Spaghettification

Inastrophysics,spaghettification(sometimes referred to as thenoodle effect)^[1]is the vertical stretching and horizontal compression of objects into long thin shapes (rather likespaghetti) in a very strong, non-homogeneous gravitational field.It is caused by extremetidal forces.In the most extreme cases, near ablack hole,the stretching and compression are so powerful that no object can resist it. Within a small region, the horizontal compression balances the vertical stretching so that a small object being spaghettified experiences no net change in volume.

Stephen Hawkingdescribed the flight of a fictionalastronautwho, passing within a black hole'sevent horizon,is "stretched like spaghetti" by thegravitational gradient(difference in gravitational force) from head to toe.^[2]The reason this happens would be that thegravitationalforce exerted by the singularity would be much stronger at one end of the body than the other. If one were to fall into a black hole feet first, the gravity at their feet would be much stronger than at their head, causing the person to be vertically stretched. Along with that, the right side of the body will be pulled to the left, and the left side of the body will be pulled to the right, horizontally compressing the person.^[3]However, the termspaghettificationwas established well before this.^[4]Spaghettification of a star was imaged for the first time in 2018 by researchers observing a pair ofcolliding galaxiesapproximately 150millionlight-yearsfrom Earth.^[5]

A simple example[edit]

The spaghettification of four objects falling towards a planet

In this example, four separate objects are in the space above a planet, positioned in a diamond formation. The four objects follow the lines of thegravitoelectric field,^[6]directed towards the celestial body's centre. In accordance with theinverse-square law,the lowest of the four objects experiences the biggest gravitational acceleration, so that the whole formation becomes stretched into a line.

These four objects are connected parts of a larger object. A rigid body will resist distortion, and internal elastic forces develop as the body distorts to balance the tidal forces, so attainingmechanical equilibrium.If the tidal forces are too large, the body may yield and flow plastically before the tidal forces can be balanced, or fracture, producing either a filament or a vertical line of broken pieces.

Examples of weak and strong tidal forces[edit]

In the gravity field due to a point mass or spherical mass, for a uniform rod oriented in the direction of gravity, thetensile forceat the center is found byintegration of the tidal forcefrom the center to one of the ends. This gives $F=.mw-parser-output .sfrac{white-space:nowrap}.mw-parser-output .sfrac.tion,.mw-parser-output .sfrac .tion{display:inline-block;vertical-align:-0.5em;font-size:85%;text-align:center}.mw-parser-output .sfrac .num{display:block;line-height:1em;margin:0.0em 0.1em;border-bottom:1px solid}.mw-parser-output .sfrac .den{display:block;line-height:1em;margin:0.1em 0.1em}.mw-parser-output .sr-only{border:0;clip:rect(0,0,0,0);clip-path:polygon(0px 0px,0px 0px,0px 0px);height:1px;margin:-1px;overflow:hidden;padding:0;position:absolute;width:1px}⁠μ l m/4r3⁠$ ,where $μ$ is thestandard gravitational parameterof the massive body, $l$ is the length of the rod, $m$ is rod's mass, and $r$ is the distance to the massive body. For non-uniform objects the tensile force is smaller if more mass is near the center, and up to twice as large if more mass is at the ends. In addition, there is a horizontal compression force toward the center.

For massive bodies with a surface, the tensile force is largest near the surface, and this maximum value is only dependent on the object and the average density of the massive body (as long as the object is small relative to the massive body). For example, for a rod with a mass of 1 kg and a length of 1 m, and a massive body with the average density of the Earth, this maximum tensile force due to the tidal force is only 0.4 μN.

Due to the high density, the tidal force near the surface of awhite dwarfis much stronger, causing in the example a maximum tensile force of up to 0.24 N. Near aneutron star,the tidal forces are again much stronger: if the rod has a tensile strength of 10,000 N and falls vertically to a neutron star of 2.1 solar masses, setting aside that it would melt, it would break at a distance of 190 km from the center, well above the surface (a neutron star typically has a radius of only about 12 km).^{[note 1]}

In the previous case, objects would actually be destroyed and people killed by the heat, not the tidal forces - but near a black hole (assuming that there is no nearby matter), objects would actually be destroyed and people killed by the tidal forces because there is no radiation (outside of theoretical Hawking radiation). Moreover, a black hole has no surface to stop a fall. Thus, the infalling object is stretched into a thin strip of matter.

