Space Phenomenon.

1.7 Singularity.

An area of space so dense the degenerate neutronic forces/pressures can not withstand the combined force per unit area of the gravitons from the stellar mass. This creates an implosion whereby the collapse only stops when the body occupies a space of infinitesimal dimension. The mass needed to overcome the degeneracy pressure must be above the Oppenheimer-Volkoff limit. The most recent calculations for this mass would put the degenerate matter at some where between two and three solar masses. Less than this would create a neutron star and below the Chandrasekhar limit of about 1.4 solar masses, the star would burn as a white dwarf. The area around the degenerate mass above the Oppenheimer-Volkoff is warped in a manner consistent with Einstein’s General Theory of Relativity whereby space times folds about the object. This folding is so intense near the central mass that even light can not overcome the acceleration of gravity and would therefore "never" escape. As one moves away from the central mass the acceleration decreases by an amount proportional to the mass of the object until a hypothetical boundary state is crossed.

Schwazschild Radius = 2GM/c2 (Kaufmann 1991).

Whereby objects with velocities equal to the speed of light in a vacuum can cross and escape. Particles with velocities lower are trapped and another boundary would be found further from the centre where these objects can escape. The boundary where objects with speeds that of c can escape is referred to as the Scharwzschild Radius or the Event Horizon.

One of the remarkable predictions of Schwarzschild's geometry was that if a mass M were compressed inside a critical radius (rs), nowadays called the Schwarzschild radius, then its gravity would become so strong that not even light could escape. The Schwarzschild radius (rs) of a mass M is given by

rs = 2 G M / c2

where G is Newton's gravitational constant, and c is the speed of light.

The Schwarzschild radius had already been derived (with the correct result, but an incorrect theory) by John Michell in 1783 in the context of Newtonian gravity and the corpuscular theory of light. Michell derived the critical radius by setting the gravitational escape velocity v equal to the speed of light c in the Newtonian formula v2 / 2 = G M / r for the escape velocity v from the surface of a star of mass M and radius r. He believed that if light were a particle then it should be affected by gravity and if gravity were above a certain threshold light would be impeded and unable to escape. Such bodies would appear perfectly black because no light would escape from them.

The Horizon

The Schwarzschild surface, the sphere at one Schwarzschild radius, is also called the event horizon of a black hole, since to an outside observer, even one positioned just outside the Schwarzschild surface, nothing can be seen beyond the horizon. In truth the observer would see all matter that had fallen into the singularity over time but observed as if it were traveling at speeds very near that of light so all objects would appear stationary as if time had stopped for them and stretched out in the direction of motion rendering them two dimensional and effectively invisible. These images would not be detectable and thus all matter would seem lost and destroyed. This is an idealised case as will be discussed below. The actual Schwarzchild radius is most commonly obscured by infalling, superheated materials.

A black hole can be described by three basic properties. This is obviously very different to any other stellar phenomenon whose identity would contain millions of sets of data on all the particles and their interactions. A singularity on the other hand has just mass, spin and charge. There are four basic forms of singularity based on the properties of spin and charge:

• An uncharged non-rotating black hole is described by the Schwarzchild solution.

• An uncharged but rotating black hole is described by the Kerr solution

• A charged non-rotating black hole is given by the Reissner NordstrØm

• A charged rotating black hole is described by the Kerr-Newman solution.

is the simplest type of singularity. The original Schwarzchild solution from 1917 was applied to singualarties in 1967 by Werner Israel. He showed that non-rotating black holes would be perfectly spherical and the only other information the system would carry would be its mass. Unfortunately Israel dealt with systems of collapse that were non-rotating and it was Kerr who later described the collapse of rotating bodies. A Schwarzschild black hole is static; meaning it has no spin and no charge. The Reissner NordstrØm Solution was developed by Heinrich Reissner in Germany in 1916 and independently by Gunnar NordstrØm in Finland. The solution describes a singularity whose spin and/or charge is none zero and though the equation is theoretically accurate such black holes are improbable in nature given that the electric charge would be a strong conductor for opposite charges and would soon become electrically neutral. If a singularity were to be charged it is believed that the immense electric field around the charged hole to be so great that the individual atoms arriving at it would be deconstructed with sub-atomic particles pulled apart before they would reach the hole, whereas this is not the case for a rotating black hole. Obviously all forms of singularity have a gravitational field of equal magnitude, which is very powerful, but not in all cases powerful enough to annihilate ordinary matter at a distance. Another difference is that with the charged hole, one can assume a point singularity, that is one can assume that all the matter of the hole is contained in a geometric point and that space-time has completely bent around this point, whereas with a rotating black hole one gets ring singularity, hence a spinning disk. A rotating black hole is sometimes referred to as a ring singularity. This is where the point becomes stretched into a doughnut shape. For a time it was believed that these types of singularity may have allowed faster than light travel. This is discussed further in the section on Einstein Rosen Poldosky Bridges. Given that most stars are rotating relative to the local inertial system and are consequently not spherically symmetrical it was found that the basic Schwarzschild solutions are not correct. Though Newtonian gravitational theory is static a rotating star in Einsteinain theory will act to produce fields. In 1963 some fifty years after the discovery of the Schwarzschild metric the Kerr solution was found. The Kerr-Newman solution was developed by Ezra Newman and colleagues in Pittsburgh in 1965 by building on the basic Kerr solution.

