Are black holes totally black and formed? Good morning, I know some similar questions have been asked but I don't find a convincing answer in these. Excuse me if I have missed the answer.  My question is:  I have learned that some black holes are formed by contraction of stard ( the exact processus does not matter here ). The problem is that the time dilatation due to gravitation is increasing with the contraction being infinite when all the matter pass inside the horizon.   But for an external observer it will take an infinite amount of time so that the black holes we see today are nearly perfect black holes but not totally since all the matter have not passed the horizon. Am I wrong here?   Furthermore, these black holes could not be totally black since all the matter of the original stars do not pass the horizon. So it would be possible for them to emit a bit of light no?   But this is not what I read so if someone could explain me, I would be grateful to him ;)
Can black holes form in a finite amount of time? One thing I know about black holes is that an object gets closer to the event horizon, gravitation time dilation make it move more slower from an outside perspective, so that it looks like it take an infinite amount of time for the object to reach the event horizon. It seems like a similar process should slow the formation of the black hole itself: As the star collapses, its gravitational time dilation make itself collapse more slowly. This make me wonder, are what astronomers claim to be black holes really black holes, or are they stars that progressively make themselves more similar to one without actually reaching the stage of having an event horizon?  EDIT: Contemplating one answer, I realize the question is ambiguous. What does finite time mean in general relativity. Here is a less ambiguous question: Is there a connected solution of 3+1 dimensional general relativity with one space-like slice not have a singularity, and another space-like slice having one.
Can you allocate an array with something equivalent to make_shared? Using AMPScript, I want to pass from a URL Attribute lookup variables and use these variables in my LookupOrderRows function.   The challenge is that not all lookup variables have to be passed by the URL e.g I might lookup just 'office' or I could also lookup both 'office' and 'score.   I've tried several approaches of Concat the string etc - but can't see to make the lookup work.  Has anyone had any success performing similar?   IF not empty( Requestparameter("office") ) then  Set @field1_name = "OFFICE" Set @field1_value = Requestparameter("office")  EndIf  IF not empty( Requestparameter("specialism") ) then  Set @field2_name = "SPECIALISM" Set @field2_value = Requestparameter("specialism")  EndIf  IF not empty( Requestparameter("score") ) then  Set @field3_name = "SCORE" Set @field3_value = Requestparameter("score")  EndIf   set @rows = LookupOrderedRows(@LeadsDE,0,"[Engagement Activity Date] desc",@Field1_Name,@Field1_Value,@Field2_Name,@Field2_Value,@Field3_Name,@Field3_Value)   My current solution is a lot If then statements and combinations i.e. :  /* OFFICE ONLY*/ IF NOT EMPTY(@input_office) AND EMPTY(@input_organisation) AND EMPTY(@input_specialism)  AND EMPTY(@input_score) then     set @rows = LookupOrderedRows(@LeadsDE,0,"[Engagement Activity Date] desc","OFFICE",@input_office) ENDIF  /* OFFICE + ORG*/ IF NOT EMPTY(@input_office) AND NOT EMPTY(@input_organisation) AND EMPTY(@input_specialism)  AND EMPTY(@input_score) then     set @rows = LookupOrderedRows(@LeadsDE,0,"[Engagement Activity Date] desc","OFFICE",@input_office,"ORGANISATION_NAME",@input_organisation) ENDIF /* OFFICE + ORG + SPECIALISM */ IF NOT EMPTY(@input_office) AND NOT EMPTY(@input_organisation) AND NOT EMPTY(@input_specialism)  AND EMPTY(@input_score) then     set @rows = LookupOrderedRows(@LeadsDE,0,"[Engagement Activity