White hole

Encyclopedia

A

, is a hypothetical region of spacetime

which cannot be entered from the outside, but from which matter

and light

may escape. In this sense it is the reverse of a black hole

, which can be entered from the outside, but from which nothing, including light, may escape. (However, it is theoretically possible for a traveler to enter a rotating black hole

, avoid the singularity, and travel into a rotating white hole which allows the traveler to escape into another universe.) White holes appear in the theory of eternal black hole

s. In addition to a black hole region in the future, such a solution of the Einstein equations has a white hole region in its past. However, this region does not exist for black holes that have formed through gravitational collapse

, nor are there any known physical processes through which a white hole could be formed.

Like black holes, white holes have properties like mass

, charge

, and angular momentum

. They attract matter like any other mass, but objects falling towards a white hole would never actually reach the white hole's event horizon

(though in the case of the maximally extended Schwarzschild solution, discussed below, the white hole event horizon in the past becomes a black hole event horizon in the future, so any object falling towards it will eventually reach the black hole horizon).

In quantum mechanics, the black hole emits Hawking radiation

, and so can come to thermal equilibrium

with a gas of radiation. Since a thermal equilibrium state is time reversal invariant, Stephen Hawking

argued that the time reverse of a black hole in thermal equilibrium is again a black hole in thermal equilibrium. This implies that black holes and white holes are the same object. The Hawking radiation from an ordinary black hole is then identified with the white hole emission. Hawking's semi-classical argument is reproduced in a quantum mechanical AdS/CFT treatment, where a black hole in anti-de Sitter space is described by a thermal gas in a gauge theory, whose time reversal is the same as itself.

known as the maximally extended version of the Schwarzschild metric

describing an eternal black hole

with no charge and no rotation. Here, "maximally extended" refers to the idea that the spacetime

should not have any "edges": for any possible trajectory of a free-falling particle (following a geodesic

) in the spacetime, it should be possible to continue this path arbitrarily far into the particle's future, unless the trajectory hits a gravitational singularity

like the one at the center of the black hole's interior. In order to satisfy this requirement, it turns out that in addition to the black hole interior region which particles enter when they fall through the event horizon

from the outside, there must be a separate white hole interior region which allows us to extrapolate the trajectories of particles which an outside observer sees rising up

, infalling particles take an infinite time to reach the black hole horizon infinitely far in the future, while outgoing particles which pass the observer have been traveling outward for an infinite time since crossing the white hole horizon infinitely far in the past (however, the particles or other objects experience only a finite proper time

between crossing the horizon and passing the outside observer). The black hole/white hole appears "eternal" from the perspective of an outside observer, in the sense that particles traveling outward from the white hole interior region can pass the observer at any time, and particles traveling inward which will eventually reach the black hole interior region can also pass the observer at any time.

Just as there are two separate interior regions of the maximally extended spacetime, there are also two separate exterior regions, sometimes called two different "universes", with the second universe allowing us to extrapolate some possible particle trajectories in the two interior regions. This means that the interior black-hole region can contain a mix of particles that fell in from either universe (and thus an observer who fell in from one universe might be able to see light that fell in from the other one), and likewise particles from the interior white-hole region can escape into either universe. All four regions can be seen in a spacetime diagram which uses Kruskal–Szekeres coordinates, see figure.

In this spacetime, it is possible to come up with coordinate systems such that if you pick a hypersurface of constant time (a set of points that all have the same time coordinate, such that every point on the surface has a space-like separation, giving what is called a 'space-like surface') and draw an "embedding diagram" depicting the curvature of space at that time, the embedding diagram will look like a tube connecting the two exterior regions, known as an "Einstein-Rosen bridge" or Schwarzschild wormhole. Depending on where the space-like hypersurface is chosen, the Einstein-Rosen bridge can either connect two black hole event horizons in each universe (with points in the interior of the bridge being part of the black hole region of the spacetime), or two white hole event horizons in each universe (with points in the interior of the bridge being part of the white hole region). It is impossible to use the bridge to cross from one universe to the other, however, because it is impossible to enter a white hole event horizon from the outside, and anyone entering a black hole horizon from either universe will inevitably hit the black hole singularity.

Note that the maximally extended Schwarzschild metric describes an idealized black hole/white hole that exists eternally from the perspective of external observers; a more realistic black hole that forms at some particular time from a collapsing star would require a different metric. When the infalling stellar matter is added to a diagram of a black hole's history, it removes the part of the diagram corresponding to the white hole interior region. But because the equations of general relativity are time-reversible (they exhibit T-symmetry

), general relativity must also allow the time-reverse of this type of "realistic" black hole that forms from collapsing matter. The time-reversed case would be a white hole that has existed since the beginning of the universe, and which emits matter until it finally "explodes" and disappears. Despite the fact that such objects are permitted theoretically, they are not taken as seriously as black holes by physicists, since there would be no processes that would naturally lead to their formation, they could only exist if they were built into the initial conditions of the Big Bang

. Additionally, it is predicted that such a white hole would be highly "unstable" in the sense that if any small amount of matter fell towards the horizon from the outside, this would prevent the white hole's explosion as seen by distant observers, with the matter emitted from the singularity never able to escape the white hole's gravitational radius.

