On limits of spacetimes -- a coordinate-free approach

A coordinate-free approach to limits of spacetimes is developed. The limits of the Schwarzschild metric as the mass parameter tends to 0 or $\infty$ are studied, extending previous results. Besides the known Petrov type D and 0 limits, three vacuum plane-wave solutions of Petrov type N are found to be limits of the Schwarzschild spacetime.Comment: 19 p

All spacetimes with vanishing curvature invariants

All Lorentzian spacetimes with vanishing invariants constructed from the Riemann tensor and its covariant derivatives are determined. A subclass of the Kundt spacetimes results and we display the corresponding metrics in local coordinates. Some potential applications of these spacetimes are discussed.Comment: 24 page

Killing Tensors and Conformal Killing Tensors from Conformal Killing Vectors

Koutras has proposed some methods to construct reducible proper conformal Killing tensors and Killing tensors (which are, in general, irreducible) when a pair of orthogonal conformal Killing vectors exist in a given space. We give the completely general result demonstrating that this severe restriction of orthogonality is unnecessary. In addition we correct and extend some results concerning Killing tensors constructed from a single conformal Killing vector. A number of examples demonstrate how it is possible to construct a much larger class of reducible proper conformal Killing tensors and Killing tensors than permitted by the Koutras algorithms. In particular, by showing that all conformal Killing tensors are reducible in conformally flat spaces, we have a method of constructing all conformal Killing tensors (including all the Killing tensors which will in general be irreducible) of conformally flat spaces using their conformal Killing vectors.Comment: 18 pages References added. Comments and reference to 2-dim case. Typos correcte

Geodesic motion in the Kundt spacetimes and the character of envelope singularity

We investigate geodesics in specific Kundt type N (or conformally flat) solutions to Einstein's equations. Components of the curvature tensor in parallelly transported tetrads are then explicitly evaluated and analyzed. This elucidates some interesting global properties of the spacetimes, such as an inherent rotation of the wave-propagation direction, or the character of singularities. In particular, we demonstrate that the characteristic envelope singularity of the rotated wave-fronts is a (non-scalar) curvature singularity, although all scalar invariants of the Riemann tensor vanish there.Comment: 21 pages, 3 figures. To appear in Class. Quantum Gra

Self-Similarity in General Relativity \endtitle

The different kinds of self-similarity in general relativity are discussed, with special emphasis on similarity of the ``first'' kind, corresponding to spacetimes admitting a homothetic vector. We then survey the various classes of self-similar solutions to Einstein's field equations and the different mathematical approaches used in studying them. We focus mainly on spatially homogenous and spherically symmetric self-similar solutions, emphasizing their possible roles as asymptotic states for more general models. Perfect fluid spherically symmetric similarity solutions have recently been completely classified, and we discuss various astrophysical and cosmological applications of such solutions. Finally we consider more general types of self-similar models.Comment: TeX document, 53 page

Nonvanishing Local Scalar Invariants even in VSI Spacetimes with all Polynomial Curvature Scalar Invariants Vanishing

VSI (`vanishing scalar invariant') spacetimes have zero values for all total scalar contractions of all polynomials in the Riemann tensor and its covariant derivatives. However, there are other ways of concocting local scalar invariants (nonpolynomial) from the Riemann tensor that need not vanish even in VSI spacetimes, such as Cartan invariants. Simple examples are given that reduce to the squared amplitude for a linearized monochromatic plane gravitational wave. These nonpolynomial local scalar invariants are also evaluated for non-VSI spacetimes such as Schwarzschild and Kerr and are estimated near the surface of the earth. Similar invariants are defined for null fluids and for electromagnetic fields.Comment: 9 pages, LaTeX, proofread version accepted 2009 January 14 for publication in Classical and Quantum Gravit

Automated office blood pressure measurements in primary care are misleading in more than one third of treated hypertensives: The VALENTINE-Greece Home Blood Pressure Monitoring study

