# Spaghettification

Tidal forces acting on a spherical body in a non-homogeneous gravitational field. The effect originates from a source to the right (or to the left) of the diagram. Longer arrows indicate stronger forces.

In astrophysics, spaghettification (sometimes referred to as the noodle effect[1]) is the vertical stretching and horizontal compression of objects into long thin shapes (rather like spaghetti) in a very strong non-homogeneous gravitational field, and is caused by extreme tidal forces. In the most extreme cases, near black holes, the stretching is so powerful that no object can withstand it, no matter how strong its components. Within a small region the horizontal compression balances the vertical stretching so that small objects being spaghettified experience no net change in volume.

In his book A Brief History of Time (1988), Stephen Hawking describes the flight of a fictional astronaut who, passing within a black hole's event horizon, is "stretched like spaghetti" by the gravitational gradient (difference in strength) from head to toe. However, the term "spaghettification" was established well before this; Nigel Calder, for example, uses it in his book The Key to the Universe: A Report on the New Physics (Viking Press, 1977), a companion to a one-off BBC TV documentary: The Key to the Universe.

## A simple example

The four objects follow the lines of the gravitoelectric field,[2] directed towards the celestial body's centre. In accordance with the inverse-square law, the lowest of the four objects experiences the biggest gravitational acceleration, so that the whole formation becomes stretched into a filament. Now imagine that the green blobs in the diagram are parts of a larger object. A rigid object will resist distortion—internal elastic forces develop as the body distorts to balance the tidal forces, so attaining mechanical equilibrium. If the tidal forces are too large, the body may yield and flow plastically before the tidal forces can be balanced, or fracture.

## Examples of weak and strong tidal forces

In the gravity field due to a point mass or spherical mass, for a uniform rope or rod oriented in the direction of gravity, the tensile force at the center is found by integration of the tidal force (see magnitude of tidal force) from the center to one of the ends. This gives $\frac{\mu l m}{4 r^3}$, where $\mu$ is the standard gravitational parameter of the massive body, l is the length of the rope or rod, m is its 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 compressive 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 rope 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 a white dwarf is much stronger, causing in the example a maximum tensile force of up to 0.24 N. Near a neutron star, the tidal forces are again much stronger: if the rope 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 (the typical radius is about 12 km).[3]

While in the previous case objects would actually be destroyed and people killed by the heat, not the tidal forces, 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. Moreover, a black hole has no surface to stop a fall. As an object falls into a black hole, the tidal forces increase to infinity, so nothing can resist them. Thus, the infalling object is stretched into a thin strip of matter. Close to the singularity, the tidal forces even tear apart molecules.

## Inside or outside the event horizon

The point at which tidal forces destroy an object or kill a person will depend on the black hole's size. 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. For small black holes whose Schwarzschild radius is much closer to the singularity, the tidal forces would kill even before the astronaut reaches the event horizon.[4][5] For example, for a black hole of 10 Sun masses[6] and the above-mentioned rope at 1000 km distance, the tensile force halfway along the rope is 325 N. It will break at a distance of 320 km, well outside the Schwarzschild radius of 30 km. For a black hole of 10,000 Sun masses it will break at a distance of 3200 km, well inside the Schwarzschild radius of 30,000 km.

## References

1. ^ Wheeler, J. Craig (2007), Cosmic catastrophes: exploding stars, black holes, and mapping the universe, 2nd edition, Cambridge University Press, p. 182, ISBN 978-0-521-85714-7
2. ^ Thorne, Kip S. ♦ Gravitomagnetism, Jets in Quasars, and the Stanford Gyroscope Experiment From the book "Near Zero: New Frontiers of Physics" (eds. J. D. Fairbank, B. S. Deaver, Jr., C. W. F. Everitt, P. F. Michelson), W. H. Freeman and Company, New York, 1988, 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) field g and a dipolar gravitomagnetic field H. The gravitoelectric monopole moment is the body's mass M; the gravitomagnetic dipole moment is its spin angular momentum S."
3. ^ An 8 m piece of the same type of rope, hence with a mass of 8 kg, would in each case break already at a distance that is 4 times as high.
4. ^ Hobson, Michael Paul; Efstathiou, George; Lasenby, Anthony N. (2006). General relativity: an introduction for physicists. Cambridge University Press. p. 265. ISBN 0-521-82951-8., Chapter 11, p. 265
5. ^ Kutner, Marc Leslie (2003). Astronomy: a physical perspective (2 ed.). Cambridge University Press. p. 150. ISBN 0-521-52927-1., Chapter 8, p. 150
6. ^ The smallest black hole that can be formed by natural processes at the current stage of the universe has over twice the mass of the Sun.