A more recently proposed view of black holes might be interpreted as shedding some light on the nature of classical white holes. Some researchers have proposed that when a black hole forms, a big bang occurs at the core, which creates a new universe that expands outside of the parent universe. See also Fecund universes.

The initial feeding of matter from the parent universe's black hole and the expansion that follows in the new universe might be thought of as a cosmological type of white hole. Unlike traditional white holes, this type of white hole would not be localized in space in the new universe, and its horizon would have to be identified with the cosmological horizon.

However, the second law of thermodynamics states that "in all energy exchanges, if no energy enters or leaves the system, the potential energy of the state will always be less than that of the initial state." White holes apparently do not follow this law, and there is much speculation on the issue of whether or not white holes exist.

**white hole**, in general relativityGeneral relativity

General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...

, is a hypothetical region of spacetime

Spacetime

In physics, spacetime is any mathematical model that combines space and time into a single continuum. Spacetime is usually interpreted with space as being three-dimensional and time playing the role of a fourth dimension that is of a different sort from the spatial dimensions...

which cannot be entered from the outside, but from which matter

Matter

Matter is a general term for the substance of which all physical objects consist. Typically, matter includes atoms and other particles which have mass. A common way of defining matter is as anything that has mass and occupies volume...

and light

Light

Light or visible light is electromagnetic radiation that is visible to the human eye, and is responsible for the sense of sight. Visible light has wavelength in a range from about 380 nanometres to about 740 nm, with a frequency range of about 405 THz to 790 THz...

may escape. In this sense it is the reverse of a black hole

Black hole

A black hole is a region of spacetime from which nothing, not even light, can escape. The theory of general relativity predicts that a sufficiently compact mass will deform spacetime to form a black hole. Around a black hole there is a mathematically defined surface called an event horizon that...

, which can be entered from the outside, but from which nothing, including light, may escape. (However, it is theoretically possible for a traveler to enter a rotating black hole

Rotating black hole

A rotating black hole is a black hole that possesses spin angular momentum.-Types of black holes:There are four known, exact, black hole solutions to Einstein's equations, which describe gravity in General Relativity. Two of these rotate...

, avoid the singularity, and travel into a rotating white hole which allows the traveler to escape into another universe.) White holes appear in the theory of eternal black hole

Kruskal-Szekeres coordinates

In general relativity Kruskal–Szekeres coordinates, named for Martin Kruskal and George Szekeres, are a coordinate system for the Schwarzschild geometry for a black hole...

s. In addition to a black hole region in the future, such a solution of the Einstein equations has a white hole region in its past. However, this region does not exist for black holes that have formed through gravitational collapse

Gravitational collapse

Gravitational collapse is the inward fall of a body due to the influence of its own gravity. In any stable body, this gravitational force is counterbalanced by the internal pressure of the body, in the opposite direction to the force of gravity...

, nor are there any known physical processes through which a white hole could be formed.

Like black holes, white holes have properties like mass

Mass

Mass can be defined as a quantitive measure of the resistance an object has to change in its velocity.In physics, mass commonly refers to any of the following three properties of matter, which have been shown experimentally to be equivalent:...

, charge

Charge

Charge or charged may refer to:* Charge , illegal contact by pushing or moving into another player's torso* Charge , a six-note trumpet or bugle piece denoting the call to rush forward...

, and angular momentum

Angular momentum

In physics, angular momentum, moment of momentum, or rotational momentum is a conserved vector quantity that can be used to describe the overall state of a physical system...

. They attract matter like any other mass, but objects falling towards a white hole would never actually reach the white hole's event horizon

Event horizon

In general relativity, an event horizon is a boundary in spacetime beyond which events cannot affect an outside observer. In layman's terms it is defined as "the point of no return" i.e. the point at which the gravitational pull becomes so great as to make escape impossible. The most common case...

(though in the case of the maximally extended Schwarzschild solution, discussed below, the white hole event horizon in the past becomes a black hole event horizon in the future, so any object falling towards it will eventually reach the black hole horizon).

In quantum mechanics, the black hole emits Hawking radiation

Hawking radiation

Hawking radiation is a thermal radiation with a black body spectrum predicted to be emitted by black holes due to quantum effects. It is named after the physicist Stephen Hawking, who provided a theoretical argument for its existence in 1974, and sometimes also after the physicist Jacob Bekenstein...

