Imagine trillions upon trillions of electrons are squeezed into a tiny region of space creating a blackhole, how do this charged blackhole emit electromagnetic field? Hawking radiation do not count and assume no materials are falling in.
By the "No Hair Theorem", three quantities "define" a black hole; Mass, Angular Momentum, and Charge. The first is easy enough to determine, look at the radius of the event horizon and you can use the Schwarzschild formula to compute the mass. Angular Momentum can be found using the cool little ergosphere Penrose "discovered". However, I don't know how to determine the charge of the black hole.   How can an electromagnetic field escape the event horizon of a Reissner-Nordström black hole? Is there any experiment we could theoretically do to a black hole to determine its charge?
Order of products of elements in a finite Abelian group Interview question: three arrays and O(N*N) How do I change my username? Some time ago, when I installed Ubuntu, I chose a rather stupid username for my account that I do not want to use anymore. How do I change this (including the name of my home directory, and the name in the terminal) without losing settings for applications? How do I keep permissions and my keys for various authentification (e.g. email, SSH, GPG and more)? What settings could possibly get lost if I changed my username? biblatex and autonum don't work together I have a cryptography workshop question I'm having trouble with as follows;  Person A creates a cipher $E_k(m)$ which produces a ciphertext from message $m$ using key $k$. The function inside $E$ is kept secret but the length of $E_k(m)$ is known.  Person B recommends "increasing" security of the cipher by instead doing :   $(E_k(m) \oplus m)\ ||\ (E_k(m) \oplus 1111...11)$      Does this in fact increase security of the cipher or increase new problems.  My thinking is, depending on the function within $E$, xoring the output of the cipher with the plaintext message $m$ could expose the key $k$, meaning the extra complexity is for nothing. Am I on the right track, or am I missing something?  I have tried searching for examples of similar schemes and found nothing (which probably means it's not a good scheme) but I need to justify my answer.   Any steers in the right direction would be greatly appreciated, I'm more than happy to do the research myself just unsure what specifically to look for.   Unfortunately the above context is all I have been provided for this question. How do the radian have a unit? Is it possible to search for down voted questions? I want to search for new downvoted questions to improve or flag them.   I tried in the searchbar: votes:-1 is:question   but votes:XX only works with positive numbers. I can't query for downvoted questions. Is there a work-around to this? If there's not, should this feature be added? Are Complex Substitutions Legal in Integration? This question has been irritating me for awhile so I thought I'd ask here.  Are complex substitutions in integration okay?  Can the following substitution used to evaluate the Fresnel integrals:  $$\int_{0}^{\infty} \sin x^2\, dx=\operatorname {Im}\left( \int_0^\infty\cos x^2\, dx + i\int_0^\infty\sin x^2\, dx\right)=\operatorname {Im}\left(\int_0^\infty \exp(ix^2)\, dx\right)$$  Letting $ix^2=-z^2 \implies x=\pm\sqrt{iz^2}=\pm \sqrt{i}z \implies z=\pm \sqrt{-i} x \implies dx = \pm\sqrt{i}\, dz$  Thus the integral becomes  $$\operatorname {Im}\left(\pm \sqrt{i}\int_0^{\pm\sqrt{-i}\infty} \exp(z^2)\, dz\right)$$  This step requires some justification, and I am hoping someone can help me justify this step as well: $$\pm \sqrt{i}\int_0^{\pm\sqrt{-i}\infty} \exp(z^2)\, dz=\pm\sqrt{i}\int^\infty_0\exp(z^2)\, dz=\pm\sqrt{i}\left(\frac{\sqrt{\pi}}{2}\right)$$  Thus  $$\operatorname {Im}\left(\int_0^\infty \exp(ix^2)\, dx\right)=\operatorname {Im}\left(\pm\frac{\sqrt{i\pi}}{2}\right)=\operatorname {Im}\left(\pm\frac{(1+i)\sqrt{\pi}}{2\sqrt{2}}\right)=\pm\frac{1}{2}\sqrt{\frac{\pi}{2}}$$  We find that the correct answer is the positive part (simply prove the integral is positive, perhaps by showing the integral can be written as an alternating sum of integrals).  