Geodesic Deviation in Regge Calculus

Geodesic deviation is the most basic manifestation of the influence of gravitational fields on matter. We investigate geodesic deviation within the framework of Regge calculus, and compare the results with the continuous formulation of general relativity on two different levels. We show that the continuum and simplicial descriptions coincide when the cumulative effect of the Regge contributions over an infinitesimal element of area is considered. This comparison provides a quantitative relation between the curvature of the continuous description and the deficit angles of Regge calculus. The results presented might also be of help in developing generic ways of including matter terms in the Regge equations.Comment: 9 pages. Latex 2e with 5 EPS figures. Submitted to CQ

Indication of asymptotic scaling in the reactions dd→p3dd\to p^3H, dd→n3dd\to n^3He and dp→dpdp\to dp

It is shown that the differential cross sections of the reactions $dd\to ^3He n$ and $dd\to ^3H p$ measured at c.m.s.scattering angle$\theta_{cm}=60^\circ$ in the interval of the deuteron beam energy 0.5 - 1.2 GeV demonstrate the scaling behaviour,$d\sigma/d t\sim s^{-22}$, which follows from constituent quark counting rules. It is found also that the differential cross section of the elastic $dp\to dp$ scattering at $\theta_{cm}=125^\circ-135^\circ$ follows the scaling regime $\sim s^{-16}$ at beam energies 0.5 - 5 GeV. These data are parameterized here using the Reggeon exchange.Comment: 6 pages, Latex, 2 eps figures; final version accepted by Pis'ma v ZHETF, corrected and completed reference

A fully (3+1)-D Regge calculus model of the Kasner cosmology

We describe the first discrete-time 4-dimensional numerical application of Regge calculus. The spacetime is represented as a complex of 4-dimensional simplices, and the geometry interior to each 4-simplex is flat Minkowski spacetime. This simplicial spacetime is constructed so as to be foliated with a one parameter family of spacelike hypersurfaces built of tetrahedra. We implement a novel two-surface initial-data prescription for Regge calculus, and provide the first fully 4-dimensional application of an implicit decoupled evolution scheme (the ``Sorkin evolution scheme''). We benchmark this code on the Kasner cosmology --- a cosmology which embodies generic features of the collapse of many cosmological models. We (1) reproduce the continuum solution with a fractional error in the 3-volume of 10^{-5} after 10000 evolution steps, (2) demonstrate stable evolution, (3) preserve the standard deviation of spatial homogeneity to less than 10^{-10} and (4) explicitly display the existence of diffeomorphism freedom in Regge calculus. We also present the second-order convergence properties of the solution to the continuum.Comment: 22 pages, 5 eps figures, LaTeX. Updated and expanded versio

Reaction mechanism and characteristics of T_{20} in d + ^3He backward elastic scattering at intermediate energies

For backward elastic scattering of deuterons by ^3He, cross sections \sigma and tensor analyzing power T_{20} are measured at E_d=140-270 MeV. The data are analyzed by the PWIA and by the general formula which includes virtual excitations of other channels, with the assumption of the proton transfer from ^3He to the deuteron. Using ^3He wave functions calculated by the Faddeev equation, the PWIA describes global features of the experimental data, while the virtual excitation effects are important for quantitative fits to the T_{20} data. Theoretical predictions on T_{20}, K_y^y (polarization transfer coefficient) and C_{yy} (spin correlation coefficient) are provided up to GeV energies.Comment: REVTEX+epsfig, 17 pages including 6 eps figs, to be published in Phys. Rev.

Relativistic hydrodynamics on spacelike and null surfaces: Formalism and computations of spherically symmetric spacetimes

We introduce a formulation of Eulerian general relativistic hydrodynamics which is applicable for (perfect) fluid data prescribed on either spacelike or null hypersurfaces. Simple explicit expressions for the characteristic speeds and fields are derived in the general case. A complete implementation of the formalism is developed in the case of spherical symmetry. The algorithm is tested in a number of different situations, predisposing for a range of possible applications. We consider the Riemann problem for a polytropic gas, with initial data given on a retarded/advanced time slice of Minkowski spacetime. We compute perfect fluid accretion onto a Schwarzschild black hole spacetime using ingoing null Eddington-Finkelstein coordinates. Tests of fluid evolution on dynamic background include constant density and TOV stars sliced along the radial null cones. Finally, we consider the accretion of self-gravitating matter onto a central black hole and the ensuing increase in the mass of the black hole horizon.Comment: 23 pages, 13 figures, submitted to Phys. Rev.

