New OOTS products from CafePress
New OOTS t-shirts, ornaments, mugs, bags, and more
Results 1 to 25 of 25
  1. - Top - End - #1
    Firbolg in the Playground
     
    Bohandas's Avatar

    Join Date
    Feb 2016

    Default Would falling into a black hole slice you to ribbons?

    People always talk about tidal forces (and eventually hitting the singularity) being what would destory an object falling into a black hole, but it seems to me that anything falling through the event horizon ought to be sliced to ribbons. I'll explain:

    Let's look at a simplified case: You're falling into a black hole head first. The hole is massive enough that there are no tidal forces, and let's imagine that it's been ejected from its galaxy so there's no accretion disc. At this particular moment your head is inside of the event horizon, but your body has not quite fallen through yet. Your head is therefore outside of causal contact with your body. To me that sounds a lot like being guillotined. And this will happen not just at your neck like in the example, but for every planck length of your body.

    Furthermore, since the gravity only gets stronger further in, wouldn't those pieces that fell in earlier remain out of causal contact with those that fell in later even after they had all fallen in?
    Last edited by Bohandas; 2021-11-14 at 04:00 PM.
    "If you want to understand biology don't think about vibrant throbbing gels and oozes, think about information technology" -Richard Dawkins

    Omegaupdate Forum

    WoTC Forums Archive + Indexing Projext

    PostImage, a free and sensible alternative to Photobucket

    Temple+ Modding Project for Atari's Temple of Elemental Evil

    Morrus' RPG Forum (EN World v2)

  2. - Top - End - #2
    Ogre in the Playground
    Join Date
    Jul 2017

    Default Re: Would falling into a black hole slice you to ribbons?

    I used to think that same thing, but someone pointed out that the gradient of how fast spacetime is getting pulled into the hole is going to be quite minimal in a case like that. Your head would be pulled in at the speed of light plus a tiny smidge (compared to a stationary observer arbitrarily far outside the hole, and understanding that "observer" might be the best term since nothing can be observed), while your feet are being pulled in at the speed of light minus a tiny smidge. Plus or minus the tiny smidge would be negligible in the case you described, so you can stretch your toes and feel your socks just fine. Then you just coast inevitably inwards until the gradient in tidal forces is enough to shred you, and then you hit a divide by zero error at the singularity.

    Note that if someone used magic to grab your feet and pull them out (difficult not just because of the extreme gravitational force pulling you inwards, but also because of how time slows to a crawl outside the event horizon compared to an outside observer), the fact that your body is not a perfectly rigid and indestructible object would mean that you're still doomed. You'd experience your feet being pulled away from you obscenely fast, ripping you in two. The outside observer may be able to save your shoe, but your hat is gone forever.

  3. - Top - End - #3
    Titan in the Playground
     
    Spore's Avatar

    Join Date
    Oct 2013
    Location
    Germany
    Gender
    Male

    Default Re: Would falling into a black hole slice you to ribbons?

    Quote Originally Posted by Bohandas View Post
    And this will happen not just at your neck like in the example, but for every planck length of your body.
    I mean your body's molecules are not touching each other, so it's still more or less a gravitational push on the macro-scale. I have studied undergrad chemistry, so I am pretty confident your molecules are pushed together and heat up considerably. So you're crushed and cooked at the same time, I assume.

    Granted I know nothing of black holes other than "incredible gravity".

  4. - Top - End - #4
    Firbolg in the Playground
     
    Rockphed's Avatar

    Join Date
    Nov 2006
    Location
    Watching the world go by
    Gender
    Male

    Default Re: Would falling into a black hole slice you to ribbons?

    My understanding (which mostly comes from reading Wikipedia during this sort of discussion), is that the event horizon is not a locally significant thing. It matters from far away since no light can get from that point out, but the gradient is smooth and can be reframed so that there is not a discontinuity.
    Quote Originally Posted by Wardog View Post
    Rockphed said it well.
    Quote Originally Posted by Sam Starfall
    When your pants are full of crickets, you don't need mnemonics.
    Dragontar by Serpentine.

    Now offering unsolicited advice.

  5. - Top - End - #5
    Titan in the Playground
     
    Yora's Avatar

    Join Date
    Apr 2009
    Location
    Germany

    Default Re: Would falling into a black hole slice you to ribbons?

