I notwithstanding don't larn why this [public] NASA video amongst audio that I posted to YouTube has acquired 1.8 1 K one thousand views – as well as is so my most viewed video although a few others amongst a higher added value of mine came closed – but lots of people but seem to move terrified when they are told that a dark hole sounds similar a vacuum cleaner that volition devour them LOL. Most of the 2,200+ comments seem to move compatible amongst this explanation.
Jitter – as well as Erwin – receive got brought a confusing signal virtually dark holes that I receive got genuinely encountered many times inward the past.
Jitter: When a large percent of the majority of the interior of a BH is turned into gravitons/waves during a collission, so wont time to come LIGO detectors potentially move able to sentiment the interior?The dots stand upwards for my (so far mostly unsuccessful) efforts to bring the basic signal that no observations done inward the asymptotic percentage i.e. exterior the dark hole(s) – as well as the LIGO experiment is a overstep illustration of that – but cannot watch within the dark hole. The dark hole interior is defined every bit the percentage where it's impossible to look, fifty-fifty inward principle, as well as dark hole itself is defined every bit an object that creates such a (non-vanishing) inaccessible percentage of the spacetime.
[...] Thanks Lubos. I notwithstanding don't sympathize how scientists tin ship away say "nothing tin ship away escape a BH" yet scientists claim that LIGO observed lots of majority escaping from 2 BHs. Sorry but it just does non brand feel to me. Can anyone help me sympathize this? At to the lowest degree every bit much every bit I sympathize the demand for Eigenstates to explicate attraction. ;-)
Erwin: Hi Luboš, I intend Jitter asks because of "...the merger of 2 dark holes amongst masses of 35 times as well as thirty times the majority of the Dominicus (in the source frame), resulting inward a post-merger dark hole of 62 solar masses..."
[...] I intend it boils downwards to the question: what create nosotros hateful past times "the majority of a BH", "is" this majority within the lawsuit horizon?
I didn't range upwards so I tried to postal service some other respond to Erwin's in conclusion question. Is the majority a "stuff" that may move counted past times counting something inward the dark hole interior?
The respond is No.
Dear Erwin - as well as Jitter,
y'all powerfulness show to imagine that the dark hole majority \(M\) has the value it has because of "something inside". But inward full general relativity, y'all can't ever larn an accurate method to calculate the precise majority past times "integrating some quantity inward the interior" of the dark hole – or a neutron star, for that matter, or whatever other celestial object.
Instead, the majority of the dark hole – but also the majority of the neutron star, a planet, or anything else - may only move measured accurately when you're outside, as well as it may move defined e.g. every bit the ADM mass. The ADM majority is defined every bit the numerator \(M\) inward \(M/r\) which determines the departure of the \(g_{00}\) factor of the metric tensor \(g_{\mu\nu}\) at infinity. At (\(r\) goes to) infinity,\[
g_{00} = 1 - \frac{2 GM}{r} + \text{small corrections}.
\] So the value of the majority is given past times how much the object - dark hole, neutron star, or anything else – curves the spacetime outside the object. And it becomes easiest to isolate the majority \(M\) past times looking how much the object curves the *very distant* spacetime of large \(r\) i.e. \(r\gg 2GM\).
In particular, the dark hole majority can't move calculated every bit whatever integral of mass/energy density such every bit \(T_{00}\). In fact, the discover energy density \(T_{00}\) is just null – the whole stress-energy tensor is null inward the whole dark hole spacetime, the dark hole spacetime is Ricci-flat so it solves the *vacuum* Einstein's equations (without a source) \(R_{\mu\nu}=0\).
And if y'all wanted to say that the whole majority \(M\) is obtained from the singularity, y'all won't move able to larn a adept calculation because the integral over the singularity would move singular. Moreover, the infinite as well as fourth dimension are genuinely interchanged within the dark hole (the signs of the components \(g_{rr}\) as well as \(g_{tt}\) larn inverted for \(r \lt 2GM\)) so the do is inward no manner equivalent to a elementary 3D book integral of \(M\delta(x)\delta(y)\delta(z)\). The Schwarzschild singularity, to option the "simplest" dark hole, is a 2nd inward time, non a house inward space. It is the terminal 2nd of life for the infalling observers. In a locally (conformally) Minkowski spell close the singularity amongst some causally Minkowskian coordinates \(t,x,y,z\) as well as \(r=|(x,y,z)|\), the Schwarzschild singularity looks similar a \(t=t_f\) hypersurface, non every bit \(r=0\).
