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Prasanna Bhogale

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:D silly headline aside, he makes a fair point.
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super cool stuff... a black hole is a LOT bigger on the inside than on the outside.
Black holes - bigger on the inside

Guess what: black holes are bigger inside than they look - and they get bigger as they get older! 

For example, take the big black hole in the center of our galaxy, called Sagittarius A*.  It's about 2 million kilometers across.  That's pretty big - but the orbit of Mercury is 60 times bigger.  This black hole is old, roughly a billion years old.  And here's the cool part:  it's been growing on the inside  all this time!  

How is this possible?  Well, since spacetime is severely warped in a black hole, its volume can be bigger than you'd guess from outside.  And its volume can change.  Since we understand general relativity quite well, we can calculate how this works!  But nobody thought of doing it until last year, when Marios Christodoulou and my friend Carlo Rovelli did it.   

How big is the black hole at the center of our galaxy?  On the inside, it can hold a million solar systems!  Its volume is about 10^34 cubic kilometers!   And it's growing at a rate of about 10^25 cubic kilometers per year!

Or suppose you have an ordinary star that turns into a black hole.  This black hole will last a long time before it evaporates due to Hawking radiation.  Christodolou and Rovelli estimate how big its volume will get before this happens.  And it gets really big - bigger than the current-day observable universe!

Before you get too excited, remember: people falling into the black hole will not have time to do anything fun inside.  They will hit the singularity in a short time.  Very very roughly speaking, the problem is not the shortage of space inside the black hole, it's the shortage of time.  

If you fall into the black hole at the center of our galaxy, it will be about 1 minute, at most, before you hit the singularity.   You will not get to see most of the space inside the black hole!   The singularity is not in the 'middle' of the black hole - it's in your future.  You will hit it before you can reach the 'middle'.  So, you will only get to see part of the 'edge regions' inside the black hole.

The 'middle regions' can only be seen by people who fell in much earlier.  And they can't see the 'edge', where you are!

And now for the serious part. 

The hard part of this problem is defining the volume inside a black hole. 

If you choose a moment in time, the black hole's event horizon at that moment is a sphere.  There are infinitely many ways to extend this sphere to a solid ball.  In other words: there are many ways to choose a slice of space inside the black hole whose boundary is your chosen sphere. 

The slice can bend forwards in time, or backwards in time.  We can choose a wiggly slice or a smooth one.  Each slice has its own volume.  

How do you choose one, so you can calculate its volume? Christodoulou and Rovelli choose the one with the largest volume. This may sound like it's cheating.  But it's not.

Think of a simpler problem one dimension down.  You have a loop of wire.  You ask me: "What's the area of the surface whose boundary is this loop?" 

I say: "That's a meaningless question!  Which surface?  There are lots!"  

You say: "Pick the best one!"

So, it's up to me.   I take some soapy water and make a soap film whose boundary is that loop.  That's the surface I use.   If the loop of wire is not too crazy in its shape, this surface is uniquely defined.   In some sense it's the "least wiggly" surface I could choose.

This surface minimizes the area.  A more wiggly surface would have more area.

Christodoulou and Rovelli are doing the same thing.  But spacetime is different than space!   If you choose a wiggly 3-dimensional spatial surface in spacetime, it will have less volume than a flatter surface with the same boundary!  

So, the way to pick the flattest, nicest spatial surface inside our black hole is to pick the one that maximizes the volume. 

If you tried to minimize the volume, you could get it as close to zero as you wanted.  And this would have nothing to do with black holes!   This would be true even in your living room.

Puzzle: why?

Here's the paper:

• Marios Christodoulou and Carlo Rovelli, How big is a black hole?,

#spnetwork arXiv:1441.2854 #generalRelativity  
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this. is. brilliant. 
Van Gogh, you beauty. 
Matemática e a Noite Estrelada de Van Gogh
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awesomeness with +Nima Doroud !!
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One expects a space research organization to be less parochial.
Statement regarding suspension of some NASA activities with Russian Government representatives:

Given Russia's ongoing violation of Ukraine's sovereignty and territorial integrity, NASA is suspending the majority of its ongoing engagements with the Russian Federation.  NASA and Roscosmos will, however, continue to work together to maintain safe and continuous operation of the International Space Station. NASA is laser focused on a plan to return human spaceflight launches to American soil, and end our reliance on Russia to get into space.  This has been a top priority of the Obama Administration’s for the past five years, and had our plan been fully funded, we would have returned American human spaceflight launches – and the jobs they support – back to the United States next year.  With the reduced level of funding approved by Congress, we’re now looking at launching from U.S. soil in 2017.  The choice here is between fully funding the plan to bring space launches back to America or continuing to send millions of dollars to the Russians.  It’s that simple.  The Obama Administration chooses to invest in America – and we are hopeful that Congress will do the same.
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yes please !
This is a campaign to get Google+ to support the LaTeX markup language for the purpose of posting to the stream.

1) From your home page click on the gear icon in the top right corner
2) Choose 'Send Feedback'
3) Type in something to the affect of "Please support LaTeX on Google+"
4) Drag the dialog box over your stream and click 'Submit'
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