Non-rotating big stars can be subject to a gravitational collapse increasing their density. When the density is so high that the mass volume shrinks below the event horizon, a black hole is formed.  Is such an "initial" black hole already considered as a singularity, or are there further shrinking processes required in order to consider the black hole to be a singularity? Do the characteristic dynamics of black holes include further shrinking processes until the mass is reduced to a point (or nearly)?
What is the exact reason that normal matter can not exist within an event horizon?  I can understand how a super-dense object like a neutron star could accrete mass until its physical radius is less than its Schwarzschild radius and an event horizon forms around it.   But why can't the neutron star remain inside the event horizon as it was before the event horizon formed? Aside from the escape velocity at the surface reaching $c$, what actually changed?  Why must all matter within an event horizon undergo complete physical collapse to a point?
If I enter the US by land, not needing ESTA, would I then need ESTA to enter by air 3 days later? I am a UK citizen, and therefore qualify for the USA's  (VWP). If I enter by  I need to apply for (and pay for) ESTA beforehand. If I enter by , I don't need ESTA. But I do get a 90 day visa waiver which allows me to go to Canada and return to the USA, on the same VWP.   My question is: If I first enter the USA on foot, from Canada (at Niagara Falls), return to Canada on foot, and then 3 days later fly from Canada into the USA, do I need ESTA? Or as my existing visa waiver is still in place, is that good enough? Sum of columns for rows containing a specific term Issue with QGIS 2.10.1 Clip and Intersect Tools I accidentally set an object as camera, how do I undo this? I have a problem with rendering in cycles. In blender render my object is rendering fine, but in cycles when I pushed F12 I got only this:    One more thing: when I click 0 on keyboard I'm not in camera persp, but in object as camera, it looks like invisible layer, I don't know how to undo this, and be in camera persp again.  Does anybody have any idea how to fix this? The SourceForge signon page says I can associate an OpenID with my existing SourceForge account:    I enter my currently-signed-in SourceForge account password I select the custom OpenID URL and enter https://openid.stackexchange.com I'm redirected to https://openid.stackexchange.com/account/login?&lt;session key bits&gt; I enter my openid.stackexchange.com login information there I get the error message:     Cannot Complete Login      Detected an attempt to send an assertion when the identifier () is not owned by the logged in user.    I don't understand what that means. Diminishing returns / non-linear reputation from “great” answers Over time I realized a very annoying property of the Stack Overflow reputation system: Easy answers to popular question are rewarded with a lot more reputation points than actually great answers. In case anybody actually needs examples for this, here are two examples from :   gained me 420 rep, I invested 2 minutes writing it, and it only was a wild guess.   took me about an hour for the research and the math and gained me 40 rep.  Now I know that you are bound to get more rep for answers that are useful to more people, and I'd say that's fine. But the current situation is quite extreme: 30% of my reputation is from 5 of my 330 answers, and they are definitely far from being my best ones.  A final example that is not from my profile, but more extreme: Do you really think  is worth 40000 reputation?  My proposition to improve that situation would be to make the reputation gain from a single answer non-linear, maybe even have it capped at a certain point. I'm not sure on how that non-linear function should look exactly, and would leave good proposals for that to users with more experience than me. prime divisor of $3n+2$ proof I have to prove that any number of the form $3n+2$ has a prime factor of the form $3m+2$. Ive started the proof  I tried saying by the division algorithm the prime factor is either the form 3m,3m+1,3m+2.  Case 1: $3m$      suppose $3m$ does divide $3n+2$. That means $3mr=3n+2$ where $r$ is some integer. But we get $mr-n= 2/3$ and since $mr-n$ is an integer that's a contradiction. Thus $3m$ does not work.  Case 2: $3m+1$ Same argument here  Case 3: $3m+2$ By the fundamental theorem of arithmetic every integer is divisible by a prime. But not sure what to do from here. Can a package overwrite the original commands in Latex? An example:  Without the amsmath package:   The equation environment numbers the equation automatically. The align environment cannot be executed.   