Metric Tensor in Weak Field Condition Suppose that we are in the Weak Field Condition, that is: $$g_{\mu\nu}=\eta _{\mu\nu}+h_{\mu\nu}$$ where $\eta _{\mu\nu}$ is the metric tensor of flat space time (Minkowski spacetime) and $h_{\mu\nu}$ is a perturbation such that: $$|h_{\mu\nu}|&lt;&lt;1$$ Perfect. But now I would like to find the tensor $g^{\mu\nu}$; by definition (it is by definition of $g^{\mu\nu}$, right?) we have: $$g_{\mu\lambda}g^{\lambda \nu}=\delta ^\nu _\mu$$ I am fine with all the above, but now it is said that from the previous equation we can derive that: $$g^{\mu\nu}=\eta^{\mu\nu}-h^{\mu\nu}$$ why? Can you show me the process behind this result?
Inverse metric in linearised gravity From what I've read, in the framework of linearised gravity, one perturbs the metric around a Minkowski background, $\eta_{\mu\nu}$, such that  $$g_{\mu\nu}(x)=\eta_{\mu\nu}+h_{\mu\nu}(x)\tag{1}$$  where $h_{\mu\nu}(x)$ is a small perturbation, i.e. $$\big\lvert h_{\mu\nu}\big\rvert&lt;&lt;1.\tag{2}$$  The inverse metric is then found by assuming the following ansatz:  $$g^{\mu\nu}(x)=\eta^{\mu\nu}+\tilde{h}^{\mu\nu}\tag{3}$$  where $\tilde{h}^{\mu\nu}$ is also small (i.e. $\big\lvert \tilde{h}_{\mu\nu}\big\rvert&lt;&lt;1$).   Using this, it is easy to find that  $$g^{\mu\nu}(x)=\eta^{\mu\nu}-h^{\mu\nu} \tag{4}$$  to first order.   My question is, what is the justification for this ansatz? Is it simply that one expects the inverse metric to have a similar form to the metric in order to satisfy $$g^{\mu\alpha}g_{\alpha\nu}=\delta^{\mu}_{\;\nu}~?\tag{5}$$
Chrome: remove URL from autocomplete which doesn't show up in history? I accidentally visited gist.gihub.com (note the missing t), and now that URL auto completes each time I start typing gist.…. How can I remove this URL?  I've tried removing it from my history, but that doesn't help:     (note the empty search results) Command-line-friendly full-text indexing? Is there such a thing as a full-text indexing engine, that can be queried from the command line and ideally wouldn't require using a gui at all ?  I'm especially interested in indexing my ebooks and papers, so that's a mixture of pdf, epub and a few djvu. (Open)Office docs would be nice, but much lower on my list. How to add a custom icon or symbol to a flag link? I'm working on a 'sample request' implementation for a commerce site using , , sessions and a little custom code.  I'd like to add an icon or a symbol to let people know that an item they are viewing has been flagged.  I'm not sure exactly how to approach this, I can imagine perhaps adding a conditional field that displays an image or check box that is then changed by  or ajax, or perhaps something more complicated in JavaScript?  It could really be as simple as adding a checkbox that is checked or unchecked as the flag link is clicked or maybe even changing the css/html on click to be identified as marked.   Anyway, grateful for any advice here. Ralink RT3290 bluetooth adapter does not work, but wifi works perfectly. I am writing a small KOMA-Script scrartcl document with multiple sections. In the table of contents, LaTeX fills the current line with dots between the end of the section name and the page number. Is there any way to customize this behavior? I would like to reduce the space between the single dots (i.e. use more dots in the same space). How soon should I "vote to close"? I need to convert one into 1, two into 2 and so on.  Is there a way to do this with a library or a class or anything? Jordan Canonical Form determined by characteristic and minimal polynomials in dimension $3$, but not beyond Lookup list dependant on the contents of another cell hope someone can help to crack this one?  I've got a table on my data entry tab (sheet 1) where each row includes two data validation drop down lists (source is on sheet2). I want the options in the second drop down list (k13) to be dependant on what is selected in the first drop down list (g13)...  ie. if you select 'Diary' in the first drop down box then the second drop down only has 'Cheese', 'Milk' and 'Yogurt' - likewise, if you select 'Fruit' in the first box - I want the only options to be available specific to that categories column in the lookup table on sheet 2 (which are 'apple', 'pear' and 'banana' in this case)?  Please help - i think this is a vlookup indirect formula?? Does Lin's  assume that the 2 data sets have linear or monotonic tendencies? Or, can I measure the concordance between 2 data sets that have a sinusoidal tendency? Tangent lines to ellipse from external point how to prove $\forall p$ prime :   $\binom{2p}{p} \equiv 2 \pmod p$ we have:  $\binom{2p}{p} = \frac{2p (2p-1)(2p-3)...1}{p!p!}$ but how to continue? I'm in first year. Our class is in lesson " Heat and Thermodynamics". While solving a numerical problem of a reversible engine he told us that 100 degree Celsius is equal to 100 kelvin. I inquired but could not get satisfactory answer. Pleas help me understand it.  Here is the numerical, please consider it: A reversibe engine works between two temperatures whose difference is 100c. If it absorbs 746J of heat from the source and rejects 546J to the sink, calculate the temperature of the source and the sink. Ans (100°C, 0°C) Is it "a SSD" or "an SSD"? Possible Duplicates:             Since SSD (solid-state drive) is pronounced es-es-dee, I'm wondering whether one should write "an SSD" or "a SSD". Saying "a SSD" out loud feels a bit off... ReadOnlyCollection or IEnumerable for exposing member collections? Is there any reason to expose an internal collection as a ReadOnlyCollection rather than an IEnumerable if the calling code only iterates over the collection?  class Bar {     private ICollection&lt;Foo&gt; foos;      // Which one is to be preferred?     public IEnumerable&lt;Foo&gt; Foos { ... }     public ReadOnlyCollection&lt;Foo&gt; Foos { ... } }   // Calling code:  foreach (var f in bar.Foos)     DoSomething(f);   As I see it IEnumerable is a subset of the interface of ReadOnlyCollection and it does not allow the user to modify the collection. So if the IEnumberable interface is enough then that is the one to use. Is that a proper way of reasoning about it or am I missing something?  Thanks /Erik How to install Tor? Need help disabling imessage? I recently changed from iphone to android and i have been having trouble recieving messages from my iphone friends since my iphones screen is broken i cant do anything on it. Any way to fix this problem through icloud or something? Is it possible to install Ubuntu without formatting any partitions? I'm sure this is a newbie question, but I can't figure this out. I have tried to follow the advice here:  and here:   But I can not seem to be able to generate any font change. I either get no change or error messages.  Here is the output of one failed attempt to change the font to Times using this command:  \rmfamily \renewcommand{\rmdefault}{ptm}     Apparently I either don't have a correct package installed or...  The output says " Metric (TFM) file not found." but I am not sure where to go from there. What really allows airplanes to fly?