Conserved quantities and the formation of black holes in the Brans-Dicke theory of gravitation

In Part I, we construct a symmetric stress-energy-momentum pseudo-tensor for the gravitational fields of Brans-Dicke theory, and use this to establish rigorously conserved integral expressions for energy-momentum Pⁱ and angular momentum J^ik. Application of the two-dimensional surface integrals to the exact static spherical vacuum solution of Brans leads to an identification of our conserved mass with the active gravitational mass. Application to the distant fields of an arbitrary stationary source reveals that Pⁱ and J^ik have the same physical interpretation as in general relativity. For gravitational waves whose wavelength is small on the scale of the background radius of curvature, averaging over several wavelengths in the Brill-Hartle-Isaacson manner produces a stress-energy-momentum tensor for gravitational radiation which may be used to calculate the changes in Pⁱ and J^ik of their source.

In Part II, we develop strong evidence in favor of a conjecture by Penrose--that, in the Brans-Dicke theory, relativistic gravitational collapse in three dimensions produce black holes identical to those of general relativity. After pointing out that any black hole solution of general relativity also satisfies Brans-Dicke theory, we establish the Schwarzschild and Kerr geometries as the only possible spherical and axially symmetric black hole exteriors, respectively. Also, we show that a Schwarzschild geometry is necessarily formed in the collapse of an uncharged sphere.

Appendices discuss relationships among relativistic gravity theories and an example of a theory in which black holes do not exist.

Stranger than fiction. [electronic resource] By the Rev. J.J. Halcombe

http://digilib.bu.edu/archive/strangerthanfict00halcrich/strangerthanfict00halcrich.djvu

Measurement of Wave Attenuation in Buried Plastic Water Distribution Pipes

Leaks in pipes are a common issue encountered in the water industry. Acoustic methods are generally successful in finding and locating leaks in metallic pipes, however, they are less effective when applied to plastic pipes. This is because leak-noise signals are heavily attenuated due to high damping in the pipe-wall and sound radiation into the soil. As result, high frequency leak noise does not travel long distances. To determine how far leak noise may travel in a pipe at any frequency, the attenuation of the wave responsible for leak noise propagation should be known. In this paper a new method to estimate this is described. The method is then applied to some measurements made on a bespoke pipe-test rig in the UK, and the results are compared with theoretical predictions.