, and so can come to thermal equilibrium

Thermal equilibrium

Thermal equilibrium is a theoretical physical concept, used especially in theoretical texts, that means that all temperatures of interest are unchanging in time and uniform in space...

with a gas of radiation. Since a thermal equilibrium state is time reversal invariant, Stephen Hawking

Stephen Hawking

Stephen William Hawking, CH, CBE, FRS, FRSA is an English theoretical physicist and cosmologist, whose scientific books and public appearances have made him an academic celebrity...

argued that the time reverse of a black hole in thermal equilibrium is again a black hole in thermal equilibrium. This implies that black holes and white holes are the same object. The Hawking radiation from an ordinary black hole is then identified with the white hole emission. Hawking's semi-classical argument is reproduced in a quantum mechanical AdS/CFT treatment, where a black hole in anti-de Sitter space is described by a thermal gas in a gauge theory, whose time reversal is the same as itself.

## Origin

White holes appear as part of a solution to the Einstein field equationsEinstein field equations

The Einstein field equations or Einstein's equations are a set of ten equations in Albert Einstein's general theory of relativity which describe the fundamental interaction of gravitation as a result of spacetime being curved by matter and energy...

known as the maximally extended version of the Schwarzschild metric

Schwarzschild metric

In Einstein's theory of general relativity, the Schwarzschild solution describes the gravitational field outside a spherical, uncharged, non-rotating mass such as a star, planet, or black hole. It is also a good approximation to the gravitational field of a slowly rotating body like the Earth or...

describing an eternal black hole

Black hole

A black hole is a region of spacetime from which nothing, not even light, can escape. The theory of general relativity predicts that a sufficiently compact mass will deform spacetime to form a black hole. Around a black hole there is a mathematically defined surface called an event horizon that...

with no charge and no rotation. Here, "maximally extended" refers to the idea that the spacetime

Spacetime

In physics, spacetime is any mathematical model that combines space and time into a single continuum. Spacetime is usually interpreted with space as being three-dimensional and time playing the role of a fourth dimension that is of a different sort from the spatial dimensions...

should not have any "edges": for any possible trajectory of a free-falling particle (following a geodesic

Geodesic (general relativity)

In general relativity, a geodesic generalizes the notion of a "straight line" to curved spacetime. Importantly, the world line of a particle free from all external, non-gravitational, force is a particular type of geodesic...

) in the spacetime, it should be possible to continue this path arbitrarily far into the particle's future, unless the trajectory hits a gravitational singularity

Gravitational singularity

A gravitational singularity or spacetime singularity is a location where the quantities that are used to measure the gravitational field become infinite in a way that does not depend on the coordinate system...

like the one at the center of the black hole's interior. In order to satisfy this requirement, it turns out that in addition to the black hole interior region which particles enter when they fall through the event horizon

Event horizon

In general relativity, an event horizon is a boundary in spacetime beyond which events cannot affect an outside observer. In layman's terms it is defined as "the point of no return" i.e. the point at which the gravitational pull becomes so great as to make escape impossible. The most common case...

from the outside, there must be a separate white hole interior region which allows us to extrapolate the trajectories of particles which an outside observer sees rising up

*away*from the event horizon. For an observer outside using Schwarzschild coordinatesSchwarzschild coordinates

In the theory of Lorentzian manifolds, spherically symmetric spacetimes admit a family of nested round spheres. In such a spacetime, a particularly important kind of coordinate chart is the Schwarzschild chart, a kind of polar spherical coordinate chart on a static and spherically symmetric...

, infalling particles take an infinite time to reach the black hole horizon infinitely far in the future, while outgoing particles which pass the observer have been traveling outward for an infinite time since crossing the white hole horizon infinitely far in the past (however, the particles or other objects experience only a finite proper time

Proper time

In relativity, proper time is the elapsed time between two events as measured by a clock that passes through both events. The proper time depends not only on the events but also on the motion of the clock between the events. An accelerated clock will measure a smaller elapsed time between two...

between crossing the horizon and passing the outside observer). The black hole/white hole appears "eternal" from the perspective of an outside observer, in the sense that particles traveling outward from the white hole interior region can pass the observer at any time, and particles traveling inward which will eventually reach the black hole interior region can also pass the observer at any time.

Just as there are two separate interior regions of the maximally extended spacetime, there are also two separate exterior regions, sometimes called two different "universes", with the second universe allowing us to extrapolate some possible particle trajectories in the two interior regions. This means that the interior black-hole region can contain a mix of particles that fell in from either universe (and thus an observer who fell in from one universe might be able to see light that fell in from the other one), and likewise particles from the interior white-hole region can escape into either universe. All four regions can be seen in a spacetime diagram which uses Kruskal–Szekeres coordinates, see figure.

