In the general theory of relativity, what is the term for a boundary in spacetime beyond which events cannot affect the observer?
"of temperature in Planck's law. This radiation is known as Hawking radiation (cf. the quantum theory section, below). There are other types of horizons. In an expanding universe, an observer may find that some regions of the past cannot be observed (""particle horizon""), and some regions of the future cannot be influenced (event horizon). Even in flat Minkowski space, when described by an accelerated observer (Rindler space), there will be horizons associated with a semi-classical radiation known as Unruh radiation. Another general feature of general relativity is the appearance of spacetime boundaries known as singularities. Spacetime can be explored by"
"The boundary past which events cannot ever be observed is an event horizon, and it represents the maximum extent of the particle horizon. The criterion for determining whether a particle horizon for the universe exists is as follows. Define a comoving distance ""d"" as In this equation, ""a"" is the scale factor, ""c"" is the speed of light, and ""t"" is the age of the Universe. If (i.e., points arbitrarily as far away as can be observed), then no event horizon exists. If , a horizon is present. Examples of cosmological models without an event horizon are universes dominated by"
"spacetime, with the Cauchy horizon being the boundary between the region of spacetime where closed timelike curves can exist and the rest of spacetime where they cannot. One of the first such bounded time travel solutions found was constructed from a traversable wormhole, based on the idea of taking one of the two ""mouths"" of the wormhole on a round-trip journey at relativistic speed to create a time difference between it and the other mouth (see the discussion at Wormhole#Time travel). General relativity does not include quantum effects on its own, and a full integration of general relativity and quantum"
"the concept of particle horizon, which represents the largest comoving distance from which light emitted in the ""past"" could have reached the observer at a given time. For events beyond that distance, light has not had time to reach our location, even if it were emitted at the time the universe began. How the particle horizon changes with time depends on the nature of the expansion of the universe. If the expansion has certain characteristics, there are parts of the universe that will never be observable, no matter how long the observer waits for light from those regions to arrive."
"Black hole A black hole is a region of spacetime exhibiting such strong gravitational effects that nothing—not even particles and electromagnetic radiation such as light—can escape from inside it. The theory of general relativity predicts that a sufficiently compact mass can deform spacetime to form a black hole. The boundary of the region from which no escape is possible is called the event horizon. Although the event horizon has an enormous effect on the fate and circumstances of an object crossing it, no locally detectable features appear to be observed. In many ways a black hole acts like an ideal"
"deep space, far from any significant source of gravity. Such observers are the privileged (""inertial"") observers Einstein described in his theory of special relativity: observers for whom light travels along straight lines at constant speed. Einstein hypothesized that the similar experiences of weightless observers and inertial observers in special relativity represented a fundamental property of gravity, and he made this the cornerstone of his theory of general relativity, formalized in his equivalence principle. Roughly speaking, the principle states that a person in a free-falling elevator cannot tell that they are in free fall. Every experiment in such a free-falling environment"
"large low-density void. To match observations we would have to be very close to the centre of this void, immediately contradicting the Copernican principle. Copernican principle In physical cosmology, the Copernican principle is an alternative name for the principle of relativity, stating that humans, on the Earth or in the Solar system, are not privileged observers of the universe. Named for Copernican heliocentrism, it is a working assumption that arises from a modified cosmological extension of Copernicus's argument of a moving Earth. In some sense, it is equivalent to the mediocrity principle. Hermann Bondi named the principle after Copernicus in"
"a particular point in space, but rather with an entire inertial reference frame that may exist anywhere in the universe (given certain lengthy mathematical specifications and caveats.) The term ""observer"" also has special meaning in other areas of science, such as quantum mechanics, and information theory. See for example, Schrödinger's cat and Maxwell's demon. In general relativity the term ""observer"" refers more commonly to a person (or a machine) making passive local measurements, a usage much closer to the ordinary English meaning of the word. In quantum mechanics, ""observation"" is synonymous with quantum measurement and ""observer"" with a measurement apparatus"
