Uniqueness and Non-uniqueness in the Einstein Constraints

The conformal thin sandwich (CTS) equations are a set of four of the Einstein equations, which generalize the Laplace-Poisson equation of Newton's theory. We examine numerically solutions of the CTS equations describing perturbed Minkowski space, and find only one solution. However, we find {\em two} distinct solutions, one even containing a black hole, when the lapse is determined by a fifth elliptic equation through specification of the mean curvature. While the relationship of the two systems and their solutions is a fundamental property of general relativity, this fairly simple example of an elliptic system with non-unique solutions is also of broader interest.Comment: 4 pages, 4 figures; abstract and introduction rewritte

Local and global properties of conformally flat initial data for black hole collisions

We study physical properties of conformal initial value data for single and binary black hole configurations obtained using conformal-imaging and conformal-puncture methods. We investigate how the total mass M_tot of a dataset with two black holes depends on the configuration of linear or angular momentum and separation of the holes. The asymptotic behavior of M_tot with increasing separation allows us to make conclusions about an unphysical ``junk'' gravitation field introduced in the solutions by the conformal approaches. We also calculate the spatial distribution of scalar invariants of the Riemann tensor which determine the gravitational tidal forces. For single black hole configurations, these are compared to known analytical solutions. Spatial distribution of the invariants allows us to make certain conclusions about the local distribution of the additional field in the numerical datasets

Detecting cold gas at intermediate redshifts: GMRT survey using Mg II systems

Intervening HI 21-cm absorption systems at z > 1.0 are very rare and only 4 confirmed detections have been reported in the literature. Despite their scarcity, they provide interesting and unique insights into the physical conditions in the interstellar medium of high-z galaxies. Moreover, they can provide independent constraints on the variation of fundamental constants. We report 3 new detections based on our ongoing Giant Metrewave Radio Telescope (GMRT) survey for 21-cm absorbers at 1.10< z_abs< 1.45 from candidate damped Lyman_alpha systems. The 21-cm lines are narrow for the z_abs = 1.3710 system towards SDSS J0108-0037 and z_abs = 1.1726 system toward SDSS J2358-1020. Based on line full-width at half maximum, the kinetic temperatures are <= 5200 K and <=800 K, respectively. The 21-cm absorption profile of the third system, z_abs =1.1908 system towards SDSS J0804+3012, is shallow, broad and complex, extending up to 100 km/s. The centroids of the 21-cm lines are found to be shifted with respect to the corresponding centroids of the metal lines derived from SDSS spectra. This may mean that the 21-cm absorption is not associated with the strongest metal line component.Comment: 13 pages with 5 figures. Accepted for publication in ApJ

Scale-invariant gravity: Spacetime recovered

The configuration space of general relativity is superspace - the space of all Riemannian 3-metrics modulo diffeomorphisms. However, it has been argued that the configuration space for gravity should be conformal superspace - the space of all Riemannian 3-metrics modulo diffeomorphisms and conformal transformations. Recently a manifestly 3-dimensional theory was constructed with conformal superspace as the configuration space. Here a fully 4-dimensional action is constructed so as to be invariant under conformal transformations of the 4-metric using general relativity as a guide. This action is then decomposed to a (3+1)-dimensional form and from this to its Jacobi form. The surprising thing is that the new theory turns out to be precisely the original 3-dimensional theory. The physical data is identified and used to find the physical representation of the theory. In this representation the theory is extremely similar to general relativity. The clarity of the 4-dimensional picture should prove very useful for comparing the theory with those aspects of general relativity which are usually treated in the 4-dimensional framework.Comment: Replaced with final version: minor changes to tex

