Wormholes in spacetimes with cosmological horizons

A generalisation of the asymptotic wormhole boundary condition for the case of spacetimes with a cosmological horizon is proposed. In particular, we consider de Sitter spacetime with small cosmological constant. The wave functions selected by this proposal are exponentially damped in WKB approximation when the scale factor is large but still much smaller than the horizon size. In addition, they only include outgoing gravitational modes in the region beyond the horizon. We argue that these wave functions represent quantum wormholes and compute the local effective interactions induced by them in low-energy field theory. These effective interactions differ from those for flat spacetime in terms that explicitly depend on the cosmological constant.Comment: 10 pages, LaTeX 2.O9, no figure

Social media and related technology:drivers of change in managing the contemporary sales force

The selling environment has undergone tremendous transformation over the past 2 decades. Perhaps the greatest change has centered on changes and advancements in technology. The latest dramatic change has been the rapidly increasing use of social media and other related technologies in the business-to-business realm. The sales world began the use of technology through the use of Web 1.0, which was primarily webpage oriented; now we see the world of social media as the paradigm of how firms should implement technology. Although there has been some recent emphasis on how marketing might implement social media into their strategies and how the individual salesperson might implement social media into his or her daily selling routine, no substantive discussion on how social media is affecting the role of the sales manager has appeared in the literature. This article systematically examines how social media is impacting the sales management function and, in fact, may be dramatically revolutionizing the position. To help the marketing and sales organization better understand the changing sales world, we present eight lessons that every sales manager needs to embrace

Colliding Black Holes: The Close Limit

The problem of the mutual attraction and joining of two black holes is of importance as both a source of gravitational waves and as a testbed of numerical relativity. If the holes start out close enough that they are initially surrounded by a common horizon, the problem can be viewed as a perturbation of a single black hole. We take initial data due to Misner for close black holes, apply perturbation theory and evolve the data with the Zerilli equation. The computed gravitational radiation agrees with and extends the results of full numerical computations.Comment: 4 pages, Revtex, 3 postscript figures included, CGPG-94/2-

Effective geometry in Astrophysics

The effective metric is introduced by means of two examples (non-linear electromagnetism and hydrodynamics),along with applications in Astrophysics. A sketch of the generality of the effect is also given.Comment: 9 pages, contributions for the proceedings of the First International Workshop on Astronomy and Relativistic Astrophysics (IWARA 2003), Olinda (Brazil

Absorption of mass and angular momentum by a black hole: Time-domain formalisms for gravitational perturbations, and the small-hole/slow-motion approximation

The first objective of this work is to obtain practical prescriptions to calculate the absorption of mass and angular momentum by a black hole when external processes produce gravitational radiation. These prescriptions are formulated in the time domain within the framework of black-hole perturbation theory. Two such prescriptions are presented. The first is based on the Teukolsky equation and it applies to general (rotating) black holes. The second is based on the Regge-Wheeler and Zerilli equations and it applies to nonrotating black holes. The second objective of this work is to apply the time-domain absorption formalisms to situations in which the black hole is either small or slowly moving. In the context of this small-hole/slow-motion approximation, the equations of black-hole perturbation theory can be solved analytically, and explicit expressions can be obtained for the absorption of mass and angular momentum. The changes in the black-hole parameters can then be understood in terms of an interaction between the tidal gravitational fields supplied by the external universe and the hole's tidally-induced mass and current quadrupole moments. For a nonrotating black hole the quadrupole moments are proportional to the rate of change of the tidal fields on the hole's world line. For a rotating black hole they are proportional to the tidal fields themselves.Comment: 36 pages, revtex4, no figures, final published versio

Head-on collision of unequal mass black holes: close-limit predictions

The close-limit method has given approximations in excellent agreement with those of numerical relativity for collisions of equal mass black holes. We consider here colliding holes with unequal mass, for which numerical relativity results are not available. We try to ask two questions: (i) Can we get approximate answers to astrophysical questions (ideal mass ratio for energy production, maximum recoil velocity, etc.), and (ii) can we better understand the limitations of approximation methods. There is some success in answering the first type of question, but more with the second, especially in connection with the issue of measures of the intrinsic mass of the colliding holes, and of the range of validity of the method.Comment: 19 pages, RevTeX + 9 postscript figure

Numerical Evidence that the Singularity in Polarized U(1) Symmetric Cosmologies on T3×RT^3 \times R is Velocity Dominated

Numerical evidence supports the conjecture that polarized U(1) symmetric cosmologies have asymptotically velocity term dominated singularities.Comment: 8 pages, RevTex, 4 figures, uses eps

Remarks on evolution of space-times in 3+1 and 4+1 dimensions

A large class of vacuum space-times is constructed in dimension 4+1 from hyperboloidal initial data sets which are not small perturbations of empty space data. These space-times are future geodesically complete, smooth up to their future null infinity, and extend as vacuum space-times through their Cauchy horizon. Dimensional reduction gives non-vacuum space-times with the same properties in 3+1 dimensions.Comment: 10pp, exposition improved; final versio

Numerical Investigation of Cosmological Singularities

Although cosmological solutions to Einstein's equations are known to be generically singular, little is known about the nature of singularities in typical spacetimes. It is shown here how the operator splitting used in a particular symplectic numerical integration scheme fits naturally into the Einstein equations for a large class of cosmological models and thus allows study of their approach to the singularity. The numerical method also naturally singles out the asymptotically velocity term dominated (AVTD) behavior known to be characteristic of some of these models, conjectured to describe others, and probably characteristic of a subclass of the rest. The method is first applied to the unpolarized Gowdy T$^3$ cosmology. Exact pseudo-unpolarized solutions are used as a code test and demonstrate that a 4th order accurate implementation of the numerical method yields acceptable agreement. For generic initial data, support for the conjecture that the singularity is AVTD with geodesic velocity (in the harmonic map target space) < 1 is found. A new phenomenon of the development of small scale spatial structure is also observed. Finally, it is shown that the numerical method straightforwardly generalizes to an arbitrary cosmological spacetime on $T^3 \times R$ with one spacelike U(1) symmetry.Comment: 37 pp +14 figures (not included, available on request), plain Te

Head--on Collision of Two Unequal Mass Black Holes

We present results from the first fully nonlinear numerical calculations of the head--on collision of two unequal mass black holes. Selected waveforms of the most dominant l=2, 3 and 4 quasinormal modes are shown, as are the total radiated energies and recoil velocities for a range of mass ratios and initial separations. Our results validate the close and distant separation limit perturbation studies, and suggest that the head--on collision scenario is not likely to produce an astrophysically significant recoil effect.Comment: 5 pages, 3 figure