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3

They are listed in here catalogue of spacetimes


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You can just write down $$\Gamma^i{}_{k\ell}=\tfrac{1}{2}\,g^{im} \left(\partial_{x^\ell}g_{mk} + \partial_{x^k} g_{m\ell} - \partial_{x^m} g_{k\ell} \right)$$ in Mathematica. The example blow is for the Schwarzschild metric. Here is the code. (You might have to patch the parts lost by my excessive use of display style.)


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As a beginner for working on relevant topics, I just write few words about your question. I hope it helps you up. Localization Principle has been great role in computing superconformal index also it gives the exact calculation in susy gauge theories. From some excellent works by Pestun, Kapustin, Willet and so on(about a decade ago?), many researcher now ...


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The method I will present here is very general and by training this is the first that comes to my mind. There might be a simpler one though. The idea is to consider another function $G(\Gamma) \equiv e^{-g F(\Gamma)}$ with $g > 0$ and $F(\Gamma) = a \sum_i n_i$. The sum I want to compute is now $S_g \equiv \sum_{\Gamma} G(\Gamma)$. This sum is actually ...


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Not a definite answer to your question, sorry, but if you absolutely can't find it on G. (or you lack the patience to dig through arxiv.org or G. for a lucky reference), one alternative that works for me when I just want confirmation is to visit amazon, stick in say "General Relativity" books and use their "look inside the book" feature. a screenshot of ...


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Frolov's Black hole Physics (Google Books link) has an entire chapter on the Kerr metric, but states at the beginning of that chapter, Mathematical properties of the Kerr metric and its generalization with electric charge included (the Kerr-Newman metric) are discussed in Appendix D. Appendix D does include Christoffel symbols of the Kerr-Newman metric ...


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The linked website from 1995 or 2005 is correct in that it says that "interlocking asperities" is not the universal explanation that it was once naively hoped to be (as in Coulomb's model of friction). Micro-scale asperity interlocking seems to be rare for typical surfaces that are sliding because, for example, sliding often tends to smooth the highest ...


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E. T. Jaynes: Probability Theory: The Logic of Science http://omega.albany.edu:8008/JaynesBook.html The book has also printed form. Jaynes also published readable and revealing papers on probability, statistical physics and other physics. Here you can find them: http://bayes.wustl.edu/etj/node1.html


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A small note on the definition. It should be $$ M(S) := \sqrt{ \frac{\text{Area}(S)}{16 \pi}} \left(1- \frac 1 {16 \pi}\int_S \theta^-\theta^+ d_{\sigma_S}\right), $$ where $\theta^\pm$ are the divergences along the two null directions. It is equal to what you have written if the 2-surface $S$ lies in a space-like 3D submanifold with vanishing extrinsic ...


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There would be a big difference between documenting the advance of truly fundamental physics, and documenting the advance of every investigation, discovery and idea which might count as physics. The fundamental advances are documented in places like encyclopedias, textbooks, and the list of Nobel Prize winners. Perhaps the closest thing to a central, ...


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Hook and Hall is probably my personal favourite as it is very clear and concise without a lot of fuss. For a totally different style to the classics maybe try "The Oxford Solid State Basics". The lecture notes on which this book was based are available (in part) online (google steve simon solid state lecture notes and you should get there without much ...


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Start with the lecture notes at the top of Slava Rychkov's blog, http://sites.google.com/site/slavarychkov/home


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If you have not seen it yet, conformal bootstrap in $1+1$ is extremely powerful, and in many cases essentially determine the whole theory. Everything is done analytically. Recent works of higher-dimensional generalizations share many basic features with the $1+1$ version, so it seems not a bad idea to start from there.


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Just a quick preliminary answer, I will fix it later. The connection to general relativity is a change of variables in which the metric is replaced by a "spin connection" and a "frame field". These quantities can then be arranged in a new matrix, so the metric field has been rewritten as a different matrix-valued field, and the transformations ...



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