Is this answer from  stating that an external observer can see a black hole mass grow,  correct?   This question (is an external observer can ever see the mass of a black hole increase--motivated by the standard view  that it will take an infinite time for the external observer to see the mass crossing the event horizon) is a question that comes time and again in [different variations][2] but asking basically the same. Many are marked as duplicates and when you go there that one is also marked as a duplicate in an endless loop (well, it ends somewhere). I also see this question is other physics forums. The multiple answers that really try to address the point are always similar: No, we cannot see it grow, or we "see" the mass growing but is actually outside the horizon (but at the same time we can never measure that), and many other variations. Many of the answers actually contradict a little each other. I do not know the actual identity of any of those who answer, and of the few that I know their identity; they are not really experts in the field.   Then I found the only answer different to all of them. It is  and it says that "he new matter to cross a critical surface that is outside the original event horizon of the smaller black hole. This occurs in finite time, even from the external observer's viewpoint, and the black hole simply grows in size" and " The time is infinite in the limit when the mass of the infalling object goes to zero and there's nothing else that makes the black hole grow. So the infalling object is just a "probe".
The event horizon of a black hole is where gravity is such that not even light can escape. This is also the point I understand that according to Einstein time dilation will be infinite for a far-away-observer.  If this is the case how can anything ever fall into a black hole.  In my thought experiment I am in a spaceship with a powerful telescope that can detect light at a wide range of wavelengths.  I have it focused on the black hole and watch as a large rock approaches the event horizon.  Am I correct in saying that from my far-away-position the rock would freeze outside the event horizon and would never pass it? If this is the case how can a black hole ever consume any material, let alone grow to millions of solar masses.  If I was able to train the telescope onto the black hole for millions of years would I still see the rock at the edge of the event horizon?  I am getting ready for the response of the object would slowly fade.  Why would it slowly fade and if it would how long would this fading take?  If it is going to red shift at some point would the red shifting not slow down to a standstill? This question has been bugging me for years!  OK - just an edit based on responses so far.  Again, please keep thinking from an observers point of view.  If observers see objects slowly fade and slowly disappear as they approach the event horizon would that mean that over time the event horizon would be "lumpy" with objects invisible, but not passed through?  We should be able to detect the "lumpiness" should we not through?
The most efficient way to implement an integer based power function pow(int, int) Adding new group layer with ArcPy? This question arises when I try to describe my itinerary to ticket service in the UK. Take for example, I plan to buy a ticket from A to B. B is the terminal. How to say its counter part A? I cannot find a proper term. I have to say "I will depart from A" or "I plan to go to B from A". Or I even use "departure place" to refer to B. I was looking at the decomposition of Fibonacci numbers using the definition of $F_n = F_{n-1} + F_{n-2}$, and noted the pattern in the coefficients of the terms were Fibonacci numbers. It appears to hold, and I believe it's true, but I haven't seen a proof for it. Does one exist?  $F_n = 1F_{n-1} + 1F_{n-2}$ $F_n = 2F_{n-2} + 1F_{n-3}$ $F_n = 3F_{n-3} + 2F_{n-4}$ $F_n = 5F_{n-4} + 3F_{n-5}$ etc  This can be generalized to $F_n = F_xF_{n-(x-1)}+F_{x-1}F_{n-x}$ Union of a finite set and a countably infinite set is countably infinite What Lagrangian counterterms might be needed in a $\phi^ 6$ theory in 3D? For some reason I can't boot my system. I get an error akin to Operating System Not Found.   I tried bootrepair, and that didn't work. So then I decided I would just save my personal files, wipe everything, and reinstall.   But in the live session, when I go to the /home directory, my username folder isn't there, instead it goes to the Live CD's desktop and other directories. Is there some other error occurring? Is there a way to recover the files? Why do you need to know who I know on Google? I just created a SE account using my Google account. It said that it needs to "Know who you are on Google" (I guess my connections). As far as I know, SE is not a social network. I can't even follow other people (seeing when they post questions and answers).  