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

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

Integration over connections in the discretized gravitational functional integrals

The result of performing integrations over connection type variables in the path integral for the discrete field theory may be poorly defined in the case of non-compact gauge group with the Haar measure exponentially growing in some directions. This point is studied in the case of the discrete form of the first order formulation of the Einstein gravity theory. Here the result of interest can be defined as generalized function (of the rest of variables of the type of tetrad or elementary areas) i. e. a functional on a set of probe functions. To define this functional, we calculate its values on the products of components of the area tensors, the so-called moments. The resulting distribution (in fact, probability distribution) has singular ($\delta$-function-like) part with support in the nonphysical region of the complex plane of area tensors and regular part (usual function) which decays exponentially at large areas. As we discuss, this also provides suppression of large edge lengths which is important for internal consistency, if one asks whether gravity on short distances can be discrete. Some another features of the obtained probability distribution including occurrence of the local maxima at a number of the approximately equidistant values of area are also considered.Comment: 22 page

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

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

On the Thermodynamics of NUT charged spaces

We discuss and compare at length the results of two methods used recently to describe the thermodynamics of Taub-NUT solutions in a deSitter background. In the first approach (\mathbb{% C}-approach), one deals with an analytically continued version of the metric while in the second approach ($\mathbb{R}$-approach), the discussion is carried out using the unmodified metric with Lorentzian signature. No analytic continuation is performed on the coordinates and/or the parameters that appear in the metric. We find that the results of both these approaches are completely equivalent modulo analytic continuation and we provide the exact prescription that relates the results in both methods. The extension of these results to the AdS/flat cases aims to give a physical interpretation of the thermodynamics of nut-charged spacetimes in the Lorentzian sector. We also briefly discuss the higher dimensional spaces and note that, analogous with the absence of hyperbolic nuts in AdS backgrounds, there are no spherical Taub-Nut-dS solutions.Comment: 35pages, 4 figures. v.4 references added,few typos corrected, to appear in Phys. Rev.

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

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

A new time-machine model with compact vacuum core

We present a class of curved-spacetime vacuum solutions which develope closed timelike curves at some particular moment. We then use these vacuum solutions to construct a time-machine model. The causality violation occurs inside an empty torus, which constitutes the time-machine core. The matter field surrounding this empty torus satisfies the weak, dominant, and strong energy conditions. The model is regular, asymptotically-flat, and topologically-trivial. Stability remains the main open question.Comment: 7 page