6,146 research outputs found
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 and be respectively the total material energy and the total
material current contained in some ball of radius . Suppose that the
dominant energy condition is satisfied. We show that if 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, .
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.
Necessary Conditions for Apparent Horizons and Singularities in Spherically Symmetric Initial Data
We establish necessary conditions for the appearance of both apparent
horizons and singularities in the initial data of spherically symmetric general
relativity when spacetime is foliated extrinsically. When the dominant energy
condition is satisfied these conditions assume a particularly simple form. Let
be the maximum value of the energy density and the radial
measure of its support. If is bounded from above by some
numerical constant, the initial data cannot possess an apparent horizon. This
constant does not depend sensitively on the gauge. An analogous inequality is
obtained for singularities with some larger constant. The derivation exploits
Poincar\'e type inequalities to bound integrals over certain spatial scalars. A
novel approach to the construction of analogous necessary conditions for
general initial data is suggested.Comment: 15 pages, revtex, to appear in 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.
Reversing the Question: Does Happiness Affect Consumption and Savings Behavior?
I examine the impact of happiness on consumption and savings behavior using data from the DNB Household Survey from the Netherlands and the German Socio-Economic Panel. Instrumenting individual happiness with regional sunshine, the results suggest that happier people save more, spend less, and have a lower marginal propensity to consume. Happier people take more time for making decisions and have more control over expenditures; they expect a longer life and (accordingly) seem more concerned about the future than the present; they also expect less inflation in the future.happiness, savings, consumption, weather
Yang-Mills theory a la string
A surface of codimension higher than one embedded in an ambient space
possesses a connection associated with the rotational freedom of its normal
vector fields. We examine the Yang-Mills functional associated with this
connection. The theory it defines differs from Yang-Mills theory in that it is
a theory of surfaces. We focus, in particular, on the Euler-Lagrange equations
describing this surface, introducing a framework which throws light on their
relationship to the Yang-Mills equations.Comment: 7 page
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