"universe with constant Hubble parameter, light emitted at the present time by objects outside the Hubble limit would never be seen by an observer on Earth. That is, the Hubble limit would coincide with a cosmological event horizon (a boundary separating events visible at some time and those that are never visible). See Hubble horizon for more details. However, the Hubble parameter is not constant in various cosmological models so that the Hubble limit does not, in general, coincide with a cosmological event horizon. For example in a decelerating Friedmann universe the Hubble sphere expands with time, and its boundary"
"is restricted to the flat spacetime known as Minkowski space. As long as the universe can be modeled as a pseudo-Riemannian manifold, a Lorentz-invariant frame that abides by special relativity can be defined for a sufficiently small neighborhood of each point in this curved spacetime. Galileo Galilei had already postulated that there is no absolute and well-defined state of rest (no privileged reference frames), a principle now called Galileo's principle of relativity. Einstein extended this principle so that it accounted for the constant speed of light, a phenomenon that had been recently observed in the Michelson–Morley experiment. He also postulated"
"are freely-falling particles whose motion cannot be determined beyond a finite time, being after the point of reaching the singularity. For example, any observer inside the event horizon of a non-rotating black hole would fall into its center within a finite period of time. The classical version of the Big Bang cosmological model of the universe contains a causal singularity at the start of time (""t""=0), where all time-like geodesics have no extensions into the past. Extrapolating backward to this hypothetical time 0 results in a universe with all spatial dimensions of size zero, infinite density, infinite temperature, and infinite"
"Copernican principle In physical cosmology, the Copernican principle is an alternative name for the principle of relativity, stating that humans, on the Earth or in the Solar system, are not privileged observers of the universe. Named for Copernican heliocentrism, it is a working assumption that arises from a modified cosmological extension of Copernicus's argument of a moving Earth. In some sense, it is equivalent to the mediocrity principle. Hermann Bondi named the principle after Copernicus in the mid-20th century, although the principle itself dates back to the 16th-17th century paradigm shift away from the Ptolemaic system, which placed Earth at"
"become nonlinear is known as the Schwinger limit. At this point the vacuum has all the properties of a birefringent medium, thus in principle a rotation of the polarization frame (the Faraday effect) can be observed in empty space. Both Einstein's theory of special and general relativity state that light should pass freely through a vacuum without being altered, a principle known as Lorentz invariance. Yet, in theory, large nonlinear self-interaction of light due to quantum fluctuations should lead to this principle being measurably violated if the interactions are strong enough. Nearly all theories of quantum gravity predict that that"
"general, the conformal time at a certain time is given in terms of the scale factor formula_1 by, or The particle horizon is the boundary between two regions at a point at a given time: one region defined by events that have already been observed by an observer, and the other by events which cannot be observed ""at that time"". It represents the furthest distance from which we can retrieve information from the past, and so defines the observable universe. Hubble radius, Hubble sphere, Hubble volume, or Hubble horizon is a conceptual horizon defining the boundary between particles that are"
"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). There is little evidence of white holes, though. 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"
"a relativity of simultaneity. An event that is simultaneous with another event in one frame of reference may be in the past or future of that event in a different frame of reference, which negates absolute simultaneity. Quoted below from his later papers, Einstein identified the term aether with ""properties of space"", a terminology that is not widely used. Einstein stated that in general relativity the ""aether"" is not absolute anymore, as the geodesic and therefore the structure of spacetime depends on the presence of matter. Special relativity eliminates absolute time (although Gödel and others suspect absolute time may be"
"of the principle of relativity that does not contain a privileged inertial frame of reference, such as the luminiferous ether or absolute space, from which Einstein inferred that no such frame exists. Einstein generalized relativity to frames of reference that were non-inertial. He achieved this by positing the Equivalence Principle, which states that the force felt by an observer in a given gravitational field and that felt by an observer in an accelerating frame of reference are indistinguishable. This led to the conclusion that the mass of an object warps the geometry of the space-time surrounding it, as described in"
