Is nonrelativistic gravity possible?

We study nonrelativistic gravity using the Hamiltonian formalism. For the dynamics of general relativity (relativistic gravity) the formalism is well known and called the Arnowitt-Deser-Misner (ADM) formalism. We show that if the lapse function is constrained correctly, then nonrelativistic gravity is described by a consistent Hamiltonian system. Surprisingly, nonrelativistic gravity can have solutions identical to relativistic gravity ones. In particular, (anti-)de Sitter black holes of Einstein gravity and IR limit of Horava gravity are locally identical.Comment: 4 pages, v2, typos corrected, published in Physical Review

Topics in the Dynamics or General Relativity

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The initial value problem and the dynamical formulation of general relativity

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The Einstein Equations of Evolution - A Geometric Approach

In this paper the exterior Einstein equations are explored from a differential geometric point of view. Using methods of global analysis and infinite-dimensional geometry, we answer sharply the question: "In what sense are the Einstein equations, written as equations of evolution, a Lagrangian dynamical system?" By using our global methods, several aspects of the lapse function and shift vector field are clarified. The geometrical significance of the shift becomes apparent when the Einstein evolution equations are written using Lie derivatives. The evolution equations are then interpreted as evolution equations as seen by an observer in space coordinates. Using the notion of body-space transitions, we then find the relationship between solutions with different shifts by finding the flow of a time-dependent vector field. The use of body and space coordinates is shown to be somewhat analogous to the use of such coordinates in Euler's equations for a rigid body and the use of Eulerian and Lagrangian coordinates in hydrodynamics. We also explore the geometry of the lapse function, and show how one can pass from one lapse function to another by integrating ordinary differential equations. This involves integrating what we call the "intrinsic shift vector field." The essence of our method is to extend the usual configuration space [fraktur M]=Riem(M) of Riemannian metrics to [script T]×[script D]×[fraktur M], where [script T]=C[infinity](M,R) is the group of relativistic time translations and [script D]=Diff(M) is the group of spatial coordinate transformations of M. The lapse and shift then enter the dynamical picture naturally as the velocities canonically conjugate to the configuration fields (xit,etat)[is-an-element-of][script T]×[script D]. On this extended configuration space, a degenerate Lagrangian system is constructed which allows precisely for the arbitrary specification of the lapse and shift functions. We reinterpret a metric given by DeWitt for [fraktur M] as a degenerate metric on [script D]×[fraktur M]. On [script D]×[fraktur M], however, the metric is quadratic in the velocity variables. The groups [script T] and [script D] also serve as symmetry groups for our dynamical system. We establish that the associated conserved quantities are just the usual "constraint equations." A precise theorem is given for a remark of Misner that in an empty space-time we must have [script H]=0. We study the relationship between the evolution equations for the time-dependent metric gt and the Ricci flat condition of the reconstructed Lorentz metric gL. Finally, we make some remarks about a possible "superphase space" for general relativity and how our treatment on [script T]×[script D]×[fraktur M] is related to ordinary superspace and superphase space

Don’t Demean “Invasives”: Conservation and Wrongful Species Discrimination

It is common for conservationists to refer to non-native species that have undesirable impacts on humans as “invasive”. We argue that the classification of any species as “invasive” constitutes wrongful discrimination. Moreover, we argue that its being wrong to categorize a species as invasive is perfectly compatible with it being morally permissible to kill animals—assuming that conservationists “kill equally”. It simply is not compatible with the double standard that conservationists tend to employ in their decisions about who lives and who dies

Symmetry breaking in general relativity

Bifurcation theory is used to analyze the space of solutions of Einstein's equations near a spacetime with symmetries. The methods developed here allow one to describe precisely how the symmetry is broken as one branches from a highly symmetric spacetime to nearby spacetimes with fewer symmetries, and finally to a generic solution with no symmetries. This phenomenon of symmetry breaking is associated with the fact that near symmetric solutions the space of solutions of Einstein's equations does not form a smooth manifold but rather has a conical structure. The geometric picture associated with this conical structure enables one to understand the breaking of symmetries. Although the results are described for pure gravity, they may be extended to classes of fields coupled to gravity, such as gauge theories. Since most of the known solutions of Einstein's equations have Killing symmetries, the study of how these symmetries are broken by small perturbations takes on considerable theoretical significance

Summertime ozone at Mount Washington: Meteorological controls at the highest peak in the northeast

This study examined the synoptic and regional-scale meteorological controls on summertime O3 at Mount Washington, the highest peak (1910 m) in the northeastern United States. Analysis of air mass transport to Mount Washington was conducted for the summers of 1998–2003 using backward trajectories. Distinct patterns in air mass history were revealed using this approach that helped explain extreme variations in O3 mixing ratios. Most enhanced (≥90th percentile) and depleted (≤10th percentile) O3 events were short-lived and spread out over the summer months. Enhanced O3 events at Mount Washington were generally associated with westerly transport, while depleted events corresponded to northwesterly transport. Periods of O3 greater than 80 ppbv during nighttime periods coincided with westerly (71%) and southwesterly (29%) transport. Periods of elevated O3 commonly occurred during regional warm sector flow or on the western edge of a surface anticyclone. Our analysis also identified a stratospheric contribution to a small percentage (∼5%) of extreme O3 events at the site, but more evidence is required to establish the significance of the contribution to background O3levels in this region

A Lattice Gauge Model of Singular Marsden-Weinstein Reduction. Part I. Kinematics

The simplest nontrivial toy model of a classical SU(3) lattice gauge theory is studied in the Hamiltonian approach. By means of singular symplectic reduction, the reduced phase space is constructed. Two equivalent descriptions of this space in terms of a symplectic covering as well as in terms of invariants are derived.Comment: 27 pages, 6 figure