The Nature of Physical Reality by Subhash Kak

Author:Subhash Kak [Kak, Subhash]
Language: eng
Format: epub
Publisher: Mount Meru Publishing
Published: 2016-04-15T18:30:00+00:00

The event horizon

We have seen that light rays passing a body get red-shifted and deflected. Light rays leaving the surface in a perpendicular direction are not deflected, while those that leave in a direction tangential to the surface are deflected the most. When the body contracts and the spacetime around it becomes extremely curved the situation is altered. When the body has contracted to a radius 1.5 times the Schwarzschild radius all light rays emitted tangentially get curved into circular orbits. This is called the radius of the photon sphere.

With respect to the observer, we can speak of a light cone which represents a spherical sheet of light emanating from the observer. Since the speed of light cannot be reached by any material body, the world line of the body cannot cross its light cone. As an object approaches a black hole its light cone tilts toward the black hole due to the curvature of spacetime. At the Schwarzschild surface, the future light cone is completely tipped into the black hole so that all light emitted by the particle falls into the black hole. Its past light cone is tipped away in such a fashion that it can receive light only from the outside world. Consequently an observer cannot have advance warning of the existence of the black hole unless that inference is made indirectly.

From a distance the object appears to approach the black hole rapidly and then disappears. In the spacetime of the object nothing untoward happens and it moves smoothly into the black hole.

Since the light emitted just outside the Schwarzschild radius is radiated out, and that emitted just inside the radius falls within, this radius forms a surface where the photons are static from the point of view of the distant observer. Owing to the fact that the special theory of relativity should apply in small regions, the conclusion to draw is that space falls inwards at the speed of light. The surface at which space falls inwards with the speed of light is the event horizon.

It was shown by Price in the 1960s that during collapse the object’s irregularities are lost. The surviving attributes for the black hole are mass, charge, and angular momentum. Solutions of Einstein's equations for this kind of a black hole were found in the 1960s. Such a black hole is commonly called a Kerr-Newman black hole. Whereas the Schwarzschild black hole does not have any charge or angular momentum, the rotating (Kerr-Newman) black hole has two characteristic surfaces. In one of these, space flows inwards with the speed of light: this is the static surface. In the other the space rotates with the speed of light: this is the event horizon. The event horizon lies inner to the static surface. The region between the two surfaces is termed the ergosphere. The static surface sphere is flattened along the axis of rotation. It was shown by Penrose in 1969 that energy can be extracted from a rotating black hole by injecting a mass into its ergosphere.

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