    When you're ecactly at the event horizon, then 50% of the space around you is the complete blackness of the black hole, and 50% is covered in the stars of the sky. And as you keep going, the amount of "no light" keeps continuing to increase. The sky with the stars keeps taking up a smaller and smaller portion of the space around you above. (In all planetary cases, the direction of gravity is "down", that convention is kept for any object, which is why it's always talked as feet first.)

    You never reac a black barrier that you pass through from your perspective. (And to get technical, not from an outside perspective either.) You will be physically inside the event horizon at some point, but with the way light travels, it can't be visibly percieved as such.
    We are not standing on the shoulders of giants, but on very tall tower of other dwarves.

    Spriggan's Den Heroic Fantasy Roleplaying

  6. - Top - End - #6
    Ogre in the Playground
     
    PaladinGuy

    Join Date
    Feb 2012
    Gender
    Male

    Default Re: Would falling into a black hole slice you to ribbons?

    The scientific term is "Spaghettification".

    The issue being as you approach the event horizon, you'll experience vastly higher gravity at the end of you closer to the singularity than the far end. So you'll stretch out like spaghetti. Sometimes scientific terms are on the nose like that. That or whoever came up with it was hungry at the time.

  7. - Top - End - #7
    Titan in the Playground
     
    Brother Oni's Avatar

    Join Date
    Nov 2007
    Location
    Cippa's River Meadow
    Gender
    Male

    Default Re: Would falling into a black hole slice you to ribbons?

    Quote Originally Posted by McNum View Post
    The scientific term is "Spaghettification".

    The issue being as you approach the event horizon, you'll experience vastly higher gravity at the end of you closer to the singularity than the far end. So you'll stretch out like spaghetti. Sometimes scientific terms are on the nose like that. That or whoever came up with it was hungry at the time.
    For a more graphic description, the Junji Ito manga, Uzumaki, has this in a number of the series' stories.

  8. - Top - End - #8
    Troll in the Playground
     
    Flumph

    Join Date
    Nov 2006
    Location
    England. Ish.
    Gender
    Male

    Default Re: Would falling into a black hole slice you to ribbons?

    Quote Originally Posted by McNum View Post
    The scientific term is "Spaghettification".

    The issue being as you approach the event horizon, you'll experience vastly higher gravity at the end of you closer to the singularity than the far end. So you'll stretch out like spaghetti. Sometimes scientific terms are on the nose like that. That or whoever came up with it was hungry at the time.
    It depends on the size of the black hole. Smaller (Stellar) ones will rip you apart before you reach the event horizon; larger ones (such as the supermassive ones in the centre of a galaxy) you can cross the event horizon and go on for quite a while before you are inevitably racked to death.
    Warning: This posting may contain wit, wisdom, pathos, irony, satire, sarcasm and puns. And traces of nut.

    "The main skill of a good ruler seems to be not preventing the conflagrations but rather keeping them contained enough they rate more as campfires." Rogar Demonblud

    "Hold on just a d*** second. UK has spam callers that try to get you to buy conservatories?!? Even y'alls spammers are higher class than ours!" Peelee

  9. - Top - End - #9
    Firbolg in the Playground
    Join Date
    Dec 2010

    Default Re: Would falling into a black hole slice you to ribbons?

    It's not that stuff at the event horizon would be cut in half. In the local infalling frame, stuff still sends photons back and forth normally, chemical bonds still work fine, etc. It's more like being a fish in a river where the river current is accelerating as you go downstream, and at one point that speed relative to the source of the river passes the fastest speed that a ripple (or fish) could possibly go against the current.

    Something following the current already won't notice that point. Something trying to go upstream with all it's might may notice that difference if they can look at the shore for comparison, but won't notice it just from the water local to it.

  10. - Top - End - #10
    Ogre in the Playground
     
    mucat's Avatar

    Join Date
    Mar 2010
    Gender
    Male

    Default Re: Would falling into a black hole slice you to ribbons?

    Quote Originally Posted by McNum View Post
    The scientific term is "Spaghettification".

    The issue being as you approach the event horizon, you'll experience vastly higher gravity at the end of you closer to the singularity than the far end. So you'll stretch out like spaghetti. Sometimes scientific terms are on the nose like that. That or whoever came up with it was hungry at the time.
    Tidal forces don't go to infinity as you pass the event horizon; it happens as you approach the singularity at the center of the black hole. By that time you're already past the event horizon and out of causal contact with the universe outside.

