temporal gradients of the scalar areal radius, $R$. These bounds are entirely independent of the particular gauge and of the magnitude of the sources. When singularities occur, we demonstrate that the geometry behaves in a universal way in the neighborhood of the singularity.Comment: 16 pages, revtex, submitted to Phys. Rev.

Are Happier People Better Citizens?

This paper presents evidence on causal influence of happiness on social capital and trust using German Socio-Economic Panel. Exploiting the unexplained cross-sectional variation in individual happiness (residuals) in 1984 to eliminate the endogeneity problem, the paper nds that happier people trust others more, and importantly, help create more social capital. Specifically, they have a higher desire to vote, perform more volunteer work, and more frequently participate in public activities. They also have a higher respect for law and order, hold more association memberships, are more attached to their neighborhood, and extend more help to others. Residual happiness appears to be an indicator of optimism, and has an inverse U-shaped relationship with social capital measures. The findings also suggest that the relationship between happiness and social capital strengthened in the world in the last decade.happiness, trust, social capital, optimism.

Concepts, Introspection, and Phenomenal Consciousness: An Information-Theoretical Approach

This essay is a sustained information-theoretic attempt to bring new light on some of the perennial problems in the philosophy of mind surrounding phenomenal consciousness and introspection. Following Dretske (1981), we present and develop an informational psychosemantics as it applies to what we call <em>sensory concepts</em>, concepts that apply, roughly, to so-called secondary qualities of objects. We show that these concepts have a special informational character and semantic structure that closely tie them to the brain states realizing conscious qualitative experiences. We then develop an account of introspection which exploits this special nature of sensory concepts. The result is a new class of concepts, which, following recent terminology, we call <em>phenomenal concepts</em>: these concepts refer to phenomenal experience itself and are the vehicles used in introspection. On our account, the connection between sensory and phenomenal concepts is very tight: it consists in different semantic uses of the same cognitive structures underlying the sensory concepts, like RED. Contrary to widespread opinion, we show that information theory contains all the resources to satisfy internalist intuitions about phenomenal consciousness, while not offending externalist ones. A consequence of this account is that it explains and predicts the so-called conceivability arguments against physicalism on the basis of the special nature of sensory and phenomenal concepts. Thus we not only show why physicalism is not threatened by such arguments, but also demonstrate its strength in virtue of its ability to predict and explain away such arguments in a principled way. However, we take the main contribution of this work to be what it provides in addition to a response to those conceivability arguments, namely, a substantive account of the interface between sensory and conceptual systems and the mechanisms of introspection as based on the special nature of the information flow between them

The Constraints in Spherically Symmetric General Relativity I --- Optical Scalars, Foliations, Bounds on the Configuration Space Variables and the Positivity of the Quasi-Local Mass

We examine the constraints of spherically symmetric general relativity with one asymptotically flat region, exploiting both the traditional metric variables and variables constructed from the optical scalars. With respect to the latter variables, there exist two linear combinations of the Hamiltonian and momentum constraints which are related by time reversal. We introduce a one-parameter family of linear extrinsic time foliations of spacetime. The values of the parameter yielding globally valid gauges correspond to the vanishing of a timelike vector in the superspace of spherically symmetric geometries. We define a quasi-local mass on spheres of fixed proper radius which we prove is positive when the constraints are satisfied. Underpinning the proof are various local bounds on the configuration variables. We prove that a reasonable definition of the gravitational binding energy is always negative. Finally, we provide a tentative characterization of the configuration space of the theory in terms of closed bounded trajectories on the parameter space of the optical scalars.Comment: 45 pages, Plain Tex, 1 figure available from the authors