In this spacetime, it is possible to come up with coordinate systems such that if you pick a hypersurface of constant time (a set of points that all have the same time coordinate, such that every point on the surface has a space-like separation, giving what is called a 'space-like surface') and draw an "embedding diagram" depicting the curvature of space at that time, the embedding diagram will look like a tube connecting the two exterior regions, known as an "Einstein-Rosen bridge" or Schwarzschild wormhole. Depending on where the space-like hypersurface is chosen, the Einstein-Rosen bridge can either connect two black hole event horizons in each universe (with points in the interior of the bridge being part of the black hole region of the spacetime), or two white hole event horizons in each universe (with points in the interior of the bridge being part of the white hole region). It is impossible to use the bridge to cross from one universe to the other, however, because it is impossible to enter a white hole event horizon from the outside, and anyone entering a black hole horizon from either universe will inevitably hit the black hole singularity.

Note that the maximally extended Schwarzschild metric describes an idealized black hole/white hole that exists eternally from the perspective of external observers; a more realistic black hole that forms at some particular time from a collapsing star would require a different metric. When the infalling stellar matter is added to a diagram of a black hole's history, it removes the part of the diagram corresponding to the white hole interior region. But because the equations of general relativity are time-reversible (they exhibit T-symmetry

T-symmetry

T Symmetry is the symmetry of physical laws under a time reversal transformation: T: t \mapsto -t.Although in restricted contexts one may find this symmetry, the observable universe itself does not show symmetry under time reversal, primarily due to the second law of thermodynamics.Time asymmetries...

), general relativity must also allow the time-reverse of this type of "realistic" black hole that forms from collapsing matter. The time-reversed case would be a white hole that has existed since the beginning of the universe, and which emits matter until it finally "explodes" and disappears. Despite the fact that such objects are permitted theoretically, they are not taken as seriously as black holes by physicists, since there would be no processes that would naturally lead to their formation, they could only exist if they were built into the initial conditions of the Big Bang

Big Bang

The Big Bang theory is the prevailing cosmological model that explains the early development of the Universe. According to the Big Bang theory, the Universe was once in an extremely hot and dense state which expanded rapidly. This rapid expansion caused the young Universe to cool and resulted in...

. Additionally, it is predicted that such a white hole would be highly "unstable" in the sense that if any small amount of matter fell towards the horizon from the outside, this would prevent the white hole's explosion as seen by distant observers, with the matter emitted from the singularity never able to escape the white hole's gravitational radius.

## Recent speculations

There are theories suggesting that white holes create new universes from matter originating in another universe's black hole.A more recently proposed view of black holes might be interpreted as shedding some light on the nature of classical white holes. Some researchers have proposed that when a black hole forms, a big bang occurs at the core, which creates a new universe that expands outside of the parent universe. See also Fecund universes.

The initial feeding of matter from the parent universe's black hole and the expansion that follows in the new universe might be thought of as a cosmological type of white hole. Unlike traditional white holes, this type of white hole would not be localized in space in the new universe, and its horizon would have to be identified with the cosmological horizon.

However, the second law of thermodynamics states that "in all energy exchanges, if no energy enters or leaves the system, the potential energy of the state will always be less than that of the initial state." White holes apparently do not follow this law, and there is much speculation on the issue of whether or not white holes exist.

## See also

- Black holeBlack holeA black hole is a region of spacetime from which nothing, not even light, can escape. The theory of general relativity predicts that a sufficiently compact mass will deform spacetime to form a black hole. Around a black hole there is a mathematically defined surface called an event horizon that...
- WormholeWormholeIn physics, a wormhole is a hypothetical topological feature of spacetime that would be, fundamentally, a "shortcut" through spacetime. For a simple visual explanation of a wormhole, consider spacetime visualized as a two-dimensional surface. If this surface is folded along a third dimension, it...
- Arrow of timeArrow of timeThe arrow of time, or time’s arrow, is a term coined in 1927 by the British astronomer Arthur Eddington to describe the "one-way direction" or "asymmetry" of time...
- Conformal Cyclic CosmologyConformal Cyclic CosmologyThe Conformal Cyclic Cosmology is a cosmological model in the framework of general relativity, advanced by the theoretical physicist Sir Roger Penrose. In CCC, the universe iterates through infinite cycles, with the future timelike infinity of each previous iteration being identified with the Big...
- White holes in fiction

## External links

- Ask an Astronomer: "What is a White Hole?"
- Schwarzschild Wormholes
- Schwarzschild Wormhole animation
- Shockwave cosmology inside a Black Hole
- Michio Kaku: Mr Parallel Universe
- End of Black Hole Is Starting of Big Bang - Discussed in Newsgroup in 1999
- Forward to the Future 1:Trapped in Time!
- Forward to the Future 2:Back to the Past, with Interest...