Colliding axisymmetric pp-waves

An exact solution is found describing the collision of axisymmetric pp-waves with M=0. They are impulsive in character and their coordinate singularities become point curvature singularities at the boundaries of the interaction region. The solution is conformally flat. Concrete examples are given, involving an ultrarelativistic black hole against a burst of pure radiation or two colliding beam- like waves.Comment: 6 pages, REVTeX, some misprints are correcte

Lathe converted for grinding aspheric surfaces

A standard overarm tracing lathe converted by the addition of an independently driven diamond grinding wheel is used for grinding aspheric surfaces. The motion of the wheel is controlled by the lathe air tracer following the template which produces the desired aspheric profile

On the extension of the concept of Thin Shells to The Einstein-Cartan Theory

This paper develops a theory of thin shells within the context of the Einstein-Cartan theory by extending the known formalism of general relativity. In order to perform such an extension, we require the general non symmetric stress-energy tensor to be conserved leading, as Cartan pointed out himself, to a strong constraint relating curvature and torsion of spacetime. When we restrict ourselves to the class of space-times satisfying this constraint, we are able to properly describe thin shells and derive the general expression of surface stress-energy tensor both in its four-dimensional and in its three-dimensional intrinsic form. We finally derive a general family of static solutions of the Einstein-Cartan theory exhibiting a natural family of null hypersurfaces and use it to apply our formalism to the construction of a null shell of matter.Comment: Latex, 21 pages, 1 combined Latex/Postscript figure; Accepted for publication in Classical and Quantum Gravit

Mixmaster Behavior in Inhomogeneous Cosmological Spacetimes

Numerical investigation of a class of inhomogeneous cosmological spacetimes shows evidence that at a generic point in space the evolution toward the initial singularity is asymptotically that of a spatially homogeneous spacetime with Mixmaster behavior. This supports a long-standing conjecture due to Belinskii et al. on the nature of the generic singularity in Einstein's equations.Comment: 4 pages plus 4 figures. A sentence has been deleted. Accepted for publication in PR

An Exact String Theory Model of Closed Time-Like Curves and Cosmological Singularities

We study an exact model of string theory propagating in a space-time containing regions with closed time-like curves (CTCs) separated from a finite cosmological region bounded by a Big Bang and a Big Crunch. The model is an non-trivial embedding of the Taub-NUT geometry into heterotic string theory with a full conformal field theory (CFT) definition, discovered over a decade ago as a heterotic coset model. Having a CFT definition makes this an excellent laboratory for the study of the stringy fate of CTCs, the Taub cosmology, and the Milne/Misner-type chronology horizon which separates them. In an effort to uncover the role of stringy corrections to such geometries, we calculate the complete set of alpha' corrections to the geometry. We observe that the key features of Taub-NUT persist in the exact theory, together with the emergence of a region of space with Euclidean signature bounded by time-like curvature singularities. Although such remarks are premature, their persistence in the exact geometry is suggestive that string theory theory is able to make physical sense of the Milne/Misner singularities and the CTCs, despite their pathological character in General Relativity. This may also support the possibility that CTCs may be viable in some physical situations, and may be a natural ingredient in pre-Big-Bang cosmological scenarios.Comment: 37 pages, 4 figures. V2: discussion of computation of metric refined, references adde

Nuttier (A)dS Black Holes in Higher Dimensions

We construct new solutions of the vacuum Einstein field equations with cosmological constant. These solutions describe spacetimes with non-trivial topology that are asymptotically dS, AdS or flat. For a negative cosmological constant these solutions are NUT charged generalizations of the topological black hole solutions in higher dimensions. We also point out the existence of such NUT charged spacetimes in odd dimensions and we explicitly construct such spaces in 5 and 7 dimensions. The existence of such spacetimes with non-trivial topology is closely related to the existence of the cosmological constant. Finally, we discuss the global structure of such solutions and possible applications in string theory.Comment: latex, 30 pages, added reference

Action functionals for relativistic perfect fluids

Action functionals describing relativistic perfect fluids are presented. Two of these actions apply to fluids whose equations of state are specified by giving the fluid energy density as a function of particle number density and entropy per particle. Other actions apply to fluids whose equations of state are specified in terms of other choices of dependent and independent fluid variables. Particular cases include actions for isentropic fluids and pressureless dust. The canonical Hamiltonian forms of these actions are derived, symmetries and conserved charges are identified, and the boundary value and initial value problems are discussed. As in previous works on perfect fluid actions, the action functionals considered here depend on certain Lagrange multipliers and Lagrangian coordinate fields. Particular attention is paid to the interpretations of these variables and to their relationships to the physical properties of the fluid.Comment: 40 pages, plain Te

Taub--NUT Dyons in Heterotic String Theory

Starting with the Taub--NUT solution to Einstein's equations, together with a constant dilaton, a dyonic Taub--NUT solution of low energy heterotic string theory with non--trivial dilaton, axion and $U(1)$ gauge fields is constructed by employing $O(1,1)$ transformations. The electromagnetic dual of this solution is constructed, using SL(2,\rline) transformations. By an appropriate change to scaled variables, the extremal limit of the dual solution is shown to correspond to the low energy limit of an exact conformal field theory presented previously.Comment: 16 pages (plain TEX), (Revised version has curvature singularities correctly identified), IASSNS-HEP-94/50, McGill/94-2

Lense-Thirring Precession in Pleba\'nski-Demia\'nski spacetimes

An exact expression of Lense-Thirring precession rate is derived for non-extremal and extremal Pleba\'nski-Demia\'nski spacetimes. This formula is used to find the exact Lense-Thirring precession rate in various axisymmetric spacetimes, like: Kerr, Kerr-Newman, Kerr-de Sitter etc. We also show, if the Kerr parameter vanishes in Pleba\'nski-Demia\'nski(PD) spacetime, the Lense-Thirring precession does not vanish due to the existence of NUT charge. To derive the LT precession rate in extremal Pleba\'nski-Demia\'nski we first derive the general extremal condition for PD spacetimes. This general result could be applied to get the extremal limit in any stationary and axisymmetric spacetimes.Comment: 9 pages, Some special modifications are mad

New Algorithm for Mixmaster Dynamics

We present a new numerical algorithm for evolving the Mixmaster spacetimes. By using symplectic integration techniques to take advantage of the exact Taub solution for the scattering between asymptotic Kasner regimes, we evolve these spacetimes with higher accuracy using much larger time steps than previously possible. The longer Mixmaster evolution thus allowed enables detailed comparison with the Belinskii, Khalatnikov, Lifshitz (BKL) approximate Mixmaster dynamics. In particular, we show that errors between the BKL prediction and the measured parameters early in the simulation can be eliminated by relaxing the BKL assumptions to yield an improved map. The improved map has different predictions for vacuum Bianchi Type IX and magnetic Bianchi Type VI$_0$ Mixmaster models which are clearly matched in the simulation.Comment: 12 pages, Revtex, 4 eps figure