By Robert Bartnik (Ed.)

The Canberra convention on Mathematical Relativity was once the spotlight of a unique application on the CMA which ran from June - August 1988. With over forty humans participating and 27 talks packed into 3 days, the convention used to be a truly stimulating and laborious adventure for all involved. This quantity includes reviews on the various talks awarded and a few contributed survey papers, and it truly is was hoping that it'll offer a great creation to themes of present and destiny curiosity in mathematical relativity.

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**Extra resources for Conference on Mathematical Relativity, Canberra, July 1988**

**Example text**

For positive p0 , one can distinguish between the following two cases. The ﬁrst possibility is p2 = −m2 < 0. Here one can choose k µ = (m, 0, 0, 0), and the little group is SO(3), since these are the only Lorentz transformations that leave a particle with k = 0 at rest. The second possibility is p2 = 0. One chooses k µ = (1, 0, 0, 1), and the little group is ISO(2), the invariance group of Euclidean geometry (rotations and translations in two dimensions). Any pµ within a given class can be obtained from the corresponding k µ by a Lorentz transformation.

2) assumes the simple form ✷f¯µν = −16πGTµν . 3) then reads ∂ν f¯µν = 0, in direct analogy to the Lorenz gauge condition ∂ν Aν = 0. ) can be found. Note that the harmonic gauge condition is consistent with ∂ν T µν = 0 (which is analogous to ∂ν j ν = 0), but not with ∇ν T µν = 0 (vanishing of covariant derivative). Therefore, although Tµν acts as a source for fµν , there is in the linear approximation no exchange of energy between matter and the gravitational ﬁeld. 8) where eµν is the polarization tensor.

46) D(1) ⊗ D(1) = D(2) ⊕ D(1) ⊕ D(0) , corresponding to the ﬁve degrees of freedom for a massive spin-2 particle, three degrees of freedom for a spin-1 particle, and one degree of freedom for a spin0 particle, respectively. The latter 3 + 1 degrees of freedom can be eliminated by the four conditions ∂ν f µν = 0 (transversality). 5). 5) have to satisfy ∂µ µ = 0—one condition—to preserve tracelessness; the condition ✷ µ = 0—needed to preserve transversality—is automatically fulﬁlled for plane waves).