The vacuum stress-energy tensor for a conformal scalar field in the exterior spacetime of straight cosmic string is calculated. traceless, falls off as fourth power distance from string, and proportional to linear mass density ${c}^{2}$\ensuremath{\mu}/G physically reasonable case \ensuremath{\mu}\ensuremath{\ll}1. energy arising fluctuations small compared with mass-energy itself. A quasiregular singularity which appears (1/4)(1/2) shown be unstable consequence divergent fluctuations.

The effects of vacuum polarization on the mildest possible sort cosmological singularity, Taub-NUT (Newman-Unti-Tamburino)-type singularities, are studied. Unlike stronger sorts singularities where physical quantities (e.g., curvature, energy density) diverge, in these universes only barrier is a pathological topology. Quantum effects, known to be important regions large spacetime found also universes, curvature may arbitrarily small or even zero. expectation value stress-energy tensor for...

Quantum singularities in general relativistic spacetimes are determined by the behaviour of quantum test particles. A static spacetime is mechanically singular if spatial portion wave operator not essentially self-adjoint. Here Weyl's limit point–limit circle criterion used to determine whether a This then applied scalar packets Levi-Civita help elucidate physical properties terms their metric parameters.

The stability properties of a class spacetimes with quasiregular singularities is discussed. Quasiregular are the end points incomplete, inextendible geodesics at which Riemann tensor and its derivatives remain least bounded in all parallel-propagated orthonormal (PPON) frames; observers approaching such singularity would find that their world lines come to an finite proper time. Taub-NUT (Newman-Unti-Tamburino)-type cosmologies investigated...

The definition of quantum singularity is extended from static space-times to conformally space-times. After the usual definitions classical and singularities are reviewed, examples in given. These include asymptotically power-law space-times, with diverging higher-order differential invariants, a space-time 2-sphere singularity. theory behind followed by an example, Friedmann-Robertson-Walker cosmic string. paper concludes discussing areas future research.

A definition of quantum singularity for the case static spacetimes has recently been extended to conformally spacetimes. Here theory behind singularities in is reviewed and then applied a class spherically symmetric, spacetimes, including as special cases those studied by Roberts, Fonarev, Husain et al. We use solutions generally coupled, massless Klein-Gordon equation test fields. In this way we find ranges metric parameters coupling coefficients which classical timelike these are healed...

We study a broad class of spacetimes whose metric coefficients reduce to powers radius r in the limit small r. Among these four-parameter 'power-law' metrics, we identify those parameters for which have classical singularities as → 0. show that large set such classically-singular is nevertheless non-singular quantum mechanically, Hamiltonian operator essentially self-adjoint, so evolution wave packets lacks ambiguity associated with scattering off singularities. Using broadest yet studied...

A stability conjecture previously developed to investigate quasiregular and nonscalar curvature singularities is extended here cover the of Cauchy horizons. In particular, Reissner-Nordstr\"om spacetime charged, nonrotating black holes considered. The predicts that addition infalling null dust with a power-law tail will produce singularity at horizon. This prediction verified using Reissner-Nordstr\"om-Vaidya studied by Hiscock. also combination outgoing scalar mass inflation results Poisson...

A previously developed Cauchy horizon stability conjecture is used to investigate the of in Kerr geometry when various fields are introduced. In particular, effects an electromagnetic field, infalling null dust, and combined outgoing dust studied. Stability predictions made one case verified. The nature any resulting singularities predicted.

The definitions of classical and quantum singularities are reviewed. Examples given both as well their utility in general relativity. In particular, the singularity structure certain interesting conformally static spherically symmetric spacetimes modeling scalar field collapse include Roberts spacetime, Husain-Martinez-Nuñez spacetime Fonarev spacetime. importance understanding is discussed.

Cosmic strings are very long, thin structures which might stretch over vast reaches of the universe. If they exist, would have been formed during phase transitions in early The space-time surrounding a straight cosmic string is flat but nontrivial: A two-dimensional spatial section cone rather than plane. This feature leads to unique gravitational effects. flatness means that many effects can be understood with no mathematics beyond trigonometry. includes observational predictions double...

Singularities in colliding gravitational plane-wave spacetimes are studied. In addition to scalar curvature singularities, delta -function and sandwich shown possess quasiregular singularities while thick non-scalar singularities. It is argued that these unstable. Scalar wave perturbations of the impulsive spacetime support this result.

The definitions of classical and quantum singularities in general relativity are reviewed. occurence mechanical certain spherically symmetric cylindrically (including infinite line mass)spacetimes is considered. A strong repulsive ``potential'' near the singularity shown to turn a classically singular spacetime into mechanically nonsingular spacetime.

An improved stability conjecture for Cauchy horizons is presented. The predicts the of based upon behavior test fields, and in case instability it also nature singularities produced. results Reissner-Nordstr\"om, Kerr, Reissner-Nordstr\"om-de Sitter, Kerr-de anti-de a type V LRS spacetime are reviewed. A new prediction made scalar fields Sitter spacetime. agrees with singularity types all cases which exact back reaction solutions have been found.

The behavior of geodesics and test minimally coupled scalar waves on the Bell-Szekeres space-time is used to probe nature quasiregular singularities present. Components stress-energy tensor in a parallel-propagated orthonormal frame diverge as does at singularities. It argued that this divergence makes unstable, converting them into curvature

The definition of quantum singularity is extended from static space-times to conformally space-times. After the usual definitions classical and singularities are reviewed, examples in given. These include asymptotically power-law space-times, with diverging higher-order differential invariants, a space-time 2-sphere singularity. theory behind followed by an example, Friedmann-Robertson-Walker cosmic string. paper concludes discussing areas future research.