Photons, neutrinos, and gravitational-wave astronomy

Summary

Before narrowing down what could be (mathematically and astrophysically) the sources of GWs, let's consider when are GR effects most relevant? A typical quantity to look at the so-called "compactness" \(M/R\) with \(M\) mass of a source and \(R\) its linear dimension. Note that in natural units (\(G=c=1\) typically used to simplify the formalism in GR), this is a dimensionless number. For low values of \(M/R\), General Relativity reduces to Newtonian gravity – as it should being an extension of this theory, and in Newtonian gravity the gravitational field is fixed and any change propagates instantly: there are no gravitational waves. N.B.: Just introducing the postulate that "gravity" has a finite speed of propagation in Newtonian physics, one can build a lot of intuition and quantitative results correct to order of magnitude for GW physics, see Schutz 1984 and LVK Collaboration 2017. For general relativity effects to matter, \(M/R\) needs to be "large": either extremely large masses regardless of the scale (see the very first ideas of what today we call a black hole from Michell 1784 and Laplace 1799), or for very dense matter limited to a very small linear scale \(R\). In the "stellar regime", we expect the densest stars, also known collectively as "compact objects" to be involved, namely white dwarfs (WD), neutron stars (NS), and black holes (BHs). In general, the source term of GWs is going to be related to the term describing the distribution in space-time of matter (the stress energy tensor \(T_{\mu\nu}\)). Q: what is the lowest order source term for electromagnetic radiation? By analogy with electromagnetism (EM), let's consider the spatial momenta of \(T_{\mu\nu}\) assuming the mass distribution of the source to be finite in extent, that is multiply by (possibly more than one factor) \(x^{\alpha}\) and integrate over the spatial volume. Like in EM, the zeroth order momentum of a charge distribution is just the total charge that is conserved, and that does no...