    The event horizon itself, as measured by the falling observer, will seem to be a more-or-less-ordinary region of spacetime, with no dramatic local effects (at least none that go to infinity. The smaller the black hole, the greater the tidal forces you'll already be experiencing. If it's a supermassive black hole, the ride past the event horizon will be very smooth from the falling observer's point of view.)

    ...which still doesn't answer Bohandas's excellent question. It's easy to run the calculations from the falling observer's point of view and see that nothing dramatic happens at the event horizon, but the whole thing should ALSO make sense as measured in other frames of reference, including that of a distant observer. And I gotta admit, the whole out-of-causal-contact-with-your-own-damned-feet argument raises an excellent point and had me stumped for a while.

    The best explanation I can come up with at the moment is this: as you freefall past the event horizon, your speed as measured by a distant observer will hit c. And even though we definitely need General Relativity to make sense of black holes, Special Relativity still applies as well. Which, among other things, means that as your speed reaches c in the inward radial direction, you will occupy ZERO length along that axis (again, as measured by that distant observer.)

    So in their coordinate system, there is never a moment when you are half-inside, half-outside the event horizon; your whole body passes the event horizon simultaneously (as a zero-length object) in their frame.

    As measured in your own freely-falling frame, you are at rest the whole time and undergo no length contraction or any other relativistic effects (except that, for a large observer and a small black hole, tidal forces may be a problem...but not yet an infinite problem. The event horizon is not a particularly special point as measured in the freely-falling frame, but the singularity is, and thus Spaghettification awaits in the near future.)

    Does this help at all? I'll give it some more thought, and maybe bounce the whole scenario off some other folks at work, and try to give a clearer explanaiton if and when I have one.
    Last edited by mucat; 2021-11-15 at 11:43 PM.

  11. - Top - End - #11
    Ogre in the Playground
    Join Date
    Jul 2017

    Default Re: Would falling into a black hole slice you to ribbons?

    Assuming an outside observer who could magically see what was really happening inside an event horizon, my best guess is that they'd see outgoing signals "heading away from the singularity" in the sense that their outward velocity against the inrushing spacetime makes them go slower than a stationary-to-that-spacetime particle would go. For simplicity we'll say Bohandas is at rest compared to the local patch of spacetime. So while a photon emitted at any point below the event horizon will never be able to reach a point farther from the singularity, it's still able to reach the particles in his body that are rushing towards the singularity even faster than it is.

  12. - Top - End - #12
    Troll in the Playground
     
    Imp

    Join Date
    Jul 2008
    Location
    Sweden
    Gender
    Male

    Default Re: Would falling into a black hole slice you to ribbons?

    Quote Originally Posted by Yora View Post
    When you're ecactly at the event horizon, then 50% of the space around you is the complete blackness of the black hole, and 50% is covered in the stars of the sky. And as you keep going, the amount of "no light" keeps continuing to increase. The sky with the stars keeps taking up a smaller and smaller portion of the space around you above. (In all planetary cases, the direction of gravity is "down", that convention is kept for any object, which is why it's always talked as feet first.)

    You never reac a black barrier that you pass through from your perspective. (And to get technical, not from an outside perspective either.) You will be physically inside the event horizon at some point, but with the way light travels, it can't be visibly percieved as such.
    The "50% space around you is complete blackness" point is the photon sphere of the black hole, the radius where light orbits. At the event horizon the whole universe will seem like a dot of light directly above you.

    Scott Manley did an excellent video on it. (VR)
    Black text is for sarcasm, also sincerity. You'll just have to read between the lines and infer from context like an animal

  13. - Top - End - #13
    Firbolg in the Playground
     
    Bohandas's Avatar

    Join Date
    Feb 2016

    Default Re: Would falling into a black hole slice you to ribbons?