Date] desc","OFFICE",@input_office,"ORGANISATION_NAME",@input_organisation,"SPECIALISM",@input_specialism) ENDIF /* OFFICE + ORG + SCORE */ IF NOT EMPTY(@input_office) AND NOT EMPTY(@input_organisation) AND EMPTY(@input_specialism)  AND NOT EMPTY(@input_score) then     set @rows = LookupOrderedRows(@LeadsDE,0,"[Engagement Activity Date] desc","OFFICE",@input_office,"ORGANISATION_NAME",@input_organisation,"Engagement Score",@input_score) ENDIF /* OFFICE + ORG + SPECIALISM + SCORE  */ IF NOT EMPTY(@input_office) AND NOT EMPTY(@input_organisation) AND NOT EMPTY(@input_specialism)  AND EMPTY(@input_score) then     set @rows = LookupOrderedRows(@LeadsDE,0,"[Engagement Activity Date] desc","OFFICE",@input_office,"ORGANISATION_NAME",@input_organisation,"SPECIALISM",@input_specialism,"Engagement Score",@input_score) ENDIF  IF NOT EMPTY(@input_office) AND EMPTY(@input_organisation) AND NOT EMPTY(@input_specialism)  AND EMPTY(@input_score) then     set @rows = LookupOrderedRows(@LeadsDE,0,"[Engagement Activity Date] desc","OFFICE",@input_office,"SPECIALISM",@input_specialism) ENDIF  IF NOT EMPTY(@input_office) AND EMPTY(@input_organisation) AND NOT EMPTY(@input_specialism)  AND NOT EMPTY(@input_score) then     set @rows = LookupOrderedRows(@LeadsDE,0,"[Engagement Activity Date] desc","OFFICE",@input_office,"SPECIALISM",@input_specialism,"Engagement Score",@input_score) ENDIF  IF NOT EMPTY(@input_office) AND EMPTY(@input_organisation) AND EMPTY(@input_specialism)  AND NOT EMPTY(@input_score) then     set @rows = LookupOrderedRows(@LeadsDE,0,"[Engagement Activity Date] desc","OFFICE",@input_office,"Engagement Score",@input_score) ENDIF Overlapping matches in Regex I can't seem to find an answer to this problem, and I'm wondering if one exists. Simplified example:  Consider a string "nnnn", where I want to find all matches of "nn" - but also those that overlap with each other. So the regex would provide the following 3 matches:   nnnn nnnn nnnn   I realize this is not exactly what regexes are meant for, but walking the string and parsing this manually seems like an awful lot of code, considering that in reality the matches would have to be done using a pattern, not a literal string. For a physics major, what are the best books/references on Greens functions for self-studying?  My mathematical background is on the level of Mathematical Methods in the physical sciences by Mary Boas. What's "Another Way In"? There's a new achievement and I'm stumped as to how to get it:     Start a game without breaking the laboratory wall   I assume it has something to do with the new Gadgets but none of them sound like they'd help. How do I get this achievement? Split string every nth character? Why do we say "is it" when asking a question rather than "it is"? What it says on the tin, a foreign friend of mine has asked and I can't tell him; apart from it sounding horrible.  For example:  "Why is it raining today?"   Instead of:  "Why it is raining today?" Most of the time, it should be really easy to determine who is my ally and who is not. The people who try to kill me are most likely my foes, whereas the people who entered the dungeon with me are probably my allies.   But sometimes it’s not that simple. What if one of my party members got replaced by an evil doppelganger, who plans to kill me in the near future? What if one of my allies infiltrated the court of the evil king and I accidentally have to fight her, while she is (unbeknownst to me) under the effect of a  spell? What if a character fell in love with the BBEG and just wants to save him from himself, while the BBEG hates the character and actively tries to murder him?  Most spells and abilities that affect others specify the targets as “creatures” or “willing creatures”. Some explicitly affect allies only. That’s why I want to know, how to determine who’s allied with whom. Do I have to think that someone is my ally for someone to count as my ally? Does someone else have to believe to be my ally in order to count? Do both of us have to agree on being allies? Is there an objective observer who determines who’s allied? Can Person A be the ally of Person B, while Person B is not the ally of Person A?  