What is the reason you need to know my Google connections?  This was on code review. Actually I have an account there, but for some reason it asked me to reconnect. This is the same on MSO; one sees this explained as "This app is requesting permission to associate you with your public Google profile": Java: creating a date object from a string and inserting into MySQL Less than or equal sign If I know for two numbers a and b that    $${a &lt; b }$$  Then is it correct to say that    $$ a \leq b $$  I know that the second statement is true as long as the first one is. It seems OK as it is true but from the other side it seems kinda weird (to me), to say that, if you know, that a is strictly less that b.It's like you lose some extra information. Does Reincarnation allows skills to be passed into other classes I'm mainly asking this for Disgaea: Afternoon of Darkness, given I have enough Mana to reincarnate a character into 4 different types of Mages (Green, Blue, Red, Star), a Cleric and then a Warrior, would the Warrior have all the spells learned from the previous classes? Subgradients of non-convex functions In  (section 2.3), it is stated that:     A point $x^*$ is a minimizer of a function $f$ (not necessarily convex) if and only if $f$ is subdifferentiable at $x^*$ and $0 \in\partial f(x^*).$   Could anybody provide me with references for a proof of the above statement?   Is there a reference where we can learn more about subgradients of non-convex functions?  In Section 3. Calculus of subgradients of the above notes,many properties of subgradients are presented for convex functions. I would like to know which ones among these properties still hold for non-convex functions.  Thank you in advance! If nonempty, nonsingleton $Y$ is a proper convex subset of a simply ordered set $X$, then $Y$ is ray or interval? This is from Exercise 7 in p. 92 in Munkres's Topology.  Except for the trivial cases such as $Y$ is empty set or singleton, it seems if $Y$ is convex in an simply ordered set $X$ then $Y$ is interval or ray.  But I cannot start my proof because I cannot use $\sup$ or $\max$ functions.  What should I do? Code block is not properly formatted when placed immediately after a list item Consider the following piece of Markdown code:  This is some regular text.      &gt;&gt;&gt; def factorial(n):     ...     return 1 if n &lt; 2 else n * factorial(n - 1)     ...   * This is a list item.      &gt;&gt;&gt; def factorial(n):     ...     return 1 if n &lt; 2 else n * factorial(n - 1)     ...    Notice that the second code block is preceded by a list item.   Why is the factorial code not properly formatted under these circumstances? To demonstrate the problem, I'll insert the Markdown code show above:    This is some regular text.  &gt;&gt;&gt; def factorial(n): ...     return 1 if n &lt; 2 else n * factorial(n - 1) ...     This is a list item                 def factorial(n):       ...     return 1 if n &lt; 2 else n * factorial(n - 1)       ...               This applies to numbered as well as unnumbered lists. I have noticed that some users have taken it upon themselves to create  that allow you to see a user's rank (percentile) among SO developers.  I like this.  I was wondering if the owners of the website are planning something like this in the future?  If so, are you planning on making this by tag?  (I care less about where I rank when compared to developers of a different language).  What I'm looking for is something like this:  C#:      User is ranked #XX (Top XX %) ASP.Net: User is ranked #YY (Top YY %) How can I tell if an ETF is expensive? For stocks, I can easily look at the price/earnings ratio, and, according to The Intelligent Investor, stand clear of those with a ratio higher than 20.  How can I tell if the current price of an ETF is a good price to buy it? Are there such simple metrics? Lyircs of Free by Natalia Kills:     I'm free      I just spent all my money       but I rocked that like it don't cost a thing   Shouldn't it be "I've just spent all my money"? As far as I remember, our English told us to use Present Prefect in such case because of the just. Which words in a title should be capitalized? I'm trying modeling things like this using oracle:  An account can have 1~5 members  So I'll have a account table and a member table with a FK of account. But is that possible to check if the account have less than 5 members?  I've tried constraint and trigger but oracle doesn't allow sub queries in constraint or condition of trigger like  CHECK( SELECT ...) or IF count(*) &gt;= 5  which make things getting hard. What dried food can I take across the American border from Canada?