    Quote Originally Posted by mucat View Post
    The best explanation I can come up with at the moment is this: as you freefall past the event horizon, your speed as measured by a distant observer will hit c. And even though we definitely need General Relativity to make sense of black holes, Special Relativity still applies as well. Which, among other things, means that as your speed reaches c in the inward radial direction, you will occupy ZERO length along that axis (again, as measured by that distant observer.)
    That makes sense.
    "If you want to understand biology don't think about vibrant throbbing gels and oozes, think about information technology" -Richard Dawkins

    Omegaupdate Forum

    WoTC Forums Archive + Indexing Projext

    PostImage, a free and sensible alternative to Photobucket

    Temple+ Modding Project for Atari's Temple of Elemental Evil

    Morrus' RPG Forum (EN World v2)

  14. - Top - End - #14
    Troll in the Playground
    Join Date
    Jan 2007

    Default Re: Would falling into a black hole slice you to ribbons?

    An outside observer can never see anything actually falling into the event horizon because the time dilation around the black hole is immense and approaches infinity at the event horizon. So a falling object would be observed to get closer and closer to the event horizon (and the descent will actually slow down from the outside point of view), with the optical signal getting fainter and fainter as the light is redshifted more prominently. Eventually the signal would be too dim to actually observe - way before anyone could see anything touch the event horizon. In fact, from the outside perspective, it would take infinite time for anything to fall beyond the event horizon.

    So neither the outside observer, nor the falling one will ever see anything being sliced by the event horizon.
    In a war it doesn't matter who's right, only who's left.

  15. - Top - End - #15
    Ettin in the Playground
     
    Griffon

    Join Date
    Jun 2013
    Location
    Bristol, UK

    Default Re: Would falling into a black hole slice you to ribbons?

    Quote Originally Posted by Radar View Post
    In fact, from the outside perspective, it would take infinite time for anything to fall beyond the event horizon.
    So what happens visually when something is falling through one of the event horizons while two black holes are merging?
    The end of what Son? The story? There is no end. There's just the point where the storytellers stop talking.

  16. - Top - End - #16
    Troll in the Playground
     
    Flumph

    Join Date
    Nov 2006
    Location
    England. Ish.
    Gender
    Male

    Default Re: Would falling into a black hole slice you to ribbons?

    Quote Originally Posted by halfeye View Post
    So what happens visually when something is falling through one of the event horizons while two black holes are merging?
    Pretty much the same as if it was a single black hole. An event horizon is an event horizon.
    Warning: This posting may contain wit, wisdom, pathos, irony, satire, sarcasm and puns. And traces of nut.

    "The main skill of a good ruler seems to be not preventing the conflagrations but rather keeping them contained enough they rate more as campfires." Rogar Demonblud

    "Hold on just a d*** second. UK has spam callers that try to get you to buy conservatories?!? Even y'alls spammers are higher class than ours!" Peelee

  17. - Top - End - #17
    Ettin in the Playground
     
    Griffon

    Join Date
    Jun 2013
    Location
    Bristol, UK

    Default Re: Would falling into a black hole slice you to ribbons?

    Quote Originally Posted by Manga Shoggoth View Post
    Pretty much the same as if it was a single black hole. An event horizon is an event horizon.
    I strongly suspect this is rubbish.

    When two black holes are merging, two event horizons become one, and for a very short space of time cease to be spherical. The size of the eventual event horizon will be bigger than either of the starting ones. The position of the resultant event horizon will be different than the position of either of the starting ones, for one thing they rotate around one another very fast. If the infalling object was nearing the part of the surface (in so far as it is a surface) of the event horizon which was facing the other black hole, it might be entirely swallowed in the merger, while it seems that if it was near the farther point from the other black hole it might emerge briefly, or maybe not. Anyway, I take it that when black holes merge, the events are not time dilated.
    Last edited by halfeye; 2021-11-17 at 07:36 PM.
    The end of what Son? The story? There is no end. There's just the point where the storytellers stop talking.

  18. - Top - End - #18
    Troll in the Playground
     
    Flumph

    Join Date
    Nov 2006
    Location
    England. Ish.
    Gender
    Male

    Default Re: Would falling into a black hole slice you to ribbons?

    Quote Originally Posted by halfeye View Post
    I strongly suspect this is rubbish.

    When two black holes are merging, two event horizons become one, and for a very short space of time cease to be spherical. The size of the eventual event horizon will be bigger than either of the starting ones. The position of the resultant event horizon will be different than the position of either of the starting ones, for one thing they rotate around one another very fast. If the infalling object was nearing the part of the surface (in so far as it is a surface) of the event horizon which was facing the other black hole, it might be entirely swallowed in the merger, while it seems that if it was near the farther point from the other black hole it might emerge briefly, or maybe not.
    When two black holes merge there will still be an event horizon. You may be correct in that it will not be a spherical event horizon, and it may well be in motion, but that makes no difference whatsoever to how it will work from our side.