The Measure of Cosmological Parameters

New, large, ground and space telescopes are contributing to an exciting and rapid period of growth in observational cosmology. The subject is now far from its earlier days of being data-starved and unconstrained, and new data are fueling a healthy interplay between observations and experiment and theory. I briefly review here the status of measurements of a number of quantities of interest in cosmology: the Hubble constant, the total mass-energy density, the matter density, the cosmological constant or dark energy component, and the total optical background light.Comment: 12 pages, 4 figures, to be published in "2001: A Spacetime Odyssey: Proceedings of the Inaugural Conference of the Michigan Center for Theoretical Physics", Michael J. Duff & James T. Liu, eds., (World Scientific, Singapore), in pres

Excision boundary conditions for black hole initial data

We define and extensively test a set of boundary conditions that can be applied at black hole excision surfaces when the Hamiltonian and momentum constraints of general relativity are solved within the conformal thin-sandwich formalism. These boundary conditions have been designed to result in black holes that are in quasiequilibrium and are completely general in the sense that they can be applied with any conformal three-geometry and slicing condition. Furthermore, we show that they retain precisely the freedom to specify an arbitrary spin on each black hole. Interestingly, we have been unable to find a boundary condition on the lapse that can be derived from a quasiequilibrium condition. Rather, we find evidence that the lapse boundary condition is part of the initial temporal gauge choice. To test these boundary conditions, we have extensively explored the case of a single black hole and the case of a binary system of equal-mass black holes, including the computation of quasi-circular orbits and the determination of the inner-most stable circular orbit. Our tests show that the boundary conditions work well.Comment: 23 pages, 23 figures, revtex4, corrected typos, added reference, minor content changes including additional post-Newtonian comparison. Version accepted by PR

Positivity of Entropy in the Semi-Classical Theory of Black Holes and Radiation

Quantum stress-energy tensors of fields renormalized on a Schwarzschild background violate the classical energy conditions near the black hole. Nevertheless, the associated equilibrium thermodynamical entropy $\Delta S$ by which such fields augment the usual black hole entropy is found to be positive. More precisely, the derivative of $\Delta S$ with respect to radius, at fixed black hole mass, is found to vanish at the horizon for {\it all} regular renormalized stress-energy quantum tensors. For the cases of conformal scalar fields and U(1) gauge fields, the corresponding second derivative is positive, indicating that $\Delta S$ has a local minimum there. Explicit calculation shows that indeed $\Delta S$ increases monotonically for increasing radius and is positive. (The same conclusions hold for a massless spin 1/2 field, but the accuracy of the stress-energy tensor we employ has not been confirmed, in contrast to the scalar and vector cases). None of these results would hold if the back-reaction of the radiation on the spacetime geometry were ignored; consequently, one must regard $\Delta S$ as arising from both the radiation fields and their effects on the gravitational field. The back-reaction, no matter how "small",Comment: 19 pages, RevTe

Issues for the Next Generation of Galaxy Surveys

I argue that the weight of the available evidence favours the conclusions that galaxies are unbiased tracers of mass, the mean mass density (excluding a cosmological constant or its equivalent) is less than the critical Einstein-de Sitter value, and an isocurvature model for structure formation offers a viable and arguably attractive model for the early assembly of galaxies. If valid these conclusions complicate our work of adding structure formation to the standard model for cosmology, but it seems sensible to pay attention to evidence.Comment: 14 pages, 3 postscript figures, uses rspublic.st

Bowen-York trumpet data and black-hole simulations

The most popular method to construct initial data for black-hole-binary simulations is the puncture method, in which compactified wormholes are given linear and angular momentum via the Bowen-York extrinsic curvature. When these data are evolved, they quickly approach a ``trumpet'' topology, suggesting that it would be preferable to use data that are in trumpet form from the outset. To achieve this, we extend the puncture method to allow the construction of Bowen-York trumpets, including an outline of an existence and uniqueness proof of the solutions. We construct boosted, spinning and binary Bowen-York puncture trumpets using a single-domain pseudospectral elliptic solver, and evolve the binary data and compare with standard wormhole-data results. We also show that for boosted trumpets the black-hole mass can be prescribed {\it a priori}, without recourse to the iterative procedure that is necessary for wormhole data.Comment: 15 pages, 14 figures. Published versio