Jekyll2023-03-16T12:11:10+00:00http://wevbarker.com/feed.xmlDr. Will Barker (威廉 巴克尔) | theoretical physics, cosmologyThis site is for theoretical, high-energy and gravitational physics and cosmology (broadly defined). More specific topics might include differential geometry, geometric algebra, gauge theories of gravity. Blog-Mu-Nu is a blog which reviews interesting arXiv preprints from [gr-qc], [hep-th] and [astro-ph].Dr. Will E. V. BarkerarXiv Jan 4th-8th 20202021-01-09T00:00:00+00:002021-01-09T00:00:00+00:00http://wevbarker.com/2021/01/09/post-1<head>
<script src="https://polyfill.io/v3/polyfill.min.js?features=es6"></script>
<script id="MathJax-script" async="" src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js">
</script>
</head>
<h2><a href="https://arxiv.org/abs/2012.14984">2012.14984</a> xPPN: An implementation of the parametrized post-Newtonian formalism using xAct for Mathematica</h2>
<p>
Many in the physics community are familiar with the <tt>xAct</tt> tensor manipulation suite for <tt>Mathematica</tt>, and those who aren't probably should be. In recent years, <tt>xAct</tt> has consolidated its place as the go-to computer algebra tool in gravitational theory, outperforming various predecessors with its powerful 'canonicalise' function, and attracting a flurry of applied package development. Some of these packages float and others sink: I'm curious to see how Manuel Hohmann's new <tt>xPPN</tt> package will fare.
</p>
<p>
Most modifications to Einstein's theory can be cast in the parametrized post-Newtonian (PPN) formalism. PPN allows the theory to be compared, as a ten-parameter modification of the Newtonian theory, against the gold standard set by GR. The implementation of PPN is usually extremely complicated, and varies substantially from theory to theory. Thus xPPN, a general implementation of the PPN formalism, is potentially very exciting.
</p>
<p>
At the heart of the implementation seems to be the definition of two bespoke manifolds for the \(3+1\) decomposition. Assuming that the covariant theory lives in some sense on \(M_4\), a spacelike foliation \(S_3\) and timelike threading \(T_1\) are introduced as separate <tt>xTensor</tt> manifolds, where \(M_4\cong T_1\times S_3\). This cuts right through the pre-existing notion of ADM decomposition in <tt>xAct</tt>, which I've wrestled with recently in the context of the <a href="https://arxiv.org/abs/2101.02645">Hamiltonian analysis</a>. In the end, I kept a single Minkowski manifold \(M_4\), and defined a set of projections accompanied by very many rules. This is not ideal, but the relevant parts of <tt>xAct</tt> (such as <tt>xCoba</tt>) have quite patchy documentation, which makes life less than easy! I won't go into the guts of the higher functions of the package, but suffice to say the post-Newtonian potentials are all defined, along with certain 'utility functions' which facilitate the human-assisted expansion. A nice walk-through is provided for a simple Brans-Dicke-like theory, but since I've not tried it out, I can't offer further comment.
</p>
<p>
My main concern is the 'theory-scope' of the package. This is of course the hardest part to implement, since you can never tell quite in what terms the next theory will be cast. The Brans-Dicke theory obviously inherits much of the machinery of GR, but with an extra scalar \(\psi\) - I expect e.g. the variations on mimetic gravity could be similarly tackled. This scalar naturally has to be defined when using the package, and presumably one may extend to higher-spin fields also. Accordingly I've already recommended <tt>xPPN</tt> to a colleague who is <a href="https://arxiv.org/abs/2007.00082">working on the new relativistic completion of MOND</a>.
However, it is often interesting to build theories out of a gauge-covariant derivative. Accordingly, the <tt>xPPN</tt> package defines three connections: Levi-Civita, teleparallel and symmetric-teleparallel. I'm very happy about the last of these, which follows on from the <a href="https://arxiv.org/abs/1903.06830">non-metricity theories</a> of Jiménez, Heisenberg and Koivisto, and is something I'd like to work on at some point. However, in the short term I'm interested in a free connection, in the context of torsion theories. This is likely workable in the <tt>xPPN</tt> setup, but might take some <tt>xAct</tt>-jitsu. Again, I'd have to try.
</p>
<p>
Overall, this paper introduces software rather than physics, and is structured accordingly. Nonetheless, I am happy to have come across <tt>xPPN</tt>, and am looking forward to trying it out in the near future.
</p>Dr. Will E. V. BarkerNew arXiv review blog coming soon!2020-12-22T00:00:00+00:002020-12-22T00:00:00+00:00http://wevbarker.com/2020/12/22/testpost<head>
<script src="https://polyfill.io/v3/polyfill.min.js?features=es6"></script>
<script id="MathJax-script" async="" src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js">
</script>
</head>
<p>
I'm setting up Blo\(g_{\mu\nu}\) to further hone my skills as a peer-review referee, and to draw well-deserved attention to new preprints that I find interesting. The idea is to write a short review of at least one preprint per week, likely drawn from the <tt>[gr-qc]</tt>, <tt>[astro-ph]</tt> or <tt>[hep-th]</tt> arXiv.
</p>
<p>
This will likely start in the new year, as I still need to figure out comments on <tt>disqus</tt>, and how to handle arXiv trackbacks and <tt>RSS</tt> so that the authors are properly credited.
</p>
<p>
The idea for Blo\(g_{\mu\nu}\) is unashamedly stolen from Dr. Sunny Vagnozzi's <a href="https://www.sunnyvagnozzi.com/blog">His Dark CMBlog</a>. Sunny's <a href="https://www.sunnyvagnozzi.com/">entire website</a> is absolutely fantastic, and you should explore it before reading any more of my posts.
</p>Dr. Will E. V. Barker