Can someone help justify this substitution?  Is this legal? How to view recently opened media files? In windows we have an option to view recently opened media files as my recent documents, I was  wondering does there exists something like that in Ubuntu?  via terminal or via GUI? What's the right way to represent phone numbers? I used Sound Juicer to rip a CD of audio for a language learning book so that I could listen to them on my Android. However, Sound Juicer seems to only have the option of numbering files without leading zeros. Like this:  track_1.mp3 track_10.mp3 track_11.mp3   This leads to some confused ordering on my music player. So, I want to add some zeros to the name, so that they're ordered properly, like this:  track_01.mp3 track_02.mp3 track_03.mp3   How do I accomplish this? I tried using GPRename, but while it has the ability to add numbers, it doesn't seem to have any options for adding leading zeros.  Is there a better program or something I can do at the command line? How to disable captive portal detection? How to remove exclamation mark on Wi-Fi or signal icon in Lollipop? When connected to the Internet, the system checks if it's in a walled garden, which is simply trying to connect to Google. If it fails, in Android 5, there'll be an exclamation mark on the WiFi icon or signal icon.   In some situations, this is annoying. Say, in China, Google is blocked, the exclamation mark will always be there, which is meaningless.  How can I disable this check, and make the system assume, connected WiFi/mobile data is connected Internet? Player looses boot after tackle Four tasks in parallel... how do I do that? I have a bunch of PNG images on a directory. I have an application called pngout that I run to compress these images. This application is called by a script I did. The problem is that this script does one at a time, something like this:  FILES=(./*.png) for f in  "${FILES[@]}" do         echo "Processing $f file..."         # take action on each file. $f store current file name         ./pngout -s0 $f R${f/\.\//} done   Processing just one file at a time, takes a lot of time. After running this app, I see that the CPU is just 10%. So I discovered that I can divide these files in 4 batches, put each batch in a directory and fire 4, from four terminal windows, four processes, so I have four instances of my script, at the same time, processing those images and the job takes 1/4 of the time.  The second problem is that I lost time dividing the images and batches and copying the script to four directories, open 4 terminal windows, bla bla...  How do that with one script, without having to divide anything?  I mean two things: first how do I from a bash script, fire a process to the background ? (just add &amp; to the end?) Second: how do I stop sending tasks to the background after sending the fourth tasks and put the script to wait until the tasks end? I mean, just sending a new task to the background as one tasks end, keeping always 4 tasks in parallel? if I do not do that the loop will fire zillions of tasks to the background and the CPU will clog. Change date and time format from csv file without using date -d I have a .csv file contains   Data1|Data2|10/24/2017 8:10:00 AM   I want to change date and time format of column 3 as following:  From 10/24/2017 8:10:00 AM (12-Hour) to 20171024 08:10:00(24-hour).  Not using -d Prove that $L(V,W)$ forms a vector space Let $V$ and $W$ be vector spaces over a field $F$. Let $L(V,W) = \{T:V\to W : T \text{ is linear} \}$, that is, $L(V,W)$ is the collection of all linear functions from $V$ to $W$. For $S,T \in L(V,W)$ and $a \in F$, define new functions $(S+T):V \to W$ and $ aT :V \to W$ by $(S+T)(x) = S(x)+T(x)$ ; $(aT)(x) = a(T(x))$.   Prove that $S+T$ belongs to $L(V,W)$ and $aT$ belongs to $L(V,W)$. How to move files to specific folders based on CSV entries? Similar to this question  and an fellow up on this one    What was the official reason by Canonical to axed the project when it was love by some many of their users and innovative? How to insert an item into an array at a specific index (JavaScript)? UK Visa Refusal: Provenance of funds/parking