Initial Data for General Relativity with Toroidal Conformal Symmetry

A new class of time-symmetric solutions to the initial value constraints of vacuum General Relativity is introduced. These data are globally regular, asymptotically flat (with possibly several asymptotic ends) and in general have no isometries, but a $U(1)\times U(1)$ group of conformal isometries. After decomposing the Lichnerowicz conformal factor in a double Fourier series on the group orbits, the solutions are given in terms of a countable family of uncoupled ODEs on the orbit space.Comment: REVTEX, 9 pages, ESI Preprint 12

The binary black-hole problem at the third post-Newtonian approximation in the orbital motion: Static part

Post-Newtonian expansions of the Brill-Lindquist and Misner-Lindquist solutions of the time-symmetric two-black-hole initial value problem are derived. The static Hamiltonians related to the expanded solutions, after identifying the bare masses in both solutions, are found to differ from each other at the third post-Newtonian approximation. By shifting the position variables of the black holes the post-Newtonian expansions of the three metrics can be made to coincide up to the fifth post-Newtonian order resulting in identical static Hamiltonians up the third post-Newtonian approximation. The calculations shed light on previously performed binary point-mass calculations at the third post-Newtonian approximation.Comment: LaTeX, 9 pages, to be submitted to Physical Review

Coupling of the lattice and superlattice deformations and hysteresis in thermal expansion for the quasi one-dimensional conductor TaS3_3

An original interferometer-based setup for measurements of length of needle-like samples is developed, and thermal expansion of o-TaS$_3$ crystals is studied. Below the Peierls transition the temperature hysteresis of length $L$ is observed, the width of the hysteresis loop $\delta L/L$ being up to $5 \cdot 10^{-5}$. The behavior of the loop is anomalous: the length changes so that it is in front of its equilibrium value. The hysteresis loop couples with that of conductivity. The sign and the value of the length hysteresis are consistent with the strain dependence of the charge-density waves (CDW) wave vector. With lowering temperature down to 100 K the CDW elastic modulus grows achieving a value comparable with the lattice Young modulus. Our results could be helpful in consideration of different systems with intrinsic superstructures.Comment: 4 pages, 3 figures. Phys. Rev. Lett., accepted for publicatio

Gravitational Mass in Asymptotically de Sitter Space-Times with Compactified Dimensions

We define gravitational mass in asymptotically de Sitter space-times with compactified dimension. It was shown that the mass can be negative for space-time with matter spreading beyond the cosmological horizon scale or large outward `momentum' in four dimension. We give simple examples with negative energy in higher dimensions even if the matter is not beyond horizon or system does not have large `momentum'. They do not have the lower bound on the mass. We also give a positive energy argument in higher dimensions and realise that elementary fermion cannot exist in our examples.Comment: 7 pages, the version to be published in Phys. Rev.

Gravitational Geons Revisited

A careful analysis of the gravitational geon solution found by Brill and Hartle is made. The gravitational wave expansion they used is shown to be consistent and to result in a gauge invariant wave equation. It also results in a gauge invariant effective stress-energy tensor for the gravitational waves provided that a generalized definition of a gauge transformation is used. To leading order this gauge transformation is the same as the usual one for gravitational waves. It is shown that the geon solution is a self-consistent solution to Einstein's equations and that, to leading order, the equations describing the geometry of the gravitational geon are identical to those derived by Wheeler for the electromagnetic geon. An appendix provides an existence proof for geon solutions to these equations.Comment: 18 pages, ReVTeX. To appear in Physical Review D. Significant changes include more details in the derivations of certain key equations and the addition of an appendix containing a proof of the existence of a geon solution to the equations derived by Wheeler. Also a reference has been added and various minor changes have been mad

A Cosmological Constant Limits the Size of Black Holes

In a space-time with cosmological constant $\Lambda>0$ and matter satisfying the dominant energy condition, the area of a black or white hole cannot exceed $4\pi/\Lambda$. This applies to event horizons where defined, i.e. in an asymptotically deSitter space-time, and to outer trapping horizons (cf. apparent horizons) in any space-time. The bound is attained if and only if the horizon is identical to that of the degenerate `Schwarzschild-deSitter' solution. This yields a topological restriction on the event horizon, namely that components whose total area exceeds $4\pi/\Lambda$ cannot merge. We discuss the conjectured isoperimetric inequality and implications for the cosmic censorship conjecture.Comment: 10 page

When Black Holes Meet Kaluza-Klein Bubbles

We explore the physical consequences of a recently discovered class of exact solutions to five dimensional Kaluza-Klein theory. We find a number of surprising features including: (1) In the presence of a Kaluza-Klein bubble, there are arbitrarily large black holes with topology S^3. (2) In the presence of a black hole or a black string, there are expanding bubbles (with de Sitter geometry) which never reach null infinity. (3) A bubble can hold two black holes of arbitrary size in static equilibrium. In particular, two large black holes can be close together without merging to form a single black hole.Comment: 23 pages, 5 figures, v2: few comments on stability modifie

Global Structure of a Black-Hole Cosmos and its Extremes

We analyze the global structure of a family of Einstein-Maxwell solutions parametrized by mass, charge and cosmological constant. In a qualitative classification there are: (i) generic black-hole solutions, describing a Wheeler wormhole in a closed cosmos of spatial topology $S^2\times S^1$; (ii) generic naked-singularity solutions, describing a pair of ``point" charges in a closed cosmos; (iii) extreme black-hole solutions, describing a pair of ``horned" particles in an otherwise closed cosmos; (iv) extreme naked-singularity solutions, in which a pair of point charges forms and then evaporates, in a way which is not even weakly censored; and (v) an ultra-extreme solution. We discuss the properties of the solutions and of various coordinate systems, and compare with the Kastor-Traschen multi-black-hole solutions.Comment: 11 pages. Diagrams not include

Making Anti-de Sitter Black Holes

It is known from the work of Banados et al. that a space-time with event horizons (much like the Schwarzschild black hole) can be obtained from 2+1 dimensional anti-de Sitter space through a suitable identification of points. We point out that this can be done in 3+1 dimensions as well. In this way we obtain black holes with event horizons that are tori or Riemann surfaces of genus higher than one. They can have either one or two asymptotic regions. Locally, the space-time is isometric to anti-de Sitter space.Comment: LaTeX, 10 pages, 6 postscript figures, uses epsf.te

Sound propagation in density wave conductors and the effect of long-range Coulomb interaction

We study theoretically the sound propagation in charge- and spin-density waves in the hydrodynamic regime. First, making use of the method of comoving frame, we construct the stress tensor appropriate for quasi-one dimensional systems within tight-binding approximation. Taking into account the screening effect of the long-range Coulomb interaction, we find that the increase of the sound velocity below the critical temperature is about two orders of magnitude less for longitudinal sound than for transverse one. It is shown that only the transverse sound wave with displacement vector parallel to the chain direction couples to the phason of the density wave, therefore we expect significant electromechanical effect only in this case.Comment: revtex, 14 pages (in preprint form), submitted to PR