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Theories of the Causes of Black Holes

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Published: Thu, 05 Apr 2018

Black Holes

The phrase “black holes” is introduced to scientific world not by a physicist but a journalist, Ann Ewing in 1964, who made a report on a meeting of the American Association for the Advancement of Science (Ewing, 1964). Some elegant French argued that the phrase has annoying sexual insinuation. After that, the famous physics John Wheeler spread the “black holes” widely in physics and the public view. Actually the concept of an object so massive that even the light can’t be escaped is proposed by Michell (1783), as well as by Laplace (Gillispie, 2000) But this idea was so radical at that time when the light was thought to be massless. The golden age of black holes came along with the establishment of the generally relativity by A. Einstein (O’Connor, 1996). Schwarzschild and Droste solved the Einstein field equations independently and a solution describing a point mass was found (Schwarzchild, 1916; Droste, 1917). The properties of the black holes are developed and explained by a group of important works. G. Lemaitre and R. Oppenheimer have interpreted the singularity (Hooft, 2009; Ruffini, 1971). The event horizon is defined as a boundary inspace and time, inside which an event can’t be observed by the outsider (Wheeler, 2007). The no-hair theory of the black hole is completed by the work of Carter (1971), Israel (1967) and Robinson (1975), declaring that a stationary black hole can be described by only three parameters: the mass, the charge and the angular momentum. The black hole thermodynamics is interpreted by Bardeen et al. (1973).

In order to get a direct physical picture of a black hole, an illustration of a non-spinning black hole is given. Based on mathematically solution, a non-spinning black hole possesses a spherically symmetric boundary, which is also the event horizon. The center of the non-spinning black hole is a singularity where the gravitational forces become infinite. The distance between the singularity and the event horizon is called the Schwarzschild radius. The surface gravity of a stationary black hole is constant over the event horizon. One thing to be noted, it is impossible by any procedure, no matter how idealized, to reduce the surface gravity to zero by a finite sequence of operations. Aphoton sphere, the radius of which is 1.5 times of the Schwarzschild radius, is a spherical special region where gravity forces the photons to travel in orbits. Generally the black hole is classified to four groups according to their mass: micro, stellar, intermediate-mass and super massive black hole. Generally the size of a black hole is approximately proportional to its mass, the heavier of a black hole, the bigger of its size. A black hole with mass of 1000 times of solar mass has a radius like the earth.

The formation of a black hole is a mystery. Einstein thought that the exotic object, like black holes, would not exist in nature even there are such solutions to Einstein gravitationalfield equations. However, more and more theoretical calculations and even important astronomical observations have proved that Einstein is wrong. Most astrophysicists have reached an agreement that the formation of a black hole usually evolves many stages. First the primary process of the evolution is the gravitational collapse, which is usually occurs after the death of a heavy object, like stars. When a star doesn’t have enough “fuel” to keep its temperature through nuclearreaction or the star is keeping absorbing matters around it by universalgravitation. After the collapse, if the mass of leftover exceeds over 3 to 4 times of solar mass, it has an opportunity to form a black hole. The second stage is the formation of the event horizon, which is also the way to distinguish the black holes and other forms of objects, such as neutron stars, which are also a result of the gravitational collapse. Thanks to the work of Kerr (2009), who proved that the event horizon could be physical not just mathematical. According to the black holes thermodynamics, the area of the event horizon of each black hole does not decrease with time. After the presence of the event horizon, a singularity will form in a black hole (Penrose, 1965). This is considered to be the third stage. A black hole can continually grow up by absorbing the matters and interstellar dust or even merges with other stars or black holes. This is considered to be a way to super massive black holes. The last stage of black holes is the evaporation. If the Hawking’s theory can be verified, a black hole is not totally black but emits its thermal radiation with a quite small quantity. This means that a black hole would loss its mass by Hawking radiation (Parikh, 2000) and vanishes eventually. Simulation results show that a small black hole owns very strong emission effects. The Hawking radiation will be discussed in details.

Once the scientific world accepts the concept of black holes, a question is launched: are the black holes keep growing and expanding? Hawking says no! By applying quantum field theory into a stationary black hole background, he found that a black hole should radiate particles like a black body near the event horizon (Hawking, 1974). Physical picture to this bizarre phenomenon is the radiation is not come from the black holes directly, but the results of particle-antiparticle formation just beyond the event horizon. Specifically, a particle-antiparticle pair generated from the vacuum fluctuations appears close to the event horizon. One of the pair escapes forms the boundary while another one falls into it (Droste, 1917). Another interesting question is: how can be detected a black hole where even light can’t escape? The direct way is to probing the Hawking radiation, unfortunately the simulation results show that the Hawking radiation is too small to be detected from the Earth. In 2008 NASA launched the Fermi Gammar-ray Space Telescope to search the Hawking radiation which is strong in the last stage of a black hole (Naeye, 2008).

