Holography and non-locality in a closed vacuum-dominated universe

A closed vacuum-dominated Friedmann universe is asymptotic to a de Sitter space with a cosmological event horizon for any observer. The holographic principle says the area of the horizon in Planck units determines the number of bits of information about the universe that will ever be available to any observer. The wavefunction describing the probability distribution of mass quanta associated with bits of information on the horizon is the boundary condition for the wavefunction specifying the probability distribution of mass quanta throughout the universe. Local interactions between mass quanta in the universe cause quantum transitions in the wavefunction specifying the distribution of mass throughout the universe, with instantaneous non-local effects throughout the universe.Comment: 4 pages, no figures, to be published in Int. J. Theor. Phys, references correcte

Spherical Harmonic Decomposition on a Cubic Grid

A method is described by which a function defined on a cubic grid (as from a finite difference solution of a partial differential equation) can be resolved into spherical harmonic components at some fixed radius. This has applications to the treatment of boundary conditions imposed at radii larger than the size of the grid, following Abrahams, Rezzola, Rupright et al.(gr-qc/9709082}. In the method described here, the interpolation of the grid data to the integration 2-sphere is combined in the same step as the integrations to extract the spherical harmonic amplitudes, which become sums over grid points. Coordinates adapted to the integration sphere are not needed.Comment: 5 pages, LaTeX uses cjour.cls (supplied

Quantum nature of black holes

I reconsider Hawking's analysis of the effects of gravitational collapse on quantum fields, taking into account interactions between the fields. The ultra-high energy vacuum fluctuations, which had been considered to be an awkward peripheral feature of the analysis, are shown to play a key role. By interactions, they can scatter particles to, or create pairs of particle at, ultra-high energies. The energies rapidly become so great that quantum gravity must play a dominant role. Thus the vicinities of black holes are essentially quantum-gravitational regimes.Comment: 7 pages, 5 figures. Honorable mention in the 2004 Gravity Research Foundation Essay Competitio

Taub-NUT space as a counterexample to almost anything Technical report no. 529

Taub-NUT space as countermeasure to almost anything - Einstein equation, classical mechanics, and differential equation

The Dynamics of General Relativity

This article--summarizing the authors' then novel formulation of General Relativity--appeared as Chapter 7 of an often cited compendium edited by L. Witten in 1962, which is now long out of print. Intentionally unretouched, this posting is intended to provide contemporary accessibility to the flavor of the original ideas. Some typographical corrections have been made: footnote and page numbering have changed--but not section nor equation numbering etc. The authors' current institutional affiliations are encoded in: [email protected], [email protected], [email protected] .Comment: 30 pages (LaTeX2e), uses amsfonts, no figure

Gravitomagnetic time delay and the Lense-Thirring effect in Brans-Dicke theory of gravity

We discuss the gravitomagnetic time delay and the Lense-Thirring effect in the context of Brans-Dicke theory of gravity. We compare the theoretical results obtained with those predicted by general relativity. We show that within the accuracy of experiments designed to measure these effects both theories predict essentially the same result.Comment: 10 pages Typeset using REVTE

Boltzmann hierarchy for the cosmic microwave background at second order including photon polarization

Non-gaussianity and B-mode polarization are particularly interesting features of the cosmic microwave background, as -- at least in the standard model of cosmology -- their only sources to first order in cosmological perturbation theory are primordial, possibly generated during inflation. If the primordial sources are small, the question arises how large is the non-gaussianity and B-mode background induced in second-order from the initially gaussian and scalar perturbations. In this paper we derive the Boltzmann hierarchy for the microwave background photon phase-space distributions at second order in cosmological perturbation theory including the complete polarization information, providing the basis for further numerical studies. As an aside we note that the second-order collision term contains new sources of B-mode polarization and that no polarization persists in the tight-coupling limit.Comment: LaTeX, 33 page

Notes on Spinoptics in a Stationary Spacetime

In arXiv:1105.5629, equations of the modified geometrical optics for circularly polarized photon trajectories in a stationary spacetime are derived by using a (1+3)-decomposed form of Maxwell's equations. We derive the same results by using a four-dimensional covariant description. In our procedure, the null nature of the modified photon trajectory naturally appears and the energy flux is apparently null. We find that, in contrast to the standard geometrical optics, the inner product of the stationary Killing vector and the tangent null vector to the modified photon trajectory is no longer a conserved quantity along light paths. This quantity is furthermore different for left and right handed photon. A similar analysis is performed for gravitational waves and an additional factor of 2 appears in the modification due to the spin-2 nature of gravitational waves.Comment: 15 pages, to appear in PR

Second order perturbations of a Schwarzschild black hole: inclusion of odd parity perturbations

We consider perturbations of a Schwarzschild black hole that can be of both even and odd parity, keeping terms up to second order in perturbation theory, for the $\ell=2$ axisymmetric case. We develop explicit formulae for the evolution equations and radiated energies and waveforms using the Regge-Wheeler-Zerilli approach. This formulation is useful, for instance, for the treatment in the ``close limit approximation'' of the collision of counterrotating black holes.Comment: 12 pages RevTe

The Long-Term Future of Space Travel

The fact that we apparently live in an accelerating universe places limitations on where humans might visit. If the current energy density of the universe is dominated by a cosmological constant, a rocket could reach a galaxy observed today at a redshift of 1.7 on a one-way journey or merely 0.65 on a round trip. Unfortunately these maximal trips are impractical as they require an infinite proper time to traverse. However, calculating the rocket trajectory in detail shows that a rocketeer could nearly reach such galaxies within a lifetime (a long lifetime admittedly -- about 100 years). For less negative values of $w$ the maximal redshift increases becoming infinite for $w\geq -1/3$.Comment: 5 pages, 3 figures, minor changes to reflect version accepted to PR