    Once something crosses the event horizon it will not come out again, no matter how the event horizon does or does not move. Because again, that's how event horizons work.

    Quote Originally Posted by halfeye View Post
    Anyway, I take it that when black holes merge, the events are not time dilated.
    All the effects of General Relativity will be in play, including time dilation, length contraction and extreme headaches. We just can't see what is happening beyond the event horizon. (And don't ask what happens at the singularity....)
    Warning: This posting may contain wit, wisdom, pathos, irony, satire, sarcasm and puns. And traces of nut.

    "The main skill of a good ruler seems to be not preventing the conflagrations but rather keeping them contained enough they rate more as campfires." Rogar Demonblud

    "Hold on just a d*** second. UK has spam callers that try to get you to buy conservatories?!? Even y'alls spammers are higher class than ours!" Peelee

  19. - Top - End - #19
    Firbolg in the Playground
     
    Bohandas's Avatar

    Join Date
    Feb 2016

    Default Re: Would falling into a black hole slice you to ribbons?

    Quote Originally Posted by Anymage View Post
    Assuming an outside observer who could magically see what was really happening inside an event horizon, my best guess is that they'd see outgoing signals "heading away from the singularity" in the sense that their outward velocity against the inrushing spacetime makes them go slower than a stationary-to-that-spacetime particle would go. For simplicity we'll say Bohandas is at rest compared to the local patch of spacetime. So while a photon emitted at any point below the event horizon will never be able to reach a point farther from the singularity, it's still able to reach the particles in his body that are rushing towards the singularity even faster than it is.
    Ok, that makes sense.

    Quote Originally Posted by Manga Shoggoth View Post
    Pretty much the same as if it was a single black hole. An event horizon is an event horizon.
    Are you talking about stuff falling out of the central areas when the horizons contract? Because I've wondered about that too

    Quote Originally Posted by Radar View Post
    An outside observer can never see anything actually falling into the event horizon because the time dilation around the black hole is immense and approaches infinity at the event horizon. So a falling object would be observed to get closer and closer to the event horizon (and the descent will actually slow down from the outside point of view), with the optical signal getting fainter and fainter as the light is redshifted more prominently. Eventually the signal would be too dim to actually observe - way before anyone could see anything touch the event horizon. In fact, from the outside perspective, it would take infinite time for anything to fall beyond the event horizon.

    So neither the outside observer, nor the falling one will ever see anything being sliced by the event horizon.
    Assuming you're not in a galactic void or some other region where hawking radiation would dominate the hole's evolution, you woukd eventually see the horizon expand past the infalling object
    "If you want to understand biology don't think about vibrant throbbing gels and oozes, think about information technology" -Richard Dawkins

    Omegaupdate Forum

    WoTC Forums Archive + Indexing Projext

    PostImage, a free and sensible alternative to Photobucket

    Temple+ Modding Project for Atari's Temple of Elemental Evil

    Morrus' RPG Forum (EN World v2)

  20. - Top - End - #20
    Ettin in the Playground
     
    Griffon

    Join Date
    Jun 2013
    Location
    Bristol, UK

    Default Re: Would falling into a black hole slice you to ribbons?

    Quote Originally Posted by Manga Shoggoth View Post
    When two black holes merge there will still be an event horizon. You may be correct in that it will not be a spherical event horizon, and it may well be in motion, but that makes no difference whatsoever to how it will work from our side.

    Once something crosses the event horizon it will not come out again, no matter how the event horizon does or does not move. Because again, that's how event horizons work.
    What about something that is about to cross the event horizon, then the horizon shrinks away from it? I'm not saying it would escape, I'm suggesting that its crossing might be delayed.

