Apparent horizon

An apparent horizon is a surface defined in general relativity as the boundary between light rays which are directed outwards and moving outwards, and those which are directed outwards but moving inwards.

Apparent horizons are not invariant properties of a spacetime. They are observer-dependent, and in particular they are distinct from absolute horizons.

See, however the articles on ergosphere, Cauchy horizon, the Reissner-Nordström solution, photon sphere, Killing horizon and naked singularity; the notion of a horizon in general relativity is subtle, and depends on fine distinctions.

Definition

The notion of an apparent horizon begins with the notion of a trapped null surface. We take a (compact, orientable, spacelike) surface, and find its outward pointing normal vectors. The basic picture to think of here is a ball with pins sticking out of it; the pins are the normal vectors.

Now we look at light rays that are directed outward, along these normal vectors. The rays will either be diverging (the usual case one would expect) or converging. Intuitively, if the light rays are converging, this means that the light is moving backwards inside of the ball. If all the rays around the entire surface are converging, we say that there is a trapped null surface.

We can take the set of all such trapped surfaces. If we are thinking in terms of a simple Schwarzschild black hole, these surfaces will fill up the black hole. The apparent horizon is then defined as the boundary of these surfaces — essentially, it is the outermost surface of the black hole, in this sense. Note, however, that a "black hole" is defined with respect to the "event horizon", which is not always the same as the apparent horizon.

Differences from the (Absolute) Event Horizon

In the context of black holes, the term event horizon refers almost exclusively to the notion of the absolute horizon. Much confusion seems to arise concerning the differences between an apparent horizon (AH) and an event horizon (EH). In general, the two need not be the same. For example, in the case of a perturbed black hole, the EH and the AH will generally not coincide as long as either horizon is fluctuating.

In the simple picture of stellar collapse leading to formation of a black hole, an event horizon will be formed before an apparent horizon.cite book | title=The large scale structure of space-time | author=S. W. Hawking and G. F. R. Ellis | publisher=Cambridge University Press | year=1975] As the black hole settles down, the two horizons will approach each other, and asymptotically become the same surface. If the AH exists, it is necessarily inside of the EH.

Apparent horizons depend on the "slicing" of a spacetime. That is, the location and even existence of an apparent horizon depends on the way spacetime is divided into space and time. For example, it is possible to slice the Schwarzschild geometry in such a way that there is "no" apparent horizon, ever, despite the fact that there is certainly an event horizon. [cite journal| title =Trapped surfaces in the Schwarzschild geometry and cosmic censorship | author =Wald, Robert M. and Iyer, Vivek | journal =Phys. Rev. D | volume =44 | number =12 | pages =R3719--R3722 | numpages =3 | year =1991 | month =Dec | doi =10.1103/PhysRevD.44.R3719 | publisher =American Physical Society]

ee also

* Trapped null surface
* Absolute horizon
* Black hole
* Event horizon
* Particle horizon
* Cosmological horizon

References


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Look at other dictionaries:

  • Apparent horizon — Horizon Ho*ri zon, n. [F., fr. L. horizon, fr. Gr. ? (sc. ?) the bounding line, horizon, fr. ? to bound, fr. ? boundary, limit.] 1. The line which bounds that part of the earth s surface visible to a spectator from a given point; the apparent… …   The Collaborative International Dictionary of English

  • Apparent horizon — Apparent Ap*par ent, a. [F. apparent, L. apparens, entis, p. pr. of apparere. See {Appear}.] 1. Capable of being seen, or easily seen; open to view; visible to the eye; within sight or view. [1913 Webster] The moon . . . apparent queen. Milton.… …   The Collaborative International Dictionary of English

  • apparent horizon — regimasis horizontas statusas T sritis Standartizacija ir metrologija apibrėžtis Tariamoji Žemės ir dangaus susikirtimo linija, kurią mato stebėtojas. atitikmenys: angl. apparent horizon; sensible horizon; visible horizon vok. sehbarer Horizont,… …   Penkiakalbis aiškinamasis metrologijos terminų žodynas

  • apparent horizon — regimasis horizontas statusas T sritis fizika atitikmenys: angl. apparent horizon; sensible horizon; visible horizon vok. scheinbarer Horizont, m; sichtbarer Horizont, m; Sichthorizont, m rus. видимый горизонт, m pranc. horizon apparent, m;… …   Fizikos terminų žodynas

  • apparent horizon — horizonto linija statusas T sritis Gynyba apibrėžtis Matoma linija, skirianti žemę (jūrą) ir dangų. atitikmenys: angl. apparent horizon pranc. horizon apparent …   NATO terminų aiškinamasis žodynas

  • apparent horizon — noun the line at which the sky and Earth appear to meet • Syn: ↑horizon, ↑visible horizon, ↑sensible horizon, ↑skyline • Hypernyms: ↑line • Part Holonyms: ↑perspective, ↑ …   Useful english dictionary

  • apparent horizon — The visible line of demarcation between land/sea and sky …   Military dictionary

  • apparent horizon — The visible line of demarcation between land or the sea and the sky …   Aviation dictionary

  • Horizon — Ho*ri zon, n. [F., fr. L. horizon, fr. Gr. ? (sc. ?) the bounding line, horizon, fr. ? to bound, fr. ? boundary, limit.] 1. The line which bounds that part of the earth s surface visible to a spectator from a given point; the apparent junction of …   The Collaborative International Dictionary of English

  • Apparent — Ap*par ent, a. [F. apparent, L. apparens, entis, p. pr. of apparere. See {Appear}.] 1. Capable of being seen, or easily seen; open to view; visible to the eye; within sight or view. [1913 Webster] The moon . . . apparent queen. Milton. [1913… …   The Collaborative International Dictionary of English


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