R. J. Torrence

Perfect fluid perturbations of cosmological spacetimes in Stewart's variables

A formalism suggested by Stewart for the study of perturbations of cosmological spacetimes is applied to the case of isentropic perfect fluid perturbations. Autonomous systems of differential equations for distinct types of perturbations, including gravitational waves, vorticity perturbations, and waves of density perturbations, arise in a natural way.

Linear wave equations as motions on a Toda lattice

A bijection is defined from the set of motions on the infinite Toda lattice of strings to a set of sequences of linear wave equations in 1+1 dimensions, the sequences being generated by a generalisation of the classical Darboux map. The bijection is applied to find probably all such wave equations for which characteristic initial data propagate without spreading.

Conformal invariance under spatial inversion of extreme Reissner-Nordström black holes

The extreme Reissner-Nordström geometry is shown to be conformally invariant under a spatial inversion. Generalization of this result to other geometries is briefly discussed.

A class of wave equations with progressive wave solutions of finite order

Abstract We obtain a family of wave equations with progressive wave solutions of finite order that combines and generalizes a subfamily involving the nonreflecting Poschl-Teller potentials and several subfamilies reported by Chang and Janis. The elementary equivalence of some of the known families is derived.

Gauge invariant canonical mechanics for charged particles

The mechanics of charged particle motion is presented in a five‐dimensional form compatible with the five‐dimensional Kaluza theory of the electromagnetic field. Gauge dependence is given an intrinsic geometrical interpretation and the role of generalized momenta is clarified. The theory is a new example of a mechanical system with constraints and offers an interesting exercise in canonical quantization with a nonstandard Poisson bracket.

Asymptotic Behavior of Vacuum Space‐Times

Newman and Penrose have given conditions on the asymptotic form of the Weyl tensor in empty space‐time that are sufficient to insure that the space‐time is asymptotically flat at null infinity and has the peeling property. We give considerably weaker conditions and show them to be sufficient for asymptotic flatness. Under the weaker conditions the asymptotic behavior of the Weyl tensor is more general than the case where the peeling property holds. The asymptotic dependence on a suitably defined radial coordinate is given for the basis null tetrad, the spin coefficients, and the tetrad components of the Weyl tensor.

Note on Kantowski-Sachs spacetimes

It is shown that a portion of de Sitter space can be expressed in the formds2=dt2−A2(t)dr2−B2(t)(dθ2+sin2θdφ2). It follows that it is a Kantowski-Sachs spacetime, according to the usual definition. This disproves the statement sometimes seen in the literature that all Kantowski-Sachs spacetimes are anisotropic.

Wake‐free waves in one and three dimensions

A recent paper by Gottlieb [J. Math. Phys. 29, 2434 (1988)] provides examples of acoustic wave equations, in various dimensions, that have nontrivial families of solutions that are progressing waves of order 1, and relates this to whether or not these equations satisfy Huygens’ principle. A statement made in that paper related to Huygens’ principle in one space dimension is clarified, and it is shown in this connection that, in general, the relationship between the possession of progressing wave solutions and the satisfaction of Huygens’ principle is more complex than the situation described by Gottlieb. In addition, the attractive properties of progressing waves of order 1 are retained by progressing waves of any finite order, and we use this to generalize in several ways Gottlieb’s results on ‘‘wake‐free’’ solutions of the acoustic equation in three dimensions.

Self-adjoint acoustic equations with progressing wave solutions

The simplest wave equations are those whose general solutions comprise progressing waves. The author constructs a comparatively large, possibly exhaustive, family of self-adjoint acoustic equations in 1+1 dimensions that are simple in this sense.

Spherically symmetric space-times transparent to scalar multipole waves

Using nonscattering potentials of Chang and Janis, a large class of spherically symmetric space-times is constructed on which all multipole solutions to the minimally coupled scalar wave equation are expressible in terms of characteristic data functions in essentially as simple a fashion as for flat space-time. The space-times are transparent to multipole waves in the same sense that flat space-time is. Both conformally flat and not conformally flat space-times are obtained. Some examples are discussed which show that the variety of transparent space-times is large even within the class of Robertson-Walker spaces.