"principle. When the field is not uniform, the simplest and most useful case to consider is that of a spherically symmetric field. By Birkhoff's theorem, such a field is described in general relativity by the Schwarzschild metric, formula_3, where formula_4 is the clock time of an observer at distance ""R"" from the center, formula_5 is the time measured by an observer at infinity, formula_6 is the Schwarzschild radius formula_7, ""..."" represents terms that vanish if the observer is at rest, formula_8 is Newton's gravitational constant, formula_9 the mass of the gravitating body, and formula_10 the speed of light. The result"
"Naked singularity In general relativity, a naked singularity is a gravitational singularity without an event horizon. In a black hole, the singularity is completely enclosed by a boundary known as the event horizon, inside which the gravitational force of the singularity is so strong that light cannot escape. Hence, objects inside the event horizon—including the singularity itself—cannot be directly observed. A naked singularity, by contrast, is observable from the outside. The theoretical existence of naked singularities is important because their existence would mean that it would be possible to observe the collapse of an object to ""infinite density"". It would"
"finite distances in systems without significant gravitation. However, in order to take gravity into account, physicists use the theory of general relativity, which is formulated in the mathematics of a non-Euclidean geometry. When this geometry is used as a model of physical space, it is known as curved space. Even in curved space, Minkowski space is still a good description in an infinitesimal region surrounding any point (barring gravitational singularities). More abstractly, we say that in the presence of gravity spacetime is described by a curved 4-dimensional manifold for which the tangent space to any point is a 4-dimensional Minkowski"
"a fixed distance away for a non-accelerating observer. It is never contacted, even by an accelerating observer. In the case of the horizon around a black hole, observers stationary with respect to a distant object will all agree on where the horizon is. While this seems to allow an observer lowered towards the hole on a rope (or rod) to contact the horizon, in practice this cannot be done. The proper distance to the horizon is finite, so the length of rope needed would be finite as well, but if the rope were lowered slowly (so that each point on"
"measurements of time and space are affected by motion between an observer and what is being observed. To say that Einstein's radical theory of relativity revolutionized science is no exaggeration. Although Einstein made many other important contributions to science, the theory of relativity alone represents one of the greatest intellectual achievements of all time. Although the concept of relativity was not introduced by Einstein, his major contribution was the recognition that the speed of light in a vacuum is constant, i.e. the same for all observers, and an absolute physical boundary for motion. This does not impact a person's day-to-day"
"Apparent horizon In general relativity, an apparent horizon is a surface that is the boundary between light rays that are directed outwards and moving outwards, and those directed outward but moving inward. Apparent horizons are not invariant properties of a spacetime, and in particular they are distinct from event horizons. Within an apparent horizon, light is not moving away from the black hole, whereas in an event horizon, light cannot escape from the black hole. It is possible for light to be currently moving away from the black hole (and so outside the apparent horizon), but in the future will"
"no event horizon. See Kerr–Newman metric for a spinning, charged ring singularity. A naked singularity could allow scientists to observe an infinitely dense material, which would under normal circumstances be impossible by the cosmic censorship hypothesis. Without an event horizon of any kind, some speculate that naked singularities could actually emit light. The cosmic censorship hypothesis says that a naked singularity cannot arise in our universe from realistic initial conditions. Naked singularity In general relativity, a naked singularity is a gravitational singularity without an event horizon. In a black hole, the singularity is completely enclosed by a boundary known as"
"a physical clock with zero peculiar velocity in the absence of matter over-/under-densities (to prevent time dilation due to relativistic effects or confusions caused by expansion of the universe). Unlike other measures of time such as temperature, redshift, particle horizon, or Hubble horizon, the cosmic time (similar and complementary to the comoving coordinates) is blind to the expansion of the universe. There are two main ways for establishing a reference point for the cosmic time. The most trivial way is to take the present time as the cosmic reference point (sometimes referred to as the lookback time) or alternatively, take"
