Initial data for stationary space-times near space-like infinity

We study Cauchy initial data for asymptotically flat, stationary vacuum space-times near space-like infinity. The fall-off behavior of the intrinsic metric and the extrinsic curvature is characterized. We prove that they have an analytic expansion in powers of a radial coordinate. The coefficients of the expansion are analytic functions of the angles. This result allow us to fill a gap in the proof found in the literature of the statement that all asymptotically flat, vacuum stationary space-times admit an analytic compactification at null infinity. Stationary initial data are physical important and highly non-trivial examples of a large class of data with similar regularity properties at space-like infinity, namely, initial data for which the metric and the extrinsic curvature have asymptotic expansion in terms of powers of a radial coordinate. We isolate the property of the stationary data which is responsible for this kind of expansion.Comment: LaTeX 2e, no figures, 12 page

A Dain Inequality with charge

We prove an upper bound for angular-momentum and charge in terms of the mass for electro-vacuum asymptotically flat axisymmetric initial data sets with simply connected orbit space

Area products for stationary black hole horizons

Area products for multi-horizon stationary black holes often have intriguing properties, and are often (though not always) independent of the mass of the black hole itself (depending only on various charges, angular momenta, and moduli). Such products are often formulated in terms of the areas of inner (Cauchy) horizons and outer (event) horizons, and sometimes include the effects of unphysical "virtual" horizons. But the conjectured mass-independence sometimes fails. Specifically, for the Schwarzschild-de Sitter [Kottler] black hole in (3+1) dimensions it is shown by explicit exact calculation that the product of event horizon area and cosmological horizon area is not mass independent. (Including the effect of the third "virtual" horizon does not improve the situation.) Similarly, in the Reissner-Nordstrom-anti-de Sitter black hole in (3+1) dimensions the product of inner (Cauchy) horizon area and event horizon area is calculated (perturbatively), and is shown to be not mass independent. That is, the mass-independence of the product of physical horizon areas is not generic. In spherical symmetry, whenever the quasi-local mass m(r) is a Laurent polynomial in aerial radius, r=sqrt{A/4\pi}, there are significantly more complicated mass-independent quantities, the elementary symmetric polynomials built up from the complete set of horizon radii (physical and virtual). Sometimes it is possible to eliminate the unphysical virtual horizons, constructing combinations of physical horizon areas that are mass independent, but they tend to be considerably more complicated than the simple products and related constructions currently being mooted in the literature.Comment: V1: 16 pages; V2: 9 pages (now formatted in PRD style). Minor change in title. Extra introduction, background, discussion. Several additional references; other references updated. Minor typos fixed. This version accepted for publication in PRD; V3: Minor typos fixed. Published versio

The Goldberg-Sachs theorem in linearized gravity

The Goldberg-Sachs theorem has been very useful in constructing algebraically special exact solutions of Einstein vacuum equation. Most of the physical meaningful vacuum exact solutions are algebraically special. We show that the Goldberg-Sachs theorem is not true in linearized gravity. This is a remarkable result, which gives light on the understanding of the physical meaning of the linearized solutions.Comment: 6 pages, no figures, LaTeX 2

Excess Body Weight and Gait Influence Energy Cost of Walking in Older Adults

Purpose: To study how excess body weight influences the energy cost of walking (Cw) and determine if overweight and obese older adults self-select stride frequency to minimize Cw. Methods: Using body mass index (BMI) men and women between the ages of 65–80 yr were separated into normal weight (NW, BMI ≤ 24.9 kg m−2, n = 13) and overweight-obese groups (OWOB, BMI ≥25.0 kg m−2, n = 13). Subjects walked at 0.83 m s−1 on an instrumented treadmill that recorded gait parameters, and completed three, six-minute walking trials; at preferred stride frequency (PSF), at +10% PSF, and at −10% PSF. Cw was determined by indirect calorimetry. Repeated measures analysis of variance was used to compare groups, and associations were tested with Pearson correlations, α = 0.05. Results: OWOB had 62% greater absolute Cw (301 ± 108 vs. 186 ± 104 J m−1, P \u3c 0.001) and 20% greater relative Cwkg (3.48 ± 0.95 vs. 2.91 ± 0.94 J kg−1 m−1, P = 0.046) than NW. Although PSF was not different between OWOB and NW (P = 0.626), Cw was 8% greater in OWOB at +10% PSF (P \u3c 0.001). At PSF OWOB spent less time in single-limb support (33.1 ± 1.5 vs. 34.9 ± 1.6 %GC, P = 0.021) and more time in double-limb support (17.5 ± 1.6 vs. 15.4 ± 1.4 %GC, P = 0.026) than NW. In OWOB, at PSF, Cw was correlated to impulse (r = −0.57, P = 0.027) and stride frequency (r = 0.51, P = 0.046). Conclusions: Excess body weight is associated with greater Cw in older adults, possibly contributing to reduced mobility in overweight and obese older persons

Estimates of the total gravitation radiation in the head-on black hole collision

We report on calculations of the total gravitational energy radiated in the head-on black hole collision, where we use the geometry of the Robinson-Trautman metrics.Comment: 10 pages, 2 figures, LaTeX2

Photon rockets and the Robinson-Trautman geometries

We point out the relation between the photon rocket spacetimes and the Robinson Trautman geometries. This allows a discussion of the issues related to the distinction between the gravitational and matter energy radiation that appear in these metrics in a more geometrical way, taking full advantage of their asymptotic properties at null infinity to separate the Weyl and Ricci radiations, and to clearly establish their gravitational energy content. We also give the exact solution for the generalized photon rockets.Comment: 7 pages, no figures, LaTeX2

On smoothness-asymmetric null infinities

We discuss the existence of asymptotically Euclidean initial data sets to the vacuum Einstein field equations which would give rise (modulo an existence result for the evolution equations near spatial infinity) to developments with a past and a future null infinity of different smoothness. For simplicity, the analysis is restricted to the class of conformally flat, axially symmetric initial data sets. It is shown how the free parameters in the second fundamental form of the data can be used to satisfy certain obstructions to the smoothness of null infinity. The resulting initial data sets could be interpreted as those of some sort of (non-linearly) distorted Schwarzschild black hole. Its developments would be so that they admit a peeling future null infinity, but at the same time have a polyhomogeneous (non-peeling) past null infinity.Comment: 13 pages, 1 figur

Bounds on the force between black holes

We treat the problem of N interacting, axisymmetric black holes and obtain two relations among physical parameters of the system including the force between the black holes. The first relation involves the total mass, the angular momenta, the distances and the forces between the black holes. The second one relates the angular momentum and area of each black hole with the forces acting on it.Comment: 13 pages, no figure