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A theorem due to

We show that a positive energy argument of Geroch can be modified to rule out a possible class of counterexamples to the cosmic censor hypothesis proposed by Penrose.

We use the stress-energy tensor and the associated energy-momentum conservation to study the interactions between two widely separated monopoles (or monopole and antimonopole). By defining a set of minimal conditions to represent the above systems, we show how the problem reduced mathematically to a known electrostatic problem. The force between the monopoles (or monopole and antimonopole) is then, to the leading order, the expected repulsive (attractive) Coulomb force. We also discuss how the Prasad-Sommerfield limit alters the problem, leading to twice the Coulomb force between a monopole and antimonopole and zero force between two monopoles.

For initial data sets which represent charged black holes we prove some inequalities which relate the total energy, the total charge, and the size of the black hole. One of them is a necessary condition for the validity of cosmic censorship.

We show that the positive energy argument of Geroch for time-symmetric initial data sets can be generalized to general initial data sets.

Several experiments have suggested that streamwise vortices, with their accompany-ing low-momentum streaks in a turbulent boundary layer have a characteristic spanwise wavelength of approximately λz+ = 100. Here a mechanism is proposed which selects a comparable spanwise wavelength and produces counter-rotating streamwise vortices in a turbulent boundary layer. Examining the equations which describe the deviation of the velocity field from its time-average, it is found that a resonance (Benney & Gustavsson 1981), is associated with the mean-velocity profile. As an integral part of this resonance, there is a mean secondary flow which has a spanwise wavelength λz+ = 90 and whose velocities exhibit a streamwise vortex structure similar to those observed.

No abstract