There are many examples for spells/abilities that care about allies, among others:   the Exalted Champion feature from the  (SCAG, p. 132-133), that grants allies within 30 feet advantage on Wisdom saving throws. the Inspiring Surge feature from the  (SCAG, p. 128), that allows one or two allies within 60 feet to make a melee weapon attack as a reaction.   With features like this, you could accidentally affect someone who’s not actually your ally. You could fail to affect someone who is actually your ally, but you don’t know it (yet). Or you could affect someone who doesn’t want to be affected (because they don’t want to be allied with you). This all depends on the interpretation of the word “ally”. I’m not sure if "ally" is a defined game term (but I don’t think so), or if I have to rely on the dictionary definition. That’s why I want to ask:  How do I determine who’s allied with whom? We are currently working on a windows based application where users capture data. Some data is captured in a table where other data is captured in text blocks. Im currently faced with the dilemma of how to align contents specifically decimal values.  Editable cells in a grid are indicated with a pencil icon which disappears once in edit mode. You will notice that the table consists of various field types, decimals and text. So what should I do and why?  A> right align all cell content  B> left align all cell content  C> right align only decimal values in cells  D> Whatever else you can suggest ID a book about a mirror world and 4th dimension I read a book about 10-15 years ago about a boy and a girl who find a mirror. What made the mirror special was, they were able to enter the reflection and be a part of the reverse image world. They end up going to school and when asked to write something on the board, it ends up being backwards, but to them looks normal.  Later, the two end up in a world with 4 dimensions. With the added dimension they can't see as they normally could. If one moved a certain way the other would see their insides. Eventually a native of that dimension made some type of device that lets them see regularly.  Other than that my memory is blank. If I remember anything else I will be sure to edit it in. How can the Xenomorph see? If you just look at a picture of one there are no eyes readily apparent but they clearly know where they are going. Could their screeching be some form of echo-location? A matrix and its transpose have the same set of eigenvalues/other version: $A$ and $A^T$ have the same spectrum Let $ \sigma(A)$ be the set of all eigenvalues of $A$. Show that $ \sigma(A) = \sigma\left(A^T\right)$ where $A^T$ is the transpose matrix of $A$. Multiple servers acting like a single one with all the hardware? by now I have 10 servers for hpc, power computing oriented. My users need to launch several processes using qmake. The users are used to work with ubuntu 9.10, and the software from the repositories is switable for them.  I've deployed ubuntu 9.10 to all 10 servers (pxe rocks).  By now we work with parallel-ssh and cluster-ssh, which allows as to launch the same process to all servers. With this tools this tools the servers remain as independent but with the same software and the same launched command.  Now we would like to go to next step and see all the servers as a single one with all the resources from the other 9 as if was its resources.   The difference would be substantial in time to process and also time to design the command to launch.  Any advice on wich software to use will be very useful?  Thanks How many times can I benefit from Advantage if I attack multiple times while not seen? A hidden ranger with Extra Attack attacks a surprised creature. Do both attacks benefit from Advantage, or just the first one?  