On Cyclically Symmetrical Spacetimes

In a recent paper Carot et al. considered the definition of cylindrical symmetry as a specialisation of the case of axial symmetry. One of their propositions states that if there is a second Killing vector, which together with the one generating the axial symmetry, forms the basis of a two-dimensional Lie algebra, then the two Killing vectors must commute, thus generating an Abelian group. In this paper a similar result, valid under considerably weaker assumptions, is derived: any two-dimensional Lie transformation group which contains a one-dimensional subgroup whose orbits are circles, must be Abelian. The method used to prove this result is extended to apply three-dimensional Lie transformation groups. It is shown that the existence of a one-dimensional subgroup with closed orbits restricts the Bianchi type of the associated Lie algebra to be I, II, III, VII_0, VIII or IX. Some results on n-dimensional Lie groups are also derived and applied to show there are severe restrictions on the structure of the allowed four-dimensional Lie transformation groups compatible with cyclic symmetry.Comment: 6 pages, LaTex. (World Scientific style file: sprocl.sty needed) To appear in Proceedings of the Spanish Relativity Meeting (EREs2000), World Scientific Publishin

First Steps: Intelligence Analysis in Canada during the Second World War

At the outset of the Second World War decision-makers in Ottawa were entirely dependent on the United Kingdom for finished intelligence on foreign military and political developments. During six years of war the intelligence work carried out in Canada expanded in several areas, and included a growing capacity to carry out intelligence analysis in several fields. An analytic group was established to exploit the mass of detailed information collected by the postal censorship programme. The Department of External Affairs created a small unit that drew on signals intercepts and other sources to assess political issues for senior officials. In the Department of National Defence, the newly-created Joint Intelligence Committee took the first steps in producing strategic intelligence assessments from a Canadian perspective. These developments were all heavily influenced by Canada’s close intelligence relations with the UK and US. A major impediment to the development of an independent analytic capacity, however, was the lack of demand for Canadian-origin intelligence assessments from senior political and military leaders in Ottawa, who continued to look to allies for intelligence to inform national-level decisions

First Steps: Intelligence Analysis in Canada during the Second World War

At the outset of the Second World War decision-makers in Ottawa were entirely dependent on the United Kingdom for finished intelligence on foreign military and political developments. During six years of war the intelligence work carried out in Canada expanded in several areas, and included a growing capacity to carry out intelligence analysis in several fields. An analytic group was established to exploit the mass of detailed information collected by the postal censorship programme. The Department of External Affairs created a small unit that drew on signals intercepts and other sources to assess political issues for senior officials. In the Department of National Defence, the newly-created Joint Intelligence Committee took the first steps in producing strategic intelligence assessments from a Canadian perspective. These developments were all heavily influenced by Canada’s close intelligence relations with the UK and US. A major impediment to the development of an independent analytic capacity, however, was the lack of demand for Canadian-origin intelligence assessments from senior political and military leaders in Ottawa, who continued to look to allies for intelligence to inform national-level decisions

Arrows, Bears and Secrets: The Role of Intelligence in Decisions on the CF-105 Program

Newly available information has made it possible for the first time to examine the role of intelligence in decisions on the CF-105 Arrow. These records show that Canadian intelligence assessments of the Soviet bomber threat differed from US estimates. In the late 1950s Canadian analysts stressed the imminent shift from bombers to ballistic missiles as the main danger to North America. The Diefenbaker government’s decision to cancel the Arrow program in 1959 was significantly influenced by this view of the changing strategic threat. In examining the role of intelligence, the article addresses a number of earlier myths, and provides a more complete picture of the decisions concerning this iconic Canadian aircraft

Harada-Maxwell Static Spherically Symmetric Spacetimes

Very recently Harada has proposed a gravitational theory which is of third order in the derivatives of the metric tensor with the property that any solution of Einstein's field equations (EFEs) possibly with a cosmological constant is necessarily a solution of the new theory. Remarkably he showed that even in a matter-dominated universe with zero cosmological constant, there is a late-time transition from decelerating to accelerating expansion. Harada also derived an exact solution which is generalisation of the Schwarzschild solution. However, this was not the most general static spherically vacuum solution of the theory and the general solution was subsequently obtained by Barnes. Recently Tarciso et al. have considered regular black holes in Harada's theory coupled to non-linear electrodynamics and scalar fields. In particular they exhibit a four-parameter solution with a zero scalar field whose source is a Maxwell electromagnetic field. It is a straightforward generalisation of Harada's vacuum solution analagous to the Reissner-Nordstrom generalistaion of the Schwarzschild solution. However, this solution is not the most general static spherically symmetric solution of the Harada-Maxwell field equations (i.e.\ Harada gravitational fields with a Maxwell electromagnetic source). The most general such solution is obtained in this paper.Comment: PDFLaTeX 7 pages. Added a paragraph to dicuss previously overlooked case c=-1, added page numbers to ref[9]. arXiv admin note: text overlap with arXiv:2309.0533

Vacuum Static Spherically Symmetric Spacetimes in Harada's Theory

Very recently Harada proposed a gravitational theory which is of third order in the derivatives of the metric tensor with the property that any solution of Einstein's field equations (EFEs) possibly with a cosmological constant is necessarily a solution of the new theory. He then applied his theory to derive a second-order ODE for the evolution of the scale factor of the FLRW metric. Remarkably he showed that, even in a matter-dominated universe with zero cosmological constant, there is a late-time transition from decelerating to accelerating expansion. Harada also derived a generalisation of the Schwarzschild solution. However, as his starting point he assumed an unnecessarily restricted form for a static spherically symmetric metric. In this note the most general spherically symmetric static vacuum solution of the theory is derived. Mantica and Molinari have shown that Harada's theory may be recast into the form of the EFEs with an additional source term in the form of a second-order conformal Killing tensor(CKT). Accordingly they have dubbed the theory conformal Killing gravity. Then, using a result in a previous paper of theirs on CKTs in generalised Robertson-Walker spacetimes, they rederived Harada's generalised evolution equation for the scale factor of the FLRW metric. However, Mantica and Molinari appear to have overlooked the fact that all solutions of the new theory (except those satisfying the EFEs) admit a non-trivial second-order Killing tensor. Such Killing tensors are invaluable when considering the geodesics of a metric as they lead to a second quadratic invariant of the motion in addition to that derived from the metric.Comment: 8 pages, no figure