Are classically singular spacetimes quantum mechanically singular as well?

Are the classical singularities of general relativistic spacetimes, normally defined by the incompleteness of classical particle paths, still singular if quantum mechanical particles are used instead? This is the question we will attempt to answer for particles obeying the quantum mechanical wave equations for scalar, null vector and spinor particles. The analysis will be restricted to certain static general relativistic spacetimes that classically contain the mildest true classical singularities, quasiregular singularities.Comment: 3 pages, no figures, submitted to the Proceedings of the Tenth Marcel Grossmann Meeting on General Relativity, Rio de Janeiro, July 20-26, 200

Spectral Geometry and One-loop Divergences on Manifolds with Conical Singularities

Geometrical form of the one-loop divergences induced by conical singularities of background manifolds is studied. To this aim the heat kernel asymptotic expansion on spaces having the structure $C_{\alpha}\times \Sigma$ near singular surface $\Sigma$ is analysed. Surface corrections to standard second and third heat coefficients are obtained explicitly in terms of angle $\alpha$ of a cone $C_{\alpha}$ and components of the Riemann tensor. These results are compared to ones to be already known for some particular cases. Physical aspects of the surface divergences are shortly discussed.Comment: preprint DSF-13/94, 13 pages, latex fil

Inhibition of the hERG Potassium Channel by a Methanesulphonate-Free E-4031 Analogue

hERG (human Ether-à-go-go Related Gene)-encoded potassium channels underlie the cardiac rapid delayed rectifier (IKr) potassium current, which is a major target for antiarrhythmic agents and diverse non-cardiac drugs linked to the drug-induced form of long QT syndrome. E-4031 is a high potency hERG channel inhibitor from the methanesulphonanilide drug family. This study utilized a methanesulphonate-lacking E-4031 analogue, “E-4031-17”, to evaluate the role of the methanesulphonamide group in E-4031 inhibition of hERG. Whole-cell patch-clamp measurements of the hERG current (IhERG) were made at physiological temperature from HEK 293 cells expressing wild-type (WT) and mutant hERG constructs. For E-4031, WT IhERG was inhibited by a half-maximal inhibitory concentration (IC50) of 15.8 nM, whilst the comparable value for E-4031-17 was 40.3 nM. Both compounds exhibited voltage- and time-dependent inhibition, but they differed in their response to successive applications of a long (10 s) depolarisation protocol, consistent with greater dissociation of E-4031-17 than the parent compound between applied commands. Voltage-dependent inactivation was left-ward voltage shifted for E-4031 but not for E-4031-17; however, inhibition by both compounds was strongly reduced by attenuated-inactivation mutations. Mutations of S6 and S5 aromatic residues (F656V, Y652A, F557L) greatly attenuated actions of both drugs. The S624A mutation also reduced IhERG inhibition by both molecules. Overall, these results demonstrate that the lack of a methanesulphonate in E-4031-17 is not an impediment to high potency inhibition of IhERG

Vacuum Polarization in the Spacetime of a Scalar-Tensor Cosmic String

We study the vacuum polarization effect in the spacetime generated by a magnetic flux cosmic string in the framework of a scalar-tensor gravity. The vacuum expectation values of the energy-momentum tensor of a conformally coupled scalar field are calculated. The dilaton's contribution to the vacuum polarization effect is shown explicitly.Comment: 11 pages, LATEX file, 2 eps figure

Particle Creation If a Cosmic String Snaps

We calculate the Bogolubov coefficients for a metric which describes the snapping of a cosmic string. If we insist on a matching condition for all times {\it and} a particle interpretation, we find no particle creation.Comment: 10 pages, MRC.PH.17/9

Semiclassical gravitational effects near a singular magnetic flux

We consider the backreaction of the vacuum polarization effect for a massive charged scalar field in the presence of a singular magnetic massless string on the background metric. Using semiclassical approach, we find the first-order (in $\hbar$ units) metric modifications and the corresponding gravitational potential and deficit angle. It is shown that, in certain region of values of coupling constant and magnetic flux, the gravitational potential and deficit angle can be positive as well as negative over all distances from the string and can even change its sign. Unlike the case of massless scalar field, the gravitational corrections were found to have short-range behavior.Comment: 14 pages, 4 figures, journal versio

On higher dimensional Einstein spacetimes with a warped extra dimension

We study a class of higher dimensional warped Einstein spacetimes with one extra dimension. These were originally identified by Brinkmann as those Einstein spacetimes that can be mapped conformally on other Einstein spacetimes, and have subsequently appeared in various contexts to describe, e.g., different braneworld models or warped black strings. After clarifying the relation between the general Brinkmann metric and other more specific coordinate systems, we analyze the algebraic type of the Weyl tensor of the solutions. In particular, we describe the relation between Weyl aligned null directions (WANDs) of the lower dimensional Einstein slices and of the full spacetime, which in some cases can be algebraically more special. Possible spacetime singularities introduced by the warp factor are determined via a study of scalar curvature invariants and of Weyl components measured by geodetic observers. Finally, we illustrate how Brinkmann's metric can be employed to generate new solutions by presenting the metric of spinning and accelerating black strings in five dimensional anti-de Sitter space.Comment: 14 pages, minor changes in the text, mainly in Section 2.

Note on the point-splitting procedure to evaluate vacuum fluctuation in certain cylindrically symmetric backgrounds

We revisit two-point function approaches used to study vacuum fluctuation in wedge-shaped regions and conical backgrounds. Appearance of divergent integrals is discussed and circumvented. The issue is considered in the context of a massless scalar field in cosmic string spacetime.Comment: REVTeX file, 7 page