"example, taking a 2-dimensional space, like the (curved) surface of the Earth, its tangent space at a specific point would be the flat approximation of the curved space. So far a world line (and the concept of tangent vectors) has been described without a means of quantifying the interval between events. The basic mathematics is as follows: The theory of special relativity puts some constraints on possible world lines. In special relativity the description of spacetime is limited to ""special"" coordinate systems that do not accelerate (and so do not rotate either), called inertial coordinate systems. In such coordinate systems,"
"the spacetime trajectory (""world line"") of the observer. The small dots indicate specific (past and future) events in spacetime. The slope of the world line (deviation from being vertical) gives the relative velocity to the observer. Note how in both pictures the view of spacetime changes when the observer accelerates. In the Newtonian description these changes are such that ""time"" is absolute: the movements of the observer do not influence whether an event occurs in the 'now' (i.e., whether an event passes the horizontal line through the observer). However, in the relativistic description the ""observability of events"" is absolute: the"
"lengths, and a clock to measure time intervals. An observer is a real or imaginary entity that can take measurements, say humans, or any other living organism—or even robots and computers. An event is something that happens at a point in space at an instant of time, or more formally a point in spacetime. The transformations connect the space and time coordinates of an event as measured by an observer in each frame. They supersede the Galilean transformation of Newtonian physics, which assumes an absolute space and time (see Galilean relativity). The Galilean transformation is a good approximation only at"
"Spacetime In physics, spacetime is any mathematical model that fuses the three dimensions of space and the one dimension of time into a single four-dimensional continuum. Spacetime diagrams can be used to visualize relativistic effects such as why different observers perceive ""where"" and ""when"" events occur. Until the turn of the 20th century, the assumption had been that the three-dimensional geometry of the universe (its spatial expression in terms of coordinates, distances, and directions) was independent of one-dimensional time. However, in 1905, Albert Einstein based on two postulates: (1) The laws of physics are invariant (i.e., identical) in all inertial"
"like an inside-out Schwarzschild black hole—each object is surrounded by a spherical event horizon. Once the other object has fallen through this horizon it can never return, and even light signals it sends will never reach the first object (at least so long as the space continues to expand exponentially). In the approximation that the expansion is exactly exponential, the horizon is static and remains a fixed physical distance away. This patch of an inflating universe can be described by the following metric: This exponentially expanding spacetime is called a de Sitter space, and to sustain it there must be"
"matter or by radiation. An example of a cosmological model with an event horizon is a universe dominated by the cosmological constant (a de Sitter universe). A calculation of the speeds of the cosmological event and particle horizons was given in a paper on the FLRW cosmological model, approximating the Universe as composed of non-interacting constituents, each one being a perfect fluid. If a particle is moving at a constant velocity in a non-expanding universe free of gravitational fields, any event that occurs in that Universe will eventually be observable by the particle, because the forward light cones from these"
"not be able to escape (e.g. because the mass of the black hole is growing) and therefore inside the event horizon. Thus the apparent horizon can be thought of as the boundary of black hole for light at this instant, whereas the event horizon is the boundary of the black hole for light in the future. The notion of a horizon in general relativity is subtle, and depends on fine distinctions. The notion of an ""apparent horizon"" begins with the notion of a trapped null surface. A (compact, orientable, spacelike) surface always has 2 independent forward-in-time pointing, lightlike, normal directions."
"Bousso's holographic bound A simple generalization of the black hole entropy bound (cf. holographic principle) to generic systems is that, in quantum gravity, the maximum entropy which can be enclosed by a spatial boundary is given by a quarter of its surface area. However, as a general rule, this simple generalization appears to be false, because the spatial boundary can be taken to be within the event horizon of a black hole. It also fails in cosmological models. Raphael Bousso came up with a modification that the spatial boundary should not be a trapped surface. This led him to come"