Normal frames for non-Riemannian connections

The principal properties of geodesic normal coordinates are the vanishing of the connection components and first derivatives of the metric components at some point. It is well-known that these hold only at points where the connection has vanishing torsion and non-metricity. However, it is shown that normal frames, possessing the essential features of normal coordinates, can still be constructed when the connection is non-Riemannian.Comment: 4 pages, plain TeX. To appear in Class. Quantum Gra

CP Violation and Arrows of Time Evolution of a Neutral KK or BB Meson from an Incoherent to a Coherent State

We study the evolution of a neutral $K$ meson prepared as an incoherent equal mixture of $K^0$ and $\bar{K^0}$. Denoting the density matrix by \rho(t) = {1/2} N(t) [\1 + \vec{\zeta}(t) \cdot \vec{\sigma} ] , the norm of the state $N(t)$ is found to decrease monotonically from one to zero, while the magnitude of the Stokes vector $|\vec{\zeta}(t)|$ increases monotonically from zero to one. This property qualifies these observables as arrows of time. Requiring monotonic behaviour of $N(t)$ for arbitrary values of $\gamma_L, \gamma_S$ and $\Delta m$ yields a bound on the CP-violating overlap $\delta = \braket{K_L}{K_S}$, which is similar to, but weaker than, the known unitarity bound. A similar requirement on $|\vec{\zeta}(t)|$ yields a new bound, $\delta^2 < {1/2} (\frac{\Delta \gamma}{\Delta m}) \sinh (\frac{3\pi}{4} \frac{\Delta \gamma}{\Delta m})$ which is particularly effective in limiting the CP-violating overlap in the $B^0$-$\bar{B^0}$ system. We obtain the Stokes parameter $\zeta_3(t)$ which shows how the average strangeness of the beam evolves from zero to $\delta$. The evolution of the Stokes vector from $|\vec{\zeta}| = 0$ to $|\vec{\zeta}| = 1$ has a resemblance to an order parameter of a system undergoing spontaneous symmetry breaking.Comment: 13 pages, 6 figures. Inserted conon "." in title; minor change in text. To appear in Physical review

Distance-Redshift in Inhomogeneous Omega0=1Omega_0=1 Friedmann-Lemaitre-Robertson-Walker Cosmology

Distance--redshift relations are given in terms of associated Legendre functions for partially filled beam observations inspatially flat Friedmann-Lemaitre-Robertson-Walker (FLRW) cosmologies. These models are dynamically pressure-free, flat FLRW on large scales but, due to mass inhomogeneities, differ in their optical properties. The partially filled beam area-redshift equation is a Lame$^{\prime}$ equation for arbitrary FLRW and is shown to simplify to the associated Legendre equation for the spatially flat, i.e. $\Omega_0=1$ case. We fit these new analytic Hubble curves to recent supernovae (SNe) data in an attempt to determine both the mass parameter $\Omega_m$ and the beam filling parameter $\nu$. We find that current data are inadequate to limit $\nu$. However, we are able to estimate what limits are possible when the number of observed SNe is increased by factor of 10 or 100, sample sizes achievable in the near future with the proposed SuperNova Acceleration Probe satellite.Comment: 9 pages, 3 figure

Finding Principal Null Direction for Numerical Relativists

We present a new method for finding principal null directions (PNDs). Because our method assumes as input the intrinsic metric and extrinsic curvature of a spacelike hypersurface, it should be particularly useful to numerical relativists. We illustrate our method by finding the PNDs of the Kastor-Traschen spacetimes, which contain arbitrarily many $Q=M$ black holes in a de Sitter back-ground.Comment: 10 pages, LaTeX style, WU-AP/38/93. Figures are available (hard copies) upon requests [[email protected] (H.Shinkai)

No news for Kerr-Schild fields

Algebraically special fields with no gravitational radiation are described. Kerr-Schild fields, which include as a concrete case the Kinnersley photon rocket, form an important subclass of them.Comment: 4 pages, Revtex