Stable characteristic evolution of generic 3-dimensional single-black-hole spacetimes

We report new results which establish that the accurate 3-dimensional numerical simulation of generic single-black-hole spacetimes has been achieved by characteristic evolution with unlimited long term stability. Our results cover a selection of distorted, moving and spinning single black holes, with evolution times up to 60,000M.Comment: 4 pages, 3 figure

Characteristic Evolution and Matching

I review the development of numerical evolution codes for general relativity based upon the characteristic initial value problem. Progress in characteristic evolution is traced from the early stage of 1D feasibility studies to 2D axisymmetric codes that accurately simulate the oscillations and gravitational collapse of relativistic stars and to current 3D codes that provide pieces of a binary black hole spacetime. Cauchy codes have now been successful at simulating all aspects of the binary black hole problem inside an artificially constructed outer boundary. A prime application of characteristic evolution is to extend such simulations to null infinity where the waveform from the binary inspiral and merger can be unambiguously computed. This has now been accomplished by Cauchy-characteristic extraction, where data for the characteristic evolution is supplied by Cauchy data on an extraction worldtube inside the artificial outer boundary. The ultimate application of characteristic evolution is to eliminate the role of this outer boundary by constructing a global solution via Cauchy-characteristic matching. Progress in this direction is discussed.Comment: New version to appear in Living Reviews 2012. arXiv admin note: updated version of arXiv:gr-qc/050809

Stationary relativistic jets

In this paper we describe a simple numerical approach which allows to study the structure of steady-state axisymmetric relativistic jets using one-dimensional time-dependent simulations. It is based on the fact that for narrow jets with vz≈cvz≈c the steady-state equations of relativistic magnetohydrodynamics can be accurately approximated by the one-dimensional time-dependent equations after the substitution z=ctz=ct. Since only the time-dependent codes are now publicly available this is a valuable and efficient alternative to the development of a high-specialised code for the time-independent equations. The approach is also much cheaper and more robust compared to the relaxation method. We tested this technique against numerical and analytical solutions found in literature as well as solutions we obtained using the relaxation method and found it sufficiently accurate. In the process, we discovered the reason for the failure of the self-similar analytical model of the jet reconfinement in relatively flat atmospheres and elucidated the nature of radial oscillations of steady-state jets

Steroid Concentrations in Plasma, Whole Blood and Brain: Effects of Saline Perfusion to Remove Blood Contamination from Brain

The brain and other organs locally synthesize steroids. Local synthesis is suggested when steroid levels are higher in tissue than in the circulation. However, measurement of both circulating and tissue steroid levels are subject to methodological considerations. For example, plasma samples are commonly used to estimate circulating steroid levels in whole blood, but steroid levels in plasma and whole blood could differ. In addition, tissue steroid measurements might be affected by blood contamination, which can be addressed experimentally by using saline perfusion to remove blood. In Study 1, we measured corticosterone and testosterone (T) levels in zebra finch (Taeniopygia guttata) plasma, whole blood, and red blood cells (RBC). We also compared corticosterone in plasma, whole blood, and RBC at baseline and after 60 min restraint stress. In Study 2, we quantified corticosterone, dehydroepiandrosterone (DHEA), T, and 17β-estradiol (E2) levels in the brains of sham-perfused or saline-perfused subjects. In Study 1, corticosterone and T concentrations were highest in plasma, significantly lower in whole blood, and lowest in RBC. In Study 2, saline perfusion unexpectedly increased corticosterone levels in the rostral telencephalon but not other regions. In contrast, saline perfusion decreased DHEA levels in caudal telencephalon and diencephalon. Saline perfusion also increased E2 levels in caudal telencephalon. In summary, when comparing local and systemic steroid levels, the inclusion of whole blood samples should prove useful. Moreover, blood contamination has little or no effect on measurement of brain steroid levels, suggesting that saline perfusion is not necessary prior to brain collection. Indeed, saline perfusion itself may elevate and lower steroid concentrations in a rapid, region-specific manner