Abstract Background This study assessed the diagnostic reliability of automated office blood pressure (OBP) measurements in treated hypertensive patients in primary care by evaluating the prevalence of white coat hypertension (WCH) and masked uncontrolled hypertension (MUCH) phenomena. Methods Primary care physicians, nationwide in Greece, assessed consecutive hypertensive patients on stable treatment using OBP (1 visit, triplicate measurements) and home blood pressure (HBP) measurements (7 days, duplicate morning and evening measurements). All measurements were performed using validated automated devices with bluetooth capacity (Omron M7 Intelli-IT). Uncontrolled OBP was defined as ≥140/90 mmHg, and uncontrolled HBP was defined as ≥135/85 mmHg. Results A total of 790 patients recruited by 135 doctors were analyzed (age: 64.5 ± 14.4 years, diabetics: 21.4%, smokers: 20.6%, and average number of antihypertensive drugs: 1.6 ± 0.8). OBP (137.5 ± 9.4/84.3 ± 7.7 mmHg, systolic/diastolic) was higher than HBP (130.6 ± 11.2/79.9 ± 8 mmHg; difference 6.9 ± 11.6/4.4 ± 7.6 mmHg, p Conclusions In primary care, automated OBP measurements are misleading in approximately 40% of treated hypertensive patients. HBP monitoring is mandatory to avoid overtreatment of subjects with WCH phenomenon and prevent undertreatment and subsequent excess cardiovascular disease in MUCH

Fulvestrant-induced expression of ErbB3 and ErbB4 receptors sensitizes oestrogen receptor-positive breast cancer cells to heregulin β1

Introduction We have previously reported that induction of epidermal growth factor receptor and ErbB2 in response to antihormonal agents may provide an early mechanism to allow breast cancer cells to evade the growth-inhibitory action of such therapies and ultimately drive resistant cell growth. More recently, the other two members of the ErbB receptor family, ErbB3 and ErbB4, have been implicated in antihormone resistance in breast cancer. In the present study, we have investigated whether induction of ErbB3 and/or ErbB4 may provide an alternative resistance mechanism to antihormonal action in a panel of four oestrogen receptor (ER)-positive breast cancer cell lines. Methods MCF-7, T47D, BT474 and MDAMB361 cell lines were exposed to fulvestrant (100 nM) for seven days, and effects on ErbB3/4 expression and signalling, as well as on cell growth, were assessed. Effects of heregulin β1 (HRGβ1) were also examined in the absence and presence of fulvestrant to determine the impact of ER blockade on the capacity of this ErbB3/4 ligand to promote signalling and cell proliferation. Results Fulvestrant potently reduced ER expression and transcriptional activity and significantly inhibited growth in MCF-7, T47D, BT474 and MDAMB361 cells. However, alongside this inhibitory activity, fulvestrant also consistently induced protein expression and activity of ErbB3 in MCF-7 and T47D cells and ErbB4 in BT474 and MDAMB361 cell lines. Consequently, fulvestrant treatment sensitised all cell lines to the actions of the ErbB3/4 ligand HRGβ1 with enhanced ErbB3/4-driven signalling activity, reexpression of cyclin D1 and significant increases in cell proliferation being observed when compared to untreated cells. Indeed, in T47D and MDAMB361 HRGβ1 was converted from a ligand having negligible or suppressive growth activity into one that potently promoted cell proliferation. Consequently, fulvestrant-mediated growth inhibition was completely overridden by HRGβ1 in all four cell lines. Conclusions These findings suggest that although antihormones such as fulvestrant may have potent acute growth-inhibitory activity in ER-positive breast cancer cells, their ability to induce and sensitise cells to growth factors may serve to reduce and ultimately limit their inhibitory activity

Concerns about anti-angiogenic treatment in patients with glioblastoma multiforme

BACKGROUND: The relevance of angiogenesis inhibition in the treatment of glioblastoma multiforme (GBM) should be considered in the unique context of malignant brain tumours. Although patients benefit greatly from reduced cerebral oedema and intracranial pressure, this important clinical improvement on its own may not be considered as an anti-tumour effect. DISCUSSION: GBM can be roughly separated into an angiogenic component, and an invasive or migratory component. Although this latter component seems inert to anti-angiogenic therapy, it is of major importance for disease progression and survival. We reviewed all relevant literature. Published data support that clinical symptoms are tempered by anti-angiogenic treatment, but that tumour invasion continues. Unfortunately, current imaging modalities are affected by anti-angiogenic treatment too, making it even harder to define tumour margins. To illustrate this we present MRI, biopsy and autopsy specimens from bevacizumab-treated patients. Moreover, while treatment of other tumour types may be improved by combining chemotherapy with anti-angiogenic drugs, inhibiting angiogenesis in GBM may antagonise the efficacy of chemotherapeutic drugs by normalising the blood-brain barrier function. SUMMARY: Although angiogenesis inhibition is of considerable value for symptom reduction in GBM patients, lack of proof of a true anti-tumour effect raises concerns about the place of this type of therapy in the treatment of GBM