Event horizon

An event horizon is in the general theory of relativity a boundary in space-time, for which it holds that events beyond this interface are generally not visible to observers who are located on this side of the interface. By " events" points are meant in space-time, which are determined by time and place. The event horizon is a boundary for information and causal relationships that result from the structure of space- time and the laws of physics, in particular in relation to the speed of light, results. The radius of the event horizon is called the Schwarzschild radius.

Each black hole has such an event horizon. Its shape and size depends, according to the state from today's models and findings of how large its mass is whether it rotated and if it is loaded. In general, the event horizon of a black hole has the shape of an ellipsoid of revolution; in the special case of a non-rotating, it electrically uncharged black hole is spherical.

The Schwarzschild radius is related to the event horizon to the effect in context, as he is the radius from the center of mass of non-rotating black holes up to the event horizon, comparable to the radius of the sphere to the sphere surface. There are at any given mass a Schwarzschild radius: if an object of any mass is compressed to a spherical volume with a radius smaller than the Schwarzschild radius (and thus a critical threshold in the density exceeds ), it collapses into a black hole.

In addition, it is assumed in various cosmological models, that the universe as a whole has an event horizon. The observable universe is the part of the universe that is within the event horizon. According to the current standard model of cosmology this event horizon is located at a distance of about 47 billion light years.

• 5.1 Rotating Black Holes
• 5.2 Electrically charged black holes

Introduction

The gravitational field of a body consisting of an outer and an inner solution where the outer solution, the gravitational field outside the body and the internal solution is described in the field in the interior of the body. In the case of a homogeneous, non-charged and non-rotating ball the Schwarzschild metric describes the internal and external gravitational field.

For an object which is itself larger than the Schwarzschild radius, there is no event horizon, since the inner part does not belong to the external Schwarzschild solution; the inner solution contains no singularities. Only when an object is smaller than its Schwarzschild radius, creates a singularity and there is an event horizon in the spacetime. In the case of non-rotating and electrically non-charged black holes, the event horizon is the surface of a sphere around the central singularity. The radius of this sphere is the Schwarzschild radius.

Is the scalar curvature of spacetime at the event horizon of the Schwarzschild metric

Wherein the speed of light, is the gravitational constant and the mass of the black hole is.

In the far field the classical law of gravity still applies as an approximation. However, this approximation leads to larger and larger deviations, the more one approaches the event horizon. In the immediate vicinity of the event horizon then, finally, the general theory of relativity must be used.

History

John Michell was the first grappled with the question of how big to make the attraction of a celestial body, so that light can not escape from its surface. Using the Newtonian theory of gravitation and the corpuscular theory he found in 1783 a relationship between the radius and the mass of a celestial body in which this effect occurs. This radius is 1916 again found in a general relativistic calculation Karl Schwarzschild, therefore he was named in his honor as the Schwarzschild radius.

Event horizon in the Schwarzschild metric

For non - rotating black holes, the event horizon in the Schwarzschild metric is defined by the same radius. The Schwarzschild radius rS a mass M is given by

The Schwarzschild volume is therefore

Thus resulting in a critical density by

Can be defined. Once a mass exceeds this density, it collapses into a black hole. For the mass of the sun the Schwarzschild radius is 2952 m, for the earth only 9 mm and for the Mount Everest 1 nm

Should also be noted that the radius of the event horizon in general relativity theory does not specify the distance from the center, but is defined on the surface of spheres. A spherical radius with the event horizon has the same area as a sphere of the same radius in the Euclidean space, viz. Due to the space-time curve, the radial distances are increased in the gravitational field ( say, the distance between two spherical shells with - defined on the spherical surface - radial coordinates and is larger than the difference between these radii ).

Meaning and properties of the event horizon of a black hole

Gravitational redshift

The frequency of a photon, which passes out of a gravitational field to a remote observer is shifted to the red ( low energy ) of the light part of the spectrum, because the photon corresponding to the potential energy is lost. The red shift is greater the closer the light source is located at the Black Hole. At the event horizon the red shift becomes infinite.

Application time for an outside observer

To an outside observer who is watching from a safe distance, like an object falling towards a black hole, it would seem as if the object would asymptotically approach the event horizon. This means that an outside observer never sees how the object reaches the event horizon, as is infinitely needed in his view, to much time.

Application time for a freely falling observer

For an observer who is moving in free fall towards the black hole, this is entirely different. This observer reached the event horizon in finite time. The apparent contradiction to the previous result stems from the fact that both analyzes are conducted in different reference systems. An object that has reached the event horizon falls (seen from the object itself ) in a finite time in the central singularity.

It should also be noted that the event horizon is not a representational border; a freely falling observer could not therefore directly determine when it passes the event horizon.

Angular momentum and electric charge

Rotating Black Holes

For rotating black holes arises from the Kerr metric, an event horizon, but in contrast to the event horizon of the Schwarzschild metric has rather the geometric properties of an ellipsoid of revolution. The dimensions of this ellipsoid depend on the angular momentum and the mass of the black hole.

The event horizon rH of a rotating black hole is given as follows:

In which

With angular momentum.

The solution for rH thus depends for a black hole of a given mass depends only on its rotation a. Here, two special cases can be identified:

For a → 0, ie for a non- rotating black hole is

And thus identical to the radius of the Schwarzschild metric. For a → GM/c2, ie for a maximum - rotating black hole is

And also gravitational radius rG is called.

The gravitational radius is often used as a unit of length in the description of the environment of a black hole.

To the event horizon of the rotating black hole is also the ergosphere in which the spacetime participates increasingly in the rotation of the black hole. Matter, light, magnetic fields, etc. must always be free to rotate within the ergosphere with the black hole. Since rotating charges always emit synchrotron radiation, the ergosphere provides an obvious explanation for the observed jets of active galaxies.

The singularity at the center of rotating black holes is annular.

Electrically charged black holes

Electrically charged, non- rotating black holes are described by the Reissner - Nordström metric; electrically charged, rotating black holes through the Kerr-Newman metric.