    All the effects of General Relativity will be in play, including time dilation, length contraction and extreme headaches. We just can't see what is happening beyond the event horizon. (And don't ask what happens at the singularity....)
    If time dilation was in full effect there could be no merger. Time dilation of light may be what happens, but if there is total time dilation then there is solid stuff all the way down, the russian frozen star scenario. There would be neutronium exposed to space without graviational compression when the event horizons merged, which would mean there would be a supernova style electro-magnetic energy release when black holes merged, however all that really comes out is gravity waves, so we know time dilation does not apply to the masses inside black holes, even if it does apply to light that gets near to them.
    Last edited by halfeye; 2021-11-18 at 06:30 PM.
    The end of what Son? The story? There is no end. There's just the point where the storytellers stop talking.

  21. - Top - End - #21
    Titan in the Playground
     
    Yora's Avatar

    Join Date
    Apr 2009
    Location
    Germany

    Default Re: Would falling into a black hole slice you to ribbons?

    Quote Originally Posted by halfeye View Post
    What about something that is about to cross the event horizon, then the horizon shrinks away from it? I'm not saying it would escape, I'm suggesting that its crossing might be delayed.
    Everything that isn't inside yet, can potentially get away, given enough energy in the right direction. Just above the surface of the event horizon there will be very extreme gravity, but it's still outside the black hole. Nothing too special happening there.
    We are not standing on the shoulders of giants, but on very tall tower of other dwarves.

    Spriggan's Den Heroic Fantasy Roleplaying

  22. - Top - End - #22
    Firbolg in the Playground
     
    Bohandas's Avatar

    Join Date
    Feb 2016

    Default Re: Would falling into a black hole slice you to ribbons?

    What about something that has crossed the event horizon and then the horizon in that area shrinks significantly (such as due to the countervailing gravity of another passing black hole other super heavy object)?
    "If you want to understand biology don't think about vibrant throbbing gels and oozes, think about information technology" -Richard Dawkins

    Omegaupdate Forum

    WoTC Forums Archive + Indexing Projext

    PostImage, a free and sensible alternative to Photobucket

    Temple+ Modding Project for Atari's Temple of Elemental Evil

    Morrus' RPG Forum (EN World v2)

  23. - Top - End - #23
    Titan in the Playground
     
    Yora's Avatar

    Join Date
    Apr 2009
    Location
    Germany

    Default Re: Would falling into a black hole slice you to ribbons?

    The event horizon can only shrink due to energy loss due to Hawking radiation. Which is extremely slow.
    Matter that has passed into the event horizon is falling towards the center at light speed. Even if the event horizon would shrink at light speed, anything alredy inside the event horizon still stays inside the event horizon.
    We are not standing on the shoulders of giants, but on very tall tower of other dwarves.

    Spriggan's Den Heroic Fantasy Roleplaying

  24. - Top - End - #24
    Firbolg in the Playground
     
    Bohandas's Avatar

    Join Date
    Feb 2016

    Default Re: Would falling into a black hole slice you to ribbons?

    I forgot about the falling at light speed part.

    That said, I'm pretty sure the horuzon can change shape. If there's another massive object nearby it'll recede on the side near the onject and bulge out on the side away from it
    "If you want to understand biology don't think about vibrant throbbing gels and oozes, think about information technology" -Richard Dawkins

    Omegaupdate Forum

    WoTC Forums Archive + Indexing Projext

    PostImage, a free and sensible alternative to Photobucket

    Temple+ Modding Project for Atari's Temple of Elemental Evil

    Morrus' RPG Forum (EN World v2)

  25. - Top - End - #25
    Firbolg in the Playground
    Join Date
    Dec 2010

    Default Re: Would falling into a black hole slice you to ribbons?

    For thinking about these things, remember that events can appear in different order and at different times in different frames. The in-falling frame is not the same as a frame which is at rest at infinity. Additionally, the event horizon isn't a physical thing, it's a mathematical construction to calculate the boundary where events on one side cannot causally influence the other. So in the case of merging black holes or things like that, rather than thinking about it like there being a paradox because the event horizon could move to expose events which shouldn't be able to causally influence the outside, you should reverse the way of thinking about it and say 'given the full trajectories of the merging black holes over the entire course of their interaction, which regions of space-time will never be able to influence the outside at infinity?' and that will define the event horizon as seen from the frame at infinity.

    So e.g. if there was some matter which was closer to one of the blackholes than where the event horizon would been in a single-blackhole metric but which due to the motion becomes able to escape to infinity later, then for those merging black holes that matter just wasn't inside their event horizon.

Posting Permissions

  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts
  •