Inside or outside the event horizon[edit]

The point at which tidal forces destroy an object or kill a person will depend on the black hole's size. For asupermassive black hole,such as those found at a galaxy's center, this point lies within theevent horizon,so an astronaut may cross the event horizon without noticing any squashing and pulling, although it remains only a matter of time, as once inside an event horizon, falling towards the center is inevitable.^[8]For small black holes whoseSchwarzschild radiusis much closer to thesingularity,the tidal forces would kill even before the astronaut reaches the event horizon.^[9]^[10]For example, for a black hole of 10 Sun masses^{[note 2]}the above-mentioned rod breaks at a distance of 320 km, well outside the Schwarzschild radius of 30 km. For a supermassive black hole of 10,000 Sun masses, it will break at a distance of 3,200 km, well inside the Schwarzschild radius of 30,000 km.

Notes[edit]

^An 8-meter rod of the same strength, with a mass of 8 kg, breaks at a distance 4 times as high.^{[citation needed]}
^The smallest non-primordial black holethat can be formed by natural processes has an estimated mass of 3–4 times that of the Sun.^[11]

References[edit]

Inline citations

^Wheeler, J. Craig (2007),Cosmic catastrophes: exploding stars, black holes, and mapping the universe(2nd ed.),Cambridge University Press,p. 182,ISBN 978-0-521-85714-7
^Hawking, Stephen(1988).A Brief History of Time.Bantam Dell Publishing Group. p. 256.ISBN 978-0-553-10953-5.
^Astronomy.OpenStax. 2016. p. 862.ISBN 978-1938168284.
^Calder, Nigel(1977).The Key to the Universe: A Report on the New Physics.Viking Press.p. 143.ISBN 978-0-67041270-9.RetrievedJuly 10,2022.Published as a companion to theBBCTV documentaryThe Key to the Universe.
^"Astronomers See Distant Eruption as Black Hole Destroys Star"(Press release). National Radio Astronomy Observatory. Phys.org. June 14, 2018.RetrievedJune 15,2018.
^Thorne, Kip S.(1988)."Gravitomagnetism, Jets in Quasars, and the Stanford Gyroscope Experiment"(PDF).In Fairbank, J. D.; Deaver, Jr., B. S.; Everitt, C. F.; Micelson, P. F. (eds.).Near Zero: New Frontiers of Physics.New York:W. H. Freeman and Company.pp. 3, 4 (575, 576).From our electrodynamical experience we can infer immediately that any rotating spherical body (e.g., the sun or the earth) will be surrounded by a radial gravitoelectric (Newtonian) fieldgand a dipolar gravitomagnetic fieldH.The gravitoelectric monopole moment is the body's mass M; the gravitomagnetic dipole moment is its spin angular momentum S.
^"Spinning Black Hole Swallowing Star Explains Superluminous Event - ESO telescopes help reinterpret brilliant explosion".eso.org.RetrievedDecember 15,2016.
^Hawley, John F.; Holcomb, Katherine A. (2005).Foundations of Modern Cosmology(illustrated ed.). Oxford University Press. p. 253.ISBN 978-0-19-853096-1.Extract of page 253
^Hobson, Michael Paul; Efstathiou, George; Lasenby, Anthony N. (2006)."11. Schwarzschild black holes".General relativity: an introduction for physicists.Cambridge University Press. p. 265.ISBN 0-521-82951-8.
^Kutner, Marc Leslie (2003)."8. General relativity".Astronomy: a physical perspective(2nd ed.). Cambridge University Press. p. 150.ISBN 0-521-52927-1.
^Thompson, T. A.; Kochanek, C. S.; Stanek, K. Z.; et al. (2019). "A noninteracting low-mass black hole–giant star binary system".Science.366(6465): 637–640.arXiv:1806.02751.Bibcode:2019Sci...366..637T.doi:10.1126/science.aau4005.PMID 31672898.S2CID 207815062.

General references

Melia, Fulvio (2003).The Black Hole at the Center of Our Galaxy.Princeton University Press.ISBN 0-691-09505-1.

External links[edit]

Neil DeGrasse Tyson: Death by Black Hole (clear explanation of the term)

[7] An 8-meter rod of the same strength, with a mass of 8 kg, breaks at a distance 4 times as high.^{[citation needed]}

[13] The smallest non-primordial black holethat can be formed by natural processes has an estimated mass of 3–4 times that of the Sun.^[11]

[1] Wheeler, J. Craig (2007),Cosmic catastrophes: exploding stars, black holes, and mapping the universe(2nd ed.),Cambridge University Press,p. 182,ISBN 978-0-521-85714-7

[2] Hawking, Stephen(1988).A Brief History of Time.Bantam Dell Publishing Group. p. 256.ISBN 978-0-553-10953-5.

[3] Astronomy.OpenStax. 2016. p. 862.ISBN 978-1938168284.

[4] Calder, Nigel(1977).The Key to the Universe: A Report on the New Physics.Viking Press.p. 143.ISBN 978-0-67041270-9.RetrievedJuly 10,2022.Published as a companion to theBBCTV documentaryThe Key to the Universe.