If the ranger used Horde Breaker on another creature, would this attack benefit from Advantage? Some time ago I closed my front door (rather forcefully) while the deadbolt was sticking out partially.  This loosened the deadbolt, and the top screw no longer held. In addition, it cracked the door on the interior side. I've attached a picture showing the damage.   The door works mainly, though it can be difficult to lock sometimes, especially when the weather gets colder.  I'm currently renting, and will soon be moving out of this house, once I buy a house. I would like to repair this door myself, and I'm hoping I don't have to replace the entire door.  Is this something that can be repaired? If so, how? I realize that a new deadbolt is probably needed, but how can I repair the wood damage around it? Solving 4 Quadratic Simultaneous Equations Consider the equations:   $$\begin{cases} ab+c+d=3\\ bc+d+a=5\\ cd+a+b=2\\ da+c+b=6 \end{cases}$$   Where $a,b,c,d \in \mathbb{R}$. How can we find $a,b,c,d$?   The furthest I've got is by adding the first two equations and the last two equations together to get: $ab+bc+c+d+d+a=(b+1)(a+c)+2d=8$ and $(d+1)(a+c)+2b=8$ We can rearrange these (assuming $b,d \neq -1$) to get $$\frac{8-2d}{b+1}=\frac{8-2b}{d+1} \implies -d^{2}+3d+4=-b^{2}+3b+4$$ Which leads us further to $$b^{2}-d^{2}-3(b-d)=0 \implies (b-d)(b+d-3)=0$$ Now since $b=d$ gives us an absurdity (equations 1 and 4 reduce to 3=6), we must have $b+d=3$. This is as far as I can get unfortunately, since trying the same approach with the other pairs doesn't work in the same way.  Help would be much appreciated; the problem is from the BMO1 2004 paper. I want to calculate $$ \int_{0}^{\infty} \frac{\arctan{2t}}{e^{2\pi t}+1} \, {\rm d}t $$ and am wondering if there at all is an analytical expression for the result. I haven't tried much so far, but expressing the denominator as the geometric series and then substituting $z=2\pi t (n+1)$. Equivalently I get $$ \sum_{n=0}^{\infty} \frac{{\rm si}\left(\pi(n+1)\right)}{2\pi (n+1)} $$ where $$ {\rm si}(x) = -\int_{x}^{\infty} \frac{\sin(t)}{t} \, {\rm d}t $$ is the shifted ${\rm Si}(x)$ function. The value is approximately $0.03618247146$, in fact I know from comparison with something else that it is exactly $\frac{\ln \pi -1}{4}$, but there should be some (direct) derivation, or?  Thanks for your input if you have any.  Edit: I tried to follow your instructions, but am now stuck. So I wrote $$ {\cal L}^{-1} \left(\frac{\psi(t)-\psi(1)}{t-1}\right)(s) =\sum_{n=0}^{\infty} \frac{e^{-sn}}{n+1} = e^s \int_s^\infty \frac{{\rm d}x}{e^{x}-1} $$ and taking the Laplace-transform \begin{align} \psi(t) &amp;= \psi(1) + (t-1)\int_0^\infty {\rm d}s \, e^{-s(t-1)} \int_s^\infty \frac{{\rm d}x}{e^{x}-1} \\ &amp;= \psi(1) + (t-1) \int_0^\infty {\rm d}x \int_{0}^{x} {\rm d}s \, \frac{e^{-s(t-1)}}{e^{x}-1} \\ &amp;= \psi(1) + \int_{0}^{\infty} {\rm d}x \, \frac{1-e^{-x(t-1)}}{e^x-1} \tag{1} \\ &amp;= -\frac{1}{t} + \psi(1) + \int_0^\infty {\rm d}x \, \frac{1-e^{-tx}}{e^x-1} \tag{2} \\ &amp;= \dots \\ &amp;=-\sum_{k=0}^{n} \frac{1}{t+k} + \psi(1) + \int_0^\infty {\rm d}x \, \frac{1-e^{-(t+n)x}}{e^x-1} \\ &amp;\stackrel{(\rm{2})}{=} -\frac{1}{2t} + \ln(t) - \int_0^\infty {\rm d}x \, \left\{ \frac{1}{2} - \frac{1}{x} + \frac{1}{e^x-1}\right\} e^{-tx} \tag{Binet 1} \end{align} where $\psi(1)=-\gamma$.  Now we integrate over $t$ from $1$ to $y$ yielding $$ \ln \Gamma(y) \stackrel{({\rm 1})}{=} \psi(1)\,(y-1) + \int_0^\infty {\rm d}x \, \frac{y-1+\frac{e^{-x(y-1)}-1}{x}}{e^x-1} $$ but what now? Substitute? How to start a GUI application from cron? How to apply a modifier in V2.9+ Why I can't apply mirror modifier? Here's screen I'm a citizen of India and I'm travelling to Nepal by air. Is an Aadhaar Card a valid document used for travelling to Nepal by air?