C J S Clarke

The large-scale bending of cosmic strings

Several theorems are proved relating the growth of spacetime curvature near a cosmic string to its ability to bend on length scales large compared with its diameter. In particular it is shown that the formation of closed loops with smaller than cosmological dimensions is incompatible with the approximation in which all the curvature of the string is confined to its core, with light deflections being given simply by the deficit angle.

On reflecting spacetimes

A survey is given of the properties of reflecting spacetimes, including new results making precise the idea that deleting higher-dimensional sets violates the reflecting condition, and linking the condition with causality violation and singularity formation.

Spherical symmetry does not imply a direct product

An example is given of a spacetime with an isometry group having spherical orbits but where the spacetime is not the direct product of a typical orbit with an orthogonal 2-space. It is shown that, if a general spacetime is not such a product, then it has a covering space which is.

Numerical relativity on a transputer array

The results of a feasibility study on using a transputer array to obtain a numerical solution of the characteristic initial value problem of general relativity are presented. Codes have been developed for two cases: gravity only, and gravity and matter. The testing of the codes is, so far, very limited, but timing results etc. are presented thus giving an indication of the expected performance.

'Elementary flatness' on a symmetry axis

The conditions of elementary flatness, trivial behaviour under parallel propagation of frames, and regularity to various degrees of differentiability, are given precise definitions and related to practical criteria. As an example, their relations are explored in the case of cylindrically symmetrical stationary dust.

Combining Cauchy and characteristic numerical evolutions in curved coordinates

In numerical relativity there would seem to be considerable advantages in combining Cauchy and characteristic methods in different regions of spacetime. Numerical experiments demonstrate, for the model problem of the scalar wave equation in flat space using general null coordinates, that there are no unforseen problems with the interface between the two regions.

A rigidity result on the ideal boundary structure of smooth spacetimes

Following a survey of the abstract boundary definition of Scott and Szekeres, a rigidity result is proved for the smooth case, showing that the topological structure of the regular part of this boundary in defined invariantly.

The global structure of the Bell-Szekeres solution

It is shown that, apart from the impulse waves themselves, the Bell-Szekeres solution has no curvature singularities. Extensions are found in which the only singularity off the impulse wave is of a quasiregular covering-space type. The global structure found is thus quite different from that found by other authors for related solutions.

The existence of Newtonian dust caustics

We prove a rigorous existence theorem in the case of one-dimensional Newtonian gravity for a pressureless fluid, in which a caustic separates a single-fluid region from a region with three superimposed fluid flows. This is of interest both for the shell crossing singularities of general relativity and for models of galaxy formation.

Cooling off with physics

You might think of ice cream as a delicious treat to be enjoyed on a sunny summers day. However, to the ice-cream scientists who recently gathered in Thessaloniki in Greece for the 2nd International Ice Cream Symposium, it is a complex composite material. Ice cream consists of three dispersed phases: ice crystals, which have a mean size of 50 μm, air bubbles with a diameter of about 70 μm, and fat droplets with a size of 1 μm. These phases are held together by what is called the matrix – not a sci-fi film, but a viscous solution of sugars, milk proteins and polysaccharides.