[5] "Astronomers See Distant Eruption as Black Hole Destroys Star"(Press release). National Radio Astronomy Observatory. Phys.org. June 14, 2018.RetrievedJune 15,2018.

[6] Thorne, Kip S.(1988)."Gravitomagnetism, Jets in Quasars, and the Stanford Gyroscope Experiment"(PDF).In Fairbank, J. D.; Deaver, Jr., B. S.; Everitt, C. F.; Micelson, P. F. (eds.).Near Zero: New Frontiers of Physics.New York:W. H. Freeman and Company.pp. 3, 4 (575, 576).From our electrodynamical experience we can infer immediately that any rotating spherical body (e.g., the sun or the earth) will be surrounded by a radial gravitoelectric (Newtonian) fieldgand a dipolar gravitomagnetic fieldH.The gravitoelectric monopole moment is the body's mass M; the gravitomagnetic dipole moment is its spin angular momentum S.

[8] "Spinning Black Hole Swallowing Star Explains Superluminous Event - ESO telescopes help reinterpret brilliant explosion".eso.org.RetrievedDecember 15,2016.

[9] Hawley, John F.; Holcomb, Katherine A. (2005).Foundations of Modern Cosmology(illustrated ed.). Oxford University Press. p. 253.ISBN 978-0-19-853096-1.Extract of page 253

[10] Hobson, Michael Paul; Efstathiou, George; Lasenby, Anthony N. (2006)."11. Schwarzschild black holes".General relativity: an introduction for physicists.Cambridge University Press. p. 265.ISBN 0-521-82951-8.

[11] Kutner, Marc Leslie (2003)."8. General relativity".Astronomy: a physical perspective(2nd ed.). Cambridge University Press. p. 150.ISBN 0-521-52927-1.

[Thompson2019-12] Thompson, T. A.; Kochanek, C. S.; Stanek, K. Z.; et al. (2019). "A noninteracting low-mass black hole–giant star binary system".Science.366(6465): 637–640.arXiv:1806.02751.Bibcode:2019Sci...366..637T.doi:10.1126/science.aau4005.PMID 31672898.S2CID 207815062.

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v t e Black holes
Outline
Types	BTZ black hole Schwarzschild Rotating Charged Virtual Kugelblitz Supermassive Primordial Direct collapse Rogue Malament–Hogarth spacetime
Size	Micro Extremal Electron Hawking star Stellar Microquasar Intermediate-mass Supermassive Active galactic nucleus Quasar LQG Blazar OVV Radio-Quiet Radio-Loud
Formation	Stellar evolution Gravitational collapse Neutron star Related links Tolman–Oppenheimer–Volkoff limit White dwarf Related links Supernova Micronova Hypernova Related links Gamma-ray burst Binary black hole Quark star Supermassive star Quasi-star Supermassive dark star X-ray binary
Properties	Astrophysical jet Gravitational singularity Ring singularity Theorems Event horizon Photon sphere Innermost stable circular orbit Ergosphere Penrose process Blandford–Znajek process Accretion disk Hawking radiation Gravitational lens Microlens Bondi accretion M–sigma relation Quasi-periodic oscillation Thermodynamics Bekenstein bound Bousso's holographic bound Immirzi parameter Schwarzschild radius Spaghettification
Issues	Black hole complementarity Information paradox Cosmic censorship ER = EPR Final parsec problem Firewall (physics) Holographic principle No-hair theorem
Metrics	Schwarzschild(Derivation) Kerr Reissner–Nordström Kerr–Newman Hayward
Alternatives	Nonsingular black hole models Black star Dark star Dark-energy star Gravastar Magnetospheric eternally collapsing object Planck star Q star Fuzzball Geon
Analogs	Optical black hole Sonic black hole
Lists	Black holes Most massive Nearest Quasars Microquasars
Related	Outline of black holes Black Hole Initiative Black hole starship Black holes in fiction Big Bang Big Bounce Compact star Exotic star Quark star Preon star Gravitational waves Gamma-ray burst progenitors Gravity well Hypercompact stellar system Membrane paradigm Naked singularity Population III star Supermassive star Quasi-star Supermassive dark star Rossi X-ray Timing Explorer Superluminal motion Timeline of black hole physics White hole Wormhole Tidal disruption event Planet Nine
Notable	Cygnus X-1 XTE J1650-500 XTE J1118+480 A0620-00 SDSS J150243.09+111557.3 Sagittarius A* Centaurus A Phoenix Cluster PKS 1302-102 OJ 287 SDSS J0849+1114 TON 618 MS 0735.6+7421 NeVe 1 Hercules A 3C 273 Q0906+6930 Markarian 501 ULAS J1342+0928 PSO J030947.49+271757.31 P172+18 AT2018hyz Swift J1644+57
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