Singularity (astronomy)

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In physics and astronomy , a singularity is a place where gravity is so strong that the curvature of space-time diverges , which is colloquially "infinite". This means that in these places the metric of spacetime also diverges and the singularity is not part of spacetime. Physical quantities such as the mass density, for the calculation of which the metric is required, are not defined there.

Geodesics that meet the singularity have a finite length, so spacetime is causally geodetically incomplete.

According to the general theory of relativity, there are singularities in space-time under very general conditions, as Stephen Hawking and Roger Penrose showed in the 1960s ( singularity theorem ). The singularities can be formulated as mathematical singularities . a. on special mass values  , angular momentum  or other parameters. The physical law in question for the limit value , whereby a critical parameter value is, is not defined, invalid and unsuitable for describing the relationships. Singularities can be point-shaped, i.e. infinitely small, or non-point-shaped, whereby space-time bends so much around the object that size information cannot be put in a meaningful relationship to the metrics of the surrounding space.

It is assumed that singularities show the limits of general relativity and that another model ( e.g. quantum gravity ) must be used to describe it.

Types of Singularities

The singularities discussed in this article are also called true, intrinsic, or curvature singularities, to indicate that they are physical properties of spacetime. In them a coordinate-independent quantity diverges, the curvature of spacetime. They are to be distinguished from so-called coordinate singularities , which are merely a mathematical property of the selected coordinates. The latter can be "transformed away" by means of a suitable coordinate transformation . This is not possible for real , essential singularities , here a new theory (a new physical law) is needed.

Singularities, for example within a normal black hole , are surrounded by an event horizon , which in principle withdraws the object from observation. It is unclear whether singularities without an event horizon (so-called naked singularities ) also exist. That singularities are shielded by event horizons, i.e. there are no naked singularities, is the subject of the hypothesis of the cosmic censor by Roger Penrose . It is unproven and represents one of the great open problems of general relativity.

Astrophysics and cosmology

In astrophysics and cosmology the term singularity is often used synonymously for black hole or in the big bang theories for the initial singularity .

In both cases, Einstein's field equations are the physical laws used for explanation. The theory on which these equations are based ( Albert Einstein's general theory of relativity) is, however, a “classical theory”, not a quantum theory . Therefore it loses its validity on very small length scales ( Planck length ) and there begins the range of a theory of quantum gravity . However, very little is known about the internal state or the structure of singularities within the framework of such a theory.

Initial singularity

In the Big Bang theories, space-time “starts” in a mathematical singularity. The first physically describable point in time is placed on the shortest possible time interval from this singularity, namely the Planck time of approx. 10 −43 seconds . The big bang theories do not describe the big bang itself, but only the development of the universe since this age. In the initial mathematical singularity, space and time are not yet present. Information on the extent or duration are thus defined from physics.

In the initial singularity, the laws of nature known to us cannot have been valid. The initial singularity was not a black hole. It had no event horizon and no outside space surrounding it.

Black holes

Black holes can be characterized by their effect on the space-time surrounding them. However, many properties of the singularity inside a black hole, such as its density , are similarly undefined as those of the initial singularity .

Karl Schwarzschild was the first to give a solution ( outer Schwarzschild solution ) for the field equations. His solution describes uncharged non-rotating, i.e. H. static black holes that do not actually exist and become singular at the central point (point singularity). In the Kruskal coordinates , the point singularity becomes a manifold described by a hyperboloid . So you can see explicitly that there is no singularity on the event horizon itself .

It was not until 1963 that the New Zealand mathematician Roy Kerr found another solution ( Kerr's solution ) for rotating black holes, which becomes singular in a one-dimensional ring in the equatorial plane. The radius of the ring singularity corresponds to the Kerr parameter. An even more general solution with an additional electrical point charge leads to the Kerr-Newman metric .

The outer Schwarzschild solution is a special case of the Kerr solution (Kerr parameter a = J c / ( G M ²) = 0, i.e. no rotation). For maximally rotating black holes, i.e. i.e. if the event horizon rotates at the speed of light , however, a  = 1. Objects with a spin of a  > 1 must therefore have an extension that is higher than the gravitational radius corresponding to their mass, otherwise the event horizon will dissolve and become a naked singularity at the poles and the equator would be visible from the outside. That bare singularities are shielded from outside observers by event horizons is the subject of the Cosmic Censorship Hypothesis . It is generally unproven and may require expansion of known physical theories, but there are indications of its validity from numerical simulations, mathematical analysis, and thought experiments.

literature

Individual evidence

  1. ↑ Jan A. Aertsen, Andreas Speer: Space and conceptions of space in the Middle Ages . Walter de Gruyter, 2013, ISBN 978-3-11-080205-4 , p. 6 ( books.google.de ).
  2. ↑ Dirk Evers: Space, Matter, Time: Theology of Creation in Dialogue with Scientific Cosmology . Mohr Siebeck, 2000, ISBN 978-3-16-147412-5 , pp. 100 ( books.google.de ).
  3. ↑ Eugenie Samuel Reich: Spin rate of black holes pinned down.
  4. ↑ Harvard Smithsonian Center for Astrophysics: Supermassive Black Hole Spins Super-Fast
  5. ↑ NASA: NuSTAR Sees Rare Blurring of Black Hole Light
  6. ↑ Jeremy Hsu: Black Holes Spin Near Speed ​​of Light
  7. ↑ Joakim Bolin, Ingemar Bengtsson: The Angular Momentum of Kerr Black Holes. Pp. 2, 10, 11.
  8. ^ William Wheaton: Rotation Speed ​​of a Black Hole
  9. ↑ Matt Visser: The Kerr spacetime: A brief introduction. P. 28.
  10. ↑ Gerald Marsh: The infinite red-shift surfaces of the Kerr solution , p. 7. arxiv : gr-qc / 0702114