So again, I hoped that my previous comment made it clear, as well as everyone should receive got known it earlier that comment, anyway – but it wasn't the case. So I promise y'all volition show to read this comment as well as sympathize it – Erwin as well as Jitter. And maybe others. The value of the dark hole majority or a celestial object's majority has null to create amongst the properties of the interior. Instead, it is given past times how much the object curves the exterior spacetime. The exterior spacetime is continuously connected to the interior. But that doesn't hateful that the interior is the "cause" of the curved shape inward the exterior. In the dark hole case, this interpretation of the cause-and-effect is strictly prohibited because the external spacetime does not belong to the time to come lite cone of the interior, so it cannot move affected past times the interior. So the events as well as majority densities inward the dark hole interior, as well as peculiarly the singularity, cannot move the motion of whatever measuring done outside, e.g. the measuring of the dark hole majority or neutron star majority done past times LIGO. LIGO only sees external properties of the objects – what has existed or so those objects since the beginning.
The Penrose causal diagram for a regular 4D Schwarzschild (neutral) dark hole. Well, an evaporating 1 – that only adds the molar at the top. Time by as well as large goes up. Light moves to the Northwest as well as Northeast, massive objects receive got to displace closer to the North (vertically up) than either West or East. Superluminal displace inward directions closer to the East or West is prohibited. Each signal describes a sphere amongst the extra coordinates \(\theta,\phi\) that are suppressed because the dark hole spacetime is spherically symmetric. However, the components of the metric tensor \(g_{\tau\tau}\) as well as \(g_{\rho\rho}\) where \((\rho,\tau)\) are the 2 Cartesian coordinates on the film are rescaled past times a full general scalar function. Near the right cease of the tooth-like spacelike singularity, this scalar factor is huge, so most of the history of the dark hole – as well as its book – is concentrated over there. The yellowish trouble is the give-and-take trouble of the surface of a collapsing star. That point, similar whatever doomed observer, is guaranteed to striking the singularity where the curved shape goes to infinity. The orangish life is the Blue Planet trouble of an observer who managed to rest outside. The reddish triangle is the dark hole interior. It is separated from the lite chocolate-brown exterior past times the dark-green lawsuit horizon. Nothing from the dark hole interior, the reddish triangle, tin ship away ever influence the "infinite future" percentage where e.g. the LIGO experiments are located.
The causal human relationship is just the contrary one. The dark hole singularity is a consequence (not the cause) of the likewise strong gravitational plain that has existed or so the object (e.g. a star that has gravitationally collapsed). The dark hole singularity is a number – it belongs to the causal future of the collapsing star – as well as the collapsing star already had the \(1-2GM/r\) factor g_{00} of the metric tensor to start with. \(GM/r\) was likewise comparable to 1 – \(M\) was likewise large or r was likewise small-scale – as well as that's why the star collapsed as well as led to the nascency of the lawsuit horizon every bit good every bit the singularity. The singularity is a consequence, non the cause, of the mass.
Is it getting clear now? The whole interior is absolutely irrelevant as well as invisible for the experiments such every bit LIGO that are done exterior the dark hole. You can't watch within whatever dark hole, non fifty-fifty amongst LIGO. I genuinely hateful it. The unobservability of the dark hole interior is the #1 thing y'all should know virtually the dark hole – it is genuinely the definition of the dark hole. And y'all seem to misunderstand it. It seems that you're working difficult to overlook as well as fool yourself as well as manipulate yourself into some misunderstanding of this rattling straightforward as well as elementary fact I am trying to bring for the fourth fourth dimension now. ;-)
In Newtonian physics, y'all may intend that the gravitational plain is just some "consequence" – a shadow of the object, a derived thing, mayhap just a virtual 1 that nosotros only imagine to exist, as well as only the object amongst its intrinsic majority is "real". But that's non a possible storey inward full general relativity. In full general relativity, the gravitational fields must move considered at to the lowest degree every bit existent every bit the majority sources – as well as for the LIGO measurements, they're to a greater extent than existent or to a greater extent than relevant. LIGO sees pure gravitational waves that are just a curved spacetime as well as they may be fifty-fifty if \(T_{\mu\nu}=0\) everywhere.
