A Non - Singular Cosmological Model with Shear and Rotation

We have investigated a non-static and rotating model of the universe with an imperfect fluid distribution. It is found that the model is free from singularity and represents an ever expanding universe with shear and rotation vanishing for large value of time.Comment: 10 pages, late

Further results on non-diagonal Bianchi type III vacuum metrics

We present the derivation, for these vacuum metrics, of the Painlev\'e VI equation first obtained by Christodoulakis and Terzis, from the field equations for both minkowskian and euclidean signatures. This allows a complete discussion and the precise connection with some old results due to Kinnersley. The hyperk\"ahler metrics are shown to belong to the Multi-Centre class and for the cases exhibiting an integrable geodesic flow the relevant Killing tensors are given. We conclude by the proof that for the Bianchi B family, excluding type III, there are no hyperk\"ahler metrics.Comment: 21 pages, no figure

Towards Canonical Quantum Gravity for G1 Geometries in 2+1 Dimensions with a Lambda--Term

The canonical analysis and subsequent quantization of the (2+1)-dimensional action of pure gravity plus a cosmological constant term is considered, under the assumption of the existence of one spacelike Killing vector field. The proper imposition of the quantum analogues of the two linear (momentum) constraints reduces an initial collection of state vectors, consisting of all smooth functionals of the components (and/or their derivatives) of the spatial metric, to particular scalar smooth functionals. The demand that the midi-superspace metric (inferred from the kinetic part of the quadratic (Hamiltonian) constraint) must define on the space of these states an induced metric whose components are given in terms of the same states, which is made possible through an appropriate re-normalization assumption, severely reduces the possible state vectors to three unique (up to general coordinate transformations) smooth scalar functionals. The quantum analogue of the Hamiltonian constraint produces a Wheeler-DeWitt equation based on this reduced manifold of states, which is completely integrated.Comment: Latex 2e source file, 25 pages, no figures, final version (accepted in CQG

Essential Constants for Spatially Homogeneous Ricci-flat manifolds of dimension 4+1

The present work considers (4+1)-dimensional spatially homogeneous vacuum cosmological models. Exact solutions -- some already existing in the literature, and others believed to be new -- are exhibited. Some of them are the most general for the corresponding Lie group with which each homogeneous slice is endowed, and some others are quite general. The characterization ``general'' is given based on the counting of the essential constants, the line-element of each model must contain; indeed, this is the basic contribution of the work. We give two different ways of calculating the number of essential constants for the simply transitive spatially homogeneous (4+1)-dimensional models. The first uses the initial value theorem; the second uses, through Peano's theorem, the so-called time-dependent automorphism inducing diffeomorphismsComment: 26 Pages, 2 Tables, latex2

Vacuum Plane Waves in 4+1 D and Exact solutions to Einstein's Equations in 3+1 D

In this paper we derive homogeneous vacuum plane-wave solutions to Einstein's field equations in 4+1 dimensions. The solutions come in five different types of which three generalise the vacuum plane-wave solutions in 3+1 dimensions to the 4+1 dimensional case. By doing a Kaluza-Klein reduction we obtain solutions to the Einstein-Maxwell equations in 3+1 dimensions. The solutions generalise the vacuum plane-wave spacetimes of Bianchi class B to the non-vacuum case and describe spatially homogeneous spacetimes containing an extremely tilted fluid. Also, using a similar reduction we obtain 3+1 dimensional solutions to the Einstein equations with a scalar field.Comment: 16 pages, no figure

Monotonic functions in Bianchi models: Why they exist and how to find them

All rigorous and detailed dynamical results in Bianchi cosmology rest upon the existence of a hierarchical structure of conserved quantities and monotonic functions. In this paper we uncover the underlying general mechanism and derive this hierarchical structure from the scale-automorphism group for an illustrative example, vacuum and diagonal class A perfect fluid models. First, kinematically, the scale-automorphism group leads to a reduced dynamical system that consists of a hierarchy of scale-automorphism invariant sets. Second, we show that, dynamically, the scale-automorphism group results in scale-automorphism invariant monotone functions and conserved quantities that restrict the flow of the reduced dynamical system.Comment: 26 pages, replaced to match published versio