Given that the black hole is rotating, assuming the original stellar body was rotating, clearly this need not be so for primordial singularities, to conserve angular momentum it must be spinning very fast. The black hole actually drags surrounding space-time with it. The area where this is most severe is known as the ergosphere. Within the ergosphere no object can remain at rest and is pulled along with the singularity. Given that the ergosphere is outside of the Schwazschild radius an object can traverse the ergosphere and not be destroyed. Therefore an object incident on the black hole could be released with significantly greater velocity than it had to start with, the added energy being gained from the black holes rotation. Figure 1 shows matter expelled along two diametrically opposite lines. This is in the form of superheated plasma emitting high energy X-Rays. The matter around the central nucleus also glows as it is heated by the acceleration. Though this can be seen in the visible wavelength the most energetic waves will be shifted into the X-ray and gamma ray spectrum. It is the combination of strong magnetic field and a dense accretion disk that allows the creation of the "soup" of very fast particles that collide with one another and with photons to generate these x-rays and gamma rays. A starburst, in contrast, produces most of its high-energy radiation from collisions between supernova ejecta and the surrounding galactic gas and dust. This impact heats gas to no more than about a billion degrees and so cannot produce any radiation more energetic than x-rays. The large numbers of gamma rays detected recently from some quasars by the Compton Gamma Ray Observatory imply that black holes are at their centers.

(The Compton Gamma Ray Observatory, by Neil Gehrels, et al.; Scientific American, December 1993).

### Figure 1 Showing Superheated Material Expelled From A Singularities Ergosphere. Image From The NASA homepage

The term black hole was first used by physicist John Wheeler but the theory had existed for some considerable time. The term dark star or black star had been presented to the Royal Society in 1783 by John Michell (An English geologist 1724-1793). Using Newton's corpuscular theory of light Michell believed that it was possible for a body to exert enough gravity such that its escape velocity would be so great that any matter regardless of how small in mass would not be able to escape the body. Michelle believed a body with diameter some 500 solar masses would exert such a force that the escape velocity would exceed that of light. The same conclusion was reached independently in 1796 by Pierre Laplace. It is possible that the theory remained forgotten for so long because of the return to the belief in light as a wave that dominated until the early twentieth century. If light were a purely wave like phenomenon it would not necessarily be affected by gravity. In 1918, Albert Einstein's theory of general relativity predicted that rotating bodies, such as black holes, drag space and time around itself as it rotates. In November of 1997, astronomers using NASA's Rossi X-ray Timing Explorer (RXTE) spacecraft made found evidence that supports this effect known as frame dragging. By observing a binary star system in which a normal star feeds the disk of accreting matter spiraling into the event horizon of a black hole it was possible to record evidence of frame dragging. In this particular case, the astronomers were observing two black holes: GRS 1915+105 and GRO J1655-40 (Dooling). The astronomers calculated the oscillations being caused by frame dragging making accretion disk precess. Precession, according to Dave Dooling, is

"seen when a toy top both spins rapidly about its own axis, yet at the same time, executes a slower circular motion about the lower vertical axis. This second circular motion is precession, and it's not only found in toy tops, but also . . . [in] accreting disks around black holes in distant space." Sketch of black hole model where mass of main star is stripped onto an accretionary disc around a singularity material is superheated and emits high levels of x-rays. See Quasar (gamma rays section).