The gravitational fields – the spacetime amongst some geometry encoded inward \(g_{\mu\nu} (x,y,z,t)\) – exists on overstep of the affair amongst nonzero \(T_{00}\). In the dark hole case, all the \(T_{\mu\nu}\) ultimately goes to null almost everywhere (I say "almost" because the claim may move debated close the singularity). It's only the metric tensor that remembers the interesting data virtually the 2 merging dark holes as well as the terminal dark hole that they combine into. And these gravitational fields encoded inward \(g_{\mu\nu}(x,y,z,t)\) receive got the belongings that earlier the merger, they expect like\[
g_{00} = 1 - \frac{2GM_1}{r_1} - \frac{2GM_2}{r_2}
\] i.e. the superposition of 2 gravitational potentials from 2 dark holes amongst masses \(M_1,M_2\) – where \(r_1,r_2\) are distances from their centers. And at afterward times after the merger is mostly completed as well as the unified novel object no longer radiates much, \(g_{00}\) may move approximated every bit \[
1 - \frac{2GM}{r}
\] for the unified \(M\) as well as a novel \(r\) – the distance from the centre of the novel larger dark hole – where \(M\) is slightly smaller than \(M_1+M_2\) because some mass-energy was radiated away inward the degree of gravitational waves.
But the merging dark holes are described past times pure geometry – a curved spacetime. There is no "matter" that sources anything that matters for the LIGO observation. The affair from the 2 stars has collapsed a long fourth dimension earlier the 2 dark holes came closed to start the merger. The 2 smaller initial dark holes receive got been stabilized for millions of years earlier they came closed to each other as well as started to consider a marriage (merger). For these millions of years, in that location were no traces of the stellar matter.
The neutron stars receive got a nonzero stress-energy tensor \(T_{\mu\nu}\), dissimilar the dark holes. But this cloth source is almost solely irrelevant for the larger initiative off component division of the whole gravitational moving ridge from the merger – it only matters inward the terminal stages when the 2 neutron stars touching as well as merge. In the initiative off part, the gravitational waves from the 2 orbiting neutron stars, only the external gravitational fields – the geometry similar to the dark hole illustration - matters. The gravitational plain curved similar \(1-2GM/r\) far from the massive objects was "always there", long earlier the beingness of a dark hole was decided. The \(1-2GM/r\) plain was in that location fifty-fifty when the majority was carried past times a "gas cloud" that wasn't a star yet. There was some value of \(M\) – defined from the numerator of \(1-2GM/r\) inward \(g_{00}\) – as well as it could only decrease when the object emitted some majority – ejections of massive particles but mostly electromagnetic as well as gravitational waves.
There were some relevant values of \(M_1,M_2,M\) presently earlier as well as after the merger. But they were just snapshots of the gravitational plain or so the 2 initial dark hole or the unmarried terminal one. The gravitational moving ridge seen past times LIGO is a number of the spacetime geometry involving the 2 merging dark holes. But the events close the singularity are a number of the interactions of the objects amongst masses \(M_1,M_2\) or the heavier stellar masses \(M_{s1},M_{s2}\), too.
What is incorrect to say is the disputation the LIGO observation is a number of some affair or events within the dark hole. It is but not. There's no well-defined "overall mass-energy" distributed inward the dark hole interior, as well as fifty-fifty if in that location were one, it just couldn't touching the dark hole exterior such every bit the LIGO experiment.
By the way, I started this weblog postal service amongst the NASA video that sounds similar a vacuum cleaner. That audio was obtained inward NASA past times rescaling some (visible past times telescopes) X-ray spectrum coming from that dark hole to us into audible frequencies. Hundreds of the 2,200 comments posted nether the video also asked how it was possible that there's audio coming from a dark hole although null tin ship away escape a dark hole – which is almost the same enquiry every bit Jitter's as well as Erwin's enquiry that I was answering above.
(On YouTube, at some moment, I gave upwards efforts to respond those questions because the reservoir of the novel people who inquire the same thing seems unlimited, as well as neither my previous answers nor the FAQ added to my video seemed to help at all.)
Well, what's prohibited is a signal coming from the dark hole interior. But the audio nosotros take away heed is the signal coming from the vicinity (i.e. a component division of the exterior), non interior, of the dark hole – it encodes the X-rays from the dinner every bit the dark hole devours the affair (mostly some gas) around. So there's genuinely no contradiction amongst causality. All the audio is coming from the dinner that gets accelerated earlier it crosses the lawsuit horizon – before it gets into the interior. We can't watch or take away heed what the gas is doing after it gets to the dark hole interior.
I won't proofread this weblog postal service because I've proofread a similar Disqus comment as well as the resulting \(\LaTeX\)ed outcome seems OK after 10 seconds. Please permit me know if y'all discover mistakes.