Towards Canonical Quantum Gravity for Geometries Admitting Maximally Symmetric Two-dimensional Surfaces

The 3+1 (canonical) decomposition of all geometries admitting two-dimensional space-like surfaces is exhibited. A proposal consisting of a specific re-normalization {\bf Assumption} and an accompanying {\bf Requirement} is put forward, which enables the canonical quantization of these geometries. The resulting Wheeler-deWitt equation is based on a re-normalized manifold parameterized by three smooth scalar functionals. The entire space of solutions to this equation is analytically given, exploiting the freedom left by the imposition of the {\bf Requirement} and contained in the third functional.Comment: 27 pages, no figures, LaTex2e source fil

Trace Anomaly and Backreaction of the Dynamical Casimir Effect

The Casimir energy for massless scalar field which satisfies priodic boundary conditions in two-dimensional domain wall background is calculated by making use of general properties of renormalized stress-tensor. The line element of domain wall is time dependent, the trace anomaly which is the nonvanishing $T^{\mu}_{\mu}$ for a conformally invariant field after renormalization, represent the back reaction of the dynamical Casimir effect.Comment: 8 pages, no figures, typos corrected, discussion added, has been accepted for the publication in GR

Some remarks on Bianchi type-II, VIII and IX models

Within the scope of anisotropic non-diagonal Bianchi type-II, VIII and IX spacetime it is shown that the off-diagonal components of the corresponding metric impose severe restrictions on the components of the energy momentum tensor in general. If the energy momentum tensor is considered to be diagonal one, the spacetime, expect a partial case of BII, becomes locally rotationally symmetric.Comment: 8 page

Salvage chemotherapy with high-dose leucovorin (LV) and 48-hour continuous infusion (CI) of 5-fluorouracil (5-FU) in combination with conventional doses of cyclophosphamide (CPM) in patients with metastatic breast cancer (MBC) pretreated with anthracycline and taxanes

The purpose of this study was to evaluate the activity and tolerance of high-dose leucovorin (LV) and infusional 5-fluorouracil (5-FU) in combination with conventional doses of cyclophosphamide (CPM) as salvage chemotherapy in patients with metastatic breast cancer (MBC) pretreated with anthracyclines and taxanes. 41 patients (median age 59 years) with MBC refractory or resistant to anthracyclines and taxanes were enrolled. The patients' performance status (WHO) was 0 in 10 patients (24%), 1 in 22 (54%), and 2 in 9 (22%). 30 (73%) patients had received 2 or more prior chemotherapy regimens. Cyclophosphamide (600 mg m−2) was given i.v. bolus on day 1 and LV (500 mg m−2 d−1) as a 2-h infusion followed by 5-FU (1.5 g m−2 d−1) over a 22 h c.i. for 2 consecutive days. Cyclophosphamide was administered every 28 days while 5-FU/LV every 14 days. In an intention-to-treat analysis, complete response (CR) was achieved in 2 (4.9%) patients and partial response (PR) in 9 (22%) (overall response rate 26.9%; 95% CI: 13.27–40.39%). Stable disease (SD) and progressive disease (PD) were observed in 9 (22%) and 21 (51%) patients, respectively. The overall response rate was 6% and 40% in patients with primary and secondary resistance to anthracyclines/taxanes, respectively (P = 0.047). The median duration of response and the median time to disease progression was 8 and 9.5 months, respectively. The median overall survival was 13 months and the probability for 1-year survival 51%. Grade 3/4 neutropenia occurred in 9 (22%) patients and 4 (9%) patients developed grade 3/4 thrombocytopenia. Non-haematological toxicity was mild. There were no cases of febrile neutropenia, toxic deaths or treatment-related hospital admissions due to toxicity. The combination of high-dose 5-FU/LV with conventional doses of cyclophosphamide is a well tolerated and effective salvage regimen in patients with MBC heavily pretreated with both anthracyclines and taxanes. © 2001 Cancer Research Campaignhttp://www.bjcancer.comhttp://www.bjcancer.co