Integer Partitions and Exclusion Statistics

We provide a combinatorial description of exclusion statistics in terms of minimal difference $p$ partitions. We compute the probability distribution of the number of parts in a random minimal $p$ partition. It is shown that the bosonic point $p=0$ is a repulsive fixed point for which the limiting distribution has a Gumbel form. For all positive $p$ the distribution is shown to be Gaussian.Comment: 16 pages, 4 .eps figures include

Newtonian and Post-Newtonian approximations of the k = 0 Friedmann Robertson Walker Cosmology

In a previous paper we derived a post-Newtonian approximation to cosmology which, in contrast to former Newtonian and post-Newtonian cosmological theories, has a well-posed initial value problem. In this paper, this new post-Newtonian theory is compared with the fully general relativistic theory, in the context of the k = 0 Friedmann Robertson Walker cosmologies. It is found that the post-Newtonian theory reproduces the results of its general relativistic counterpart, whilst the Newtonian theory does not.Comment: 11 pages, Latex, corrected typo

An explanation of the Newman-Janis Algorithm

After the original discovery of the Kerr metric, Newman and Janis showed that this solution could be ``derived'' by making an elementary complex transformation to the Schwarzschild solution. The same method was then used to obtain a new stationary axisymmetric solution to Einstein's field equations now known as the Kerr-newman metric, representing a rotating massive charged black hole. However no clear reason has ever been given as to why the Newman-Janis algorithm works, many physicist considering it to be an ad hoc procedure or ``fluke'' and not worthy of further investigation. Contrary to this belief this paper shows why the Newman-Janis algorithm is successful in obtaining the Kerr-Newman metric by removing some of the ambiguities present in the original derivation. Finally we show that the only perfect fluid generated by the Newman-Janis algorithm is the (vacuum) Kerr metric and that the only Petrov typed D solution to the Einstein-Maxwell equations is the Kerr-Newman metric.Comment: 14 pages, no figures, submitted to Class. Quantum Gra

A Radiation Scalar for Numerical Relativity

This letter describes a scalar curvature invariant for general relativity with a certain, distinctive feature. While many such invariants exist, this one vanishes in regions of space-time which can be said unambiguously to contain no gravitational radiation. In more general regions which incontrovertibly support non-trivial radiation fields, it can be used to extract local, coordinate-independent information partially characterizing that radiation. While a clear, physical interpretation is possible only in such radiation zones, a simple algorithm can be given to extend the definition smoothly to generic regions of space-time.Comment: 4 pages, 1 EPS figur

Transverse frames for Petrov type I spacetimes: a general algebraic procedure

We develop an algebraic procedure to rotate a general Newman-Penrose tetrad in a Petrov type I spacetime into a frame with Weyl scalars $\Psi_{1}$ and $\Psi_{3}$ equal to zero, assuming that initially all the Weyl scalars are non vanishing. The new frame highlights the physical properties of the spacetime. In particular, in a Petrov Type I spacetime, setting $\Psi_{1}$ and $\Psi_{3}$ to zero makes apparent the superposition of a Coulomb-type effect $\Psi_{2}$ with transverse degrees of freedom $\Psi_{0}$ and $\Psi_{4}$.Comment: 10 pages, submitted to Classical Quantum Gravit

How to measure spatial distances?

The use of time--like geodesics to measure temporal distances is better justified than the use of space--like geodesics for a measurement of spatial distances. We give examples where a ''spatial distance'' cannot be appropriately determined by the length of a space--like geodesic.Comment: 4 pages, latex, no figure

On the back reaction of gravitational and particle emission and absorption from straight thick cosmic strings: A toy model

The emission and absorption of gravitational waves and massless particles of an infinitely long straight cosmic string with finite thickness are studied. It is shown in a general term that the back reaction of the emission and absorption {\em always} makes the symmetry axis of the string singular. The singularity is a scalar singularity and cannot be removed.Comment: To appear in Gen. Relativ. Gra

Ideally embedded space-times

Due to the growing interest in embeddings of space-time in higher-dimensional spaces we consider a specific type of embedding. After proving an inequality between intrinsically defined curvature invariants and the squared mean curvature, we extend the notion of ideal embeddings from Riemannian geometry to the indefinite case. Ideal embeddings are such that the embedded manifold receives the least amount of tension from the surrounding space. Then it is shown that the de Sitter spaces, a Robertson-Walker space-time and some anisotropic perfect fluid metrics can be ideally embedded in a five-dimensional pseudo-Euclidean space.Comment: layout changed and typos corrected; uses revtex

General Relativistic Dynamics of Irrotational Dust: Cosmological Implications

The non--linear dynamics of cosmological perturbations of an irrotational collisionless fluid is analyzed within General Relativity. Relativistic and Newtonian solutions are compared, stressing the different role of boundary conditions in the two theories. Cosmological implications of relativistic effects, already present at second order in perturbation theory, are studied and the dynamical role of the magnetic part of the Weyl tensor is elucidated.Comment: 12 pages , DFPD 93/A/6

Initial Conditions and the Structure of the Singularity in Pre-Big-Bang Cosmology

We propose a picture, within the pre-big-bang approach, in which the universe emerges from a bath of plane gravitational and dilatonic waves. The waves interact gravitationally breaking the exact plane symmetry and lead generically to gravitational collapse resulting in a singularity with the Kasner-like structure. The analytic relations between the Kasner exponents and the initial data are explicitly evaluated and it is shown that pre-big-bang inflation may occur within a dense set of initial data. Finally, we argue that plane waves carry zero gravitational entropy and thus are, from a thermodynamical point of view, good candidates for the universe to emerge from.Comment: 18 pages, LaTeX, epsfig. 3 figures included. Minor changes; paragraph added in the introduction, references added and typos corrected. Final version published in Classical and Quantum Gravit