Spaghettification

For the computer programming term, see Spaghetti code.

Astronaut falling into a black hole (schematic illustration of the spaghettification effect)

Tidal forces acting on a spherical body in a non-homogeneous gravitational field. In this diagram, the gravitational force originates from a source to the right. It shows both the tidal field (thick red arrows) and the gravity field (thin blue arrows) exerted on the body's surface and center (label O) by a source (label S).

In astrophysics, spaghettification, ^[1] or noodle effect ^[2] is the vertical stretching and horizontal compression of objects into long thin shapes in a very strong, non-homogeneous gravitational field. The term was popularized by Stephen Hawking who described the flight of a fictional astronaut who, passing within a black hole's event horizon, is "stretched like spaghetti". ^{[3] [4]} It is caused by extreme tidal forces. In the most extreme cases, near a black 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. 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. ^[5]

A simple example

The spaghettification of four objects falling towards a planet

The concept can be illustrated with four objects in space above a planet, positioned in a diamond formation. The force on each object is directed towards the planets center. In accordance with the inverse-square law, the lowest of the four objects experiences the biggest gravitational acceleration, and two objects on each side are pulled towards each other, so that the whole formation becomes stretched along the line to the planet and compressed transversely. ^[3]

If these four objects are connected parts of a larger rigid object, then it will resist distortion. Internal elastic forces develop as the body distorts to balance the tidal forces, to maintain mechanical equilibrium. If the tidal forces become too large, the body may yield creating a narrow line of broken pieces.

The forces responsible for spaghettification are called tidal forces. The radial tidal force across an object of mass m and size ${\displaystyle \Delta r}$ at a distance r from an object of mass M can be estimated with Newton's law of gravity: $${\displaystyle \Delta F=\Delta r{\frac {2GmM}{r^{3}}}}$$ where G is the gravitational constant. ^[3]

Relation to the event horizon

Spaghettification of a star by a supermassive black hole

The point at which tidal forces destroy an object or kill a person is proportional to the black hole's mass. This point is not the event horizon. For a supermassive black hole, such as those found at a galaxy's center, this point lies within the event 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. ^[7] Stellar black holes have much higher spacetime curvature at their event horizon, so the tidal forces would spaghettify the astronaut before the event horizon. ^{[8] [9]}

References

1. Calder, Nigel (1977). The Key to the Universe: A Report on the New Physics . Viking Press. p. 143. ISBN   978-0-67041270-9 . Retrieved July 10, 2022. Published as a companion to the BBC TV documentary The Key to the Universe.
2. Wheeler, J. Craig (2007). Cosmic catastrophes: exploding stars, black holes, and mapping the universe (2nd ed.). Cambridge; New York: Cambridge University Press. p. 182. ISBN   978-0-521-85714-7. OCLC   73954922.
3. Pinochet, Jorge (July 1, 2022). "The little robot, black holes, and spaghettification". Physics Education. 57 (4): 045008. doi:10.1088/1361-6552/ac5727. ISSN   0031-9120.
4. Hawking, Stephen (1988). A Brief History of Time . Bantam Dell Publishing Group. p. 256. ISBN   978-0-553-10953-5.
5. Fraknoi, Andrew; Morrison, David; C. Wolff, Sidney (2016). Astronomy. OpenStax. p. 862. ISBN   9781938168284.
6. Price, Daniel J.; Liptai, David; Mandel, Ilya; Shepherd, Joanna; Lodato, Giuseppe; Levin, Yuri (2024). "Eddington Envelopes: The Fate of Stars on Parabolic Orbits Tidally Disrupted by Supermassive Black Holes". The Astrophysical Journal Letters. 971 (2): L46. arXiv: 2404.09381 . Bibcode:2024ApJ...971L..46P. doi: 10.3847/2041-8213/ad6862 .
7. Hawley, John Frederick; Holcomb, Katherine A. (2005). Foundations of modern cosmology (2nd ed.). Oxford; New York: Oxford University Press. p. 253. ISBN   978-0-19-853096-1.
8. Hobson, Michael Paul; Efstathiou, Georges; Lasenby, Anthony N. (2006). General relativity: an introduction for physicists. Cambridge: Cambridge University Press. p. 265. ISBN   978-0-521-82951-9.
9. Kutner, Marc L. (2003). Astronomy: a physical perspective (2nd ed.). Cambridge: Cambridge University Press. p. 150. ISBN   978-0-521-52927-3.

External links

• Neil DeGrasse Tyson: Death by Black Hole (clear explanation of the term)
• Crew, Bec (March 24, 2017). "An Encounter With a Neutron Star Would Dwarf Our Entire Nuclear Arsenal". ScienceAlert. Retrieved October 5, 2024. Describes Science Channel video of spaghettification in a neutron star.