A note on the peeling theorem in higher dimensions

We demonstrate the ``peeling property'' of the Weyl tensor in higher dimensions in the case of even dimensions (and with some additional assumptions), thereby providing a first step towards understanding of the general peeling behaviour of the Weyl tensor, and the asymptotic structure at null infinity, in higher dimensions.Comment: 5 pages, to appear in Class. Quantum Gra

The Gauge Fields and Ghosts in Rindler Space

We consider 2d Maxwell system defined on the Rindler space with metric ds^2=\exp(2a\xi)\cdot(d\eta^2-d\xi^2) with the goal to study the dynamics of the ghosts. We find an extra contribution to the vacuum energy in comparison with Minkowski space time with metric ds^2= dt^2-dx^2. This extra contribution can be traced to the unphysical degrees of freedom (in Minkowski space). The technical reason for this effect to occur is the property of Bogolubov's coefficients which mix the positive and negative frequencies modes. The corresponding mixture can not be avoided because the projections to positive -frequency modes with respect to Minkowski time t and positive -frequency modes with respect to the Rindler observer's proper time \eta are not equivalent. The exact cancellation of unphysical degrees of freedom which is maintained in Minkowski space can not hold in the Rindler space. In BRST approach this effect manifests itself as the presence of BRST charge density in L and R parts. An inertial observer in Minkowski vacuum |0> observes a universe with no net BRST charge only as a result of cancellation between the two. However, the Rindler observers who do not ever have access to the entire space time would see a net BRST charge. In this respect the effect resembles the Unruh effect. The effect is infrared (IR) in nature, and sensitive to the horizon and/or boundaries. We interpret the extra energy as the formation of the "ghost condensate" when the ghost degrees of freedom can not propagate, but nevertheless do contribute to the vacuum energy. Exact computations in this simple 2d model support the claim made in [1] that the ghost contribution might be responsible for the observed dark energy in 4d FLRW universe.Comment: Final version to appear in Phys. Rev. D. Comments on relation with energy momentum computations and few new refs are adde

Evolution of magnetic fields through cosmological perturbation theory

The origin of galactic and extra-galactic magnetic fields is an unsolved problem in modern cosmology. A possible scenario comes from the idea of these fields emerged from a small field, a seed, which was produced in the early universe (phase transitions, inflation, ...) and it evolves in time. Cosmological perturbation theory offers a natural way to study the evolution of primordial magnetic fields. The dynamics for this field in the cosmological context is described by a cosmic dynamo like equation, through the dynamo term. In this paper we get the perturbed Maxwell's equations and compute the energy momentum tensor to second order in perturbation theory in terms of gauge invariant quantities. Two possible scenarios are discussed, first we consider a FLRW background without magnetic field and we study the perturbation theory introducing the magnetic field as a perturbation. The second scenario, we consider a magnetized FLRW and build up the perturbation theory from this background. We compare the cosmological dynamo like equation in both scenarios

A Concise Introduction to Perturbation Theory in Cosmology

We give a concise, self-contained introduction to perturbation theory in cosmology at linear and second order, striking a balance between mathematical rigour and usability. In particular we discuss gauge issues and the active and passive approach to calculating gauge transformations. We also construct gauge-invariant variables, including the second order tensor perturbation on uniform curvature hypersurfaces.Comment: revtex4, 16 pages, 3 figures; v2: minor changes, typos corrected, reference added, version accepted by CQ

Light-cone coordinates based at a geodesic world line

Continuing work initiated in an earlier publication [Phys. Rev. D 69, 084007 (2004)], we construct a system of light-cone coordinates based at a geodesic world line of an arbitrary curved spacetime. The construction involves (i) an advanced-time or a retarded-time coordinate that labels past or future light cones centered on the world line, (ii) a radial coordinate that is an affine parameter on the null generators of these light cones, and (iii) angular coordinates that are constant on each generator. The spacetime metric is calculated in the light-cone coordinates, and it is expressed as an expansion in powers of the radial coordinate in terms of the irreducible components of the Riemann tensor evaluated on the world line. The formalism is illustrated in two simple applications, the first involving a comoving world line of a spatially-flat cosmology, the other featuring an observer placed on the axis of symmetry of Melvin's magnetic universe.Comment: 11 pages, 1 figur