With the amsmath package:   align and equation work seamlessly in numbering equations: I can use equation to write my first two equations, and align to write my third equation, and Latex will still number them correctly.   My questions are:   Is the code for the command equation after loading the amsmath package still the same as it was before loading the package? Moreover, if this is the case, then, in general, can loading different packages cause conflicts? And how do we avoid it? Is there an algorithm to decide if a symlink loops? Unix systems usually just error out if they are confronted with a path that contains a symlink loop or just too many symlinks, because they have a limit to the number of symlinks they will traverse in one path lookup. But is there a way to actually decide if a given path resolves to something or contains a loop, even if it contains more links than a unix is willing to follow? Or is this a formally undecidable problem? And if it can be decided, can it be decided in a reasonable amount of time/memory (e.g. without having to visit all files on a filesystem)?  Some examples:  a/b/c/d where a/b is a symlink to ../e and e is a symlink to f and f is a symlink to a/b  a/b/c/d where a/b/c is a symlink to ../c  a/b/c/d where a/b/c is a symlink to ../c/d  a/b/c/d where a/b/c is a symlink to /a/b/e where a/b/e is a symlink to /a/b/f where a/b/f is a symlink to /a/b/g   Edit:  To clarify, I am not asking about finding loops in the file system, I am asking about a decision algorithm that decides of a given path whether it resolves to a definite file/directory or whether it does not resolve at all. For example in the following system, there is a loop, but the given path still resolves fine:  / -- a -- b where b is a symlink to /a   This directory tree clearly has a cycle, but the path a/b/b/b/b/b still resolves fine to /a. Ok, so I'm such a newbie to Ubuntu and I bought a Windows 8 pre-installed laptop last month.  I updated to Windows 8.1 and then I thought about installing Ubuntu as a dual boot so I could mess around and learn more about it.   So I followed a Youtube tutorial (  ) and I got my stuff working fine.   The first few times I booted I got the GRUB menu instead of my default HP Boot OS Manager, and I was able to select my OS.   So I went to sleep and the next day I turned on my computer and the GRUB menu did not show up. I tried several times and it didn't automatically show up.  In order for me to see the GRUB menu I had to turn on my PC and on start had to press ESC to pause startup and press F9 to get boot options. Then from there I had to pick from OS Boot, Ubuntu, Ubuntu (Yes there were two Ubuntus available) and a default EFI file thingy.   When I click the first Ubuntu I get the GRUB Menu (I was too scared to try the second in case I screwed my laptop up) and I can safely load Ubuntu from there and use it (although I do have to increase my brightness every time I load Ubuntu because it somehow reduces my brightness to complete darkness on boot)  So my problem here is why isn't my GRUB showing on boot, after it worked on the first day?   My laptop is a HP TouchSmart j-078CA.  EDIT 1: FYI I just switched to Ubuntu LiveCD to check my Installation and found out that one of my partition is flagged as msftres. Here is a screenshot of my GParted on a LiveCD: What can I do to give the players the same feel their characters would have about wilderness travel? I find that in a lot of our group's games, traveling long distances through wilderness is too easy.  In real life, it's quite arduous traveling overland.  No one who's just walked a hundred miles is eager to repeat the trip.  But here's the problem -- for the players, it's trivial to travel a long way.  You just say "then we walk over the Groblick Hills to Dorridge", and you get there.  The players find it easy, but there's no way the characters would be eager to set out on a long stretch across the wilderness.  What can I do to give the players the same feel their characters would have about wilderness travel?  One thing I'd like to avoid (if possible) is to just make it perilous by throwing in a bunch of fantasy monster encounters.  Imagine some hobbits off in Gondor -- sure, they'd love to go home to the Shire, but it's mighty tempting to stay an extra day in the inn before setting off on the journey. Earning a PhD help you learn tools and techniques in your field, and lets you become an expert in a very specific field of science. However, once you get your degree and try to enter the labor market, you're competing against people who are younger than you (i.e. recently graduated non-phd engineers) and may have actual work experience (i.e. non-phd engineers with a few years in the market).  There are, of course, some positions in which they cannot compete, including research and teaching position. Those are the minority, though... in most other fields it seems that holding a PhD is not as important as (for example) work experience.  So, I would like to know:   Is work experience more important than having a PhD in the many work environments? What skills can I acquire/demonstrate during my PhD to become more "valuable" than a non-PhD candidate for the same job? There is a line in the middle of my stroke. How do I fix that? Why didn't Harry Potter tell Aunt Petunia he was rich to improve how he was treated by Dursleys? This is a follow-up question to   One reason Aunt Petunia mistreated Harry was that she did not know he was rich. If she knew, she would naturally have treated this golden goose nicely. Her retirement would be secured if Harry financially supported her in old age.  Why didn't Harry tell Aunt Petunia he was rich? Surely every boy wants to be treated nicely by his family. Tweak showlabels/showkeys - wrap the label What are all the correct answers to the Squirrel's questions, and what is the reward when I get them all correct? Marketing Cloud IP Warming - is it critical that we send up to the weekly limits by domain? I have a LAMP server with following configuration.  CPU : Intel(R) Xeon(R) CPU   RAM : 32 GB  HDD : 80 GB  Running on virtual environment.  All the things in the server are running smoothly. But I have noticed that the RAM usage is the server is increasing each day without any reason.   This is the current memory usage on my server.  # free -g              total       used       free     shared    buffers     cached Mem:            31         13         17          0          0         10 -/+ buffers/cache:          1         29 Swap:            2          0          2   And you can see the last 8 weeks memory usage below.   And i have executed the following command to find how much memory each process is consuming.  # ps -eo size,pid,user,command --sort -size | awk '{ hr=$1/1024 ; printf("%13.2f Mb ",hr) } { for ( x=4 ; x&lt;=NF ; x++ ) { printf("%s ",$x) } print "" }'          0.00 Mb COMMAND        2253.62 Mb /usr/libexec/mysqld --basedir=/usr --datadir=/var/lib/mysql --user=mysql --pid-file=/var/run/mysqld/mysqld.pid --skip-external-locking --socket=/var/lib/mysql/mysql.sock        1171.66 Mb java -jar /etc/vmagent/bin/VMAgent.jar         138.27 Mb /sbin/audispd         127.75 Mb /usr/sbin/named -u named -c /etc/named.conf -u named -t /var/named/run-root          74.29 Mb auditd          73.03 Mb automount          43.14 Mb /usr/bin/spamd --username=popuser --daemonize --nouser-config --helper-home-dir=/var/qmail --max-children 5 --create-prefs --virtual-config-dir=/var/qmail/mailnames/%d/%l/.spamassassin --pidfile=/var/run/spamd/spamd_full.pid --socketpath=/tmp/spamd_full.sock          43.14 Mb spamd child          43.14 Mb spamd child          37.13 Mb /usr/sbin/httpd          37.02 Mb /usr/sbin/httpd          36.52 Mb /usr/sbin/httpd          36.46 Mb /usr/sbin/httpd          36.23 Mb /usr/sbin/httpd ................   For troubleshooting , i have restarted the MySQL and APACHE servers. But the result was same. Restarting the entire server will fix the issue, but i want to know what is the real issue.  Let me know if you have any idea about this issue.  Thanks,  Arun S Can I run CAT5/6 cables parallel to electrical cables? I am building a new house and am planning to hardwire network cables into each room.   Can I run CAT5/6 cables parallel to electrical wires without introducing any general safety issues or losing much in connection quality?  Wiring runs for up to 25 metres from patch panel and distribution board in garage to rooms.   My research indicates that is should be fine if they are in separate conduits or if the CAT cables are shielded. Difference between negative and positive temperatures written as absolute value or the negative integer? **In a chemistry class, students were learning about boiling point of various elements.Reuben has compiled a table that gives boiling points of each of various elements.  The lowest boiling point is of Element X: – 200 degrees Fahrenheit. The highest boiling point is of Element Y: 550 degrees Fahrenheit  Find the difference between the lowest and highest boiling point**    I know how to calculate the difference. -200 – 550 = -750.  I am not sure if the answer is written as a negative or positive. Isn’t difference in temperature always written as its absolute value? Will the answer be – 750 F or 750 F ?  Would greatly appreciate if you could explain what the correct answer is.