Beyond the detection of Hawking radiation. Many indirect approaches to detecting black holes are proposed and realized by astrophysicists. The X-ray binaries, a binary star system, emit bright X-ray spectrum. The XUV radiation is generally considered to be caused by a compact star being accreting interstellar gas and dust. The presence of the X-ray binary gives an opportunity to locating a black hole. In 1999, Celotti reported the existence of the sofr X-ray transients and predicted that a black hole may be formed in the region (Celotti, 1999). Still more data and needed to verify this finding. Another way to detect a black hole is based on the massive gravitational effect caused by the black holes. On candidate is the gravitational lens effect which deforms the space structure to bend the light as if a lens. The way to observe the gravitational lens effect is to observe the orbit of a star near the vicinity of a black hole. The evidence of the black holes caused gravitational lens is found by Bozza et al. (2010) around Sagittarius A*. A widely accepted view is that a super massive black holes exists in nearly the center of every galaxy, not just active ones.

When an observer is falling into a black hole, what kind of experience would he have? Theorists argue that if another observer out of the black holes tries to describe the falling one he should never be able to cross the horizon. This means, the falling one should take infinite time to cross the event horizon if he were not torn apart by tidal forces even before reaching the horizon. On the other hand, for this observer falling across the event horizon, he takes only a finite proper time in his own coordinate. However, he will not find any Hawking radiation. In fact this paradox comes from the contradiction between the general gravitational theory and the quantum mechanism. The two theories are successful in their own regions, general gravitational theory for cosmic and the quantum mechanism for atomic particles, but they can’t fit each other. The funny thing is that Einstein is against the quantum mechanism even he is one of the founders to it and even he was rewarded the Nobile Prize for his important work in quantum mechanism. Until now this is still an open question to the theoretical and astronomical physicists.

The black holes attract attentions both from scientists and the public. At first, it is only a mathematical expression for a special space time structure where nothing can be escape from it and described in scientific fictions. However with the appearances of more and more indirect evidences, it turns out to be reality with certain possibility. From scientific view of point, the black holes own unique properties and components, such as singularity, the event horizon, Hawking radiation. The black holes can provide particular physical conditions where new physical laws and principles can be verified. The researches on black holes push the frontier of astronomy, including worm holes, interstellar travel between stars, cosmic settlement. Fortunately we have plenty of time, maybe millions of years.

References

Bardeen, J. M. et al. (1973). The four laws of black hole mechanics. Communication Mathematical Physics, Vol. 31. pp. 161-170.

Bozza, V. (2010). Gravitational lensing by black holes.General Relativity and Gravitation, Vol. 42. No.42. pp. 2269–2300.

Carter, B. (1971). Axisymmetric black hole has only two degrees of freedom. Physical Review Letters Vol. 26. No. 6. pp.331-333.

Celotti, A.; Miller, J. C.; Sciama, D. W. (1999). Astrophysical evidence for the existence of black holes.Classical and Quantum Gravity, Vol. 16. No.12. pp. A3–A21.

Droste, J.(1917). On the field of a single centre in Einstein’s theory of gravitation, and the motion of a particle in that field. Proceedings Royal Academy Amsterdam, Vol.19.No. 1. pp. 197–215.

Droste, J.(2009). On the field of a single centre in Einstein’s theory of gravitation, and the motion of a particle in that field. Proceedings Royal Academy Amsterdam,Vol. 19. No.1. pp.197–215.

Gillispie, C., & Laplace, P. (2000). 1749–1827: a life in exact science. Princeton University Press.

Hawking, S. W. (1974). Black hole explosions? Nature,Vol. 248.No. 5443. pp. 30–31.

Hooft, G.t. (2009). Introduction to the theory of black holes. Institute for Theoretical Physics / Spinoza Institute. pp.47–48.

Israel, W. (1967). Event Horizons in Static Vacuum Space-Times.Physical Review Vol. 164. No. 5. pp. 1776-1779.

Kerr, R. P. (2009). The Kerr and Kerr-Schild metrics. Spacetime. Cambridge University Press.

Michell, J. (1784). Philosophical Transactions of the Royal Society, No.74. pp. 35–57.

Naeye, R.(2008). Testing fundamental physics. NASA.

O’Connor, J.J., and Robertson, E.F. (1996). General relativity.University of St. Andrews, Scotland.

Parikh, M., Wilczek, F. (2000). Hawking radiation as tunneling. Physical Review Letters, No. 26. No. 21. pp. 1344-1346.

Penrose, R.(1965). Gravitational collapse and space-time singularities. Physical Review Letters,Vol. 14. No.3. pp. 57-59.

Quinion, M.(2008). Black Hole.World Wide Words.

Robinson, D. (1975). Uniqueness of the Kerr black hole. Physical Review Letters,Vol. 34. No. 14. pp. 905-906.

Ruffini, R.;Wheeler, J. A.(1971). Introducing the black hole.Physics Today,Vol. 24No. 1. pp. 30–41.

Schwarzschild, K.(1916). Über das gravitationsfeld eines massenpunktes nach der Einsteinschen theorie.Sitzungsberichte der Königlich Preussischen Akademie der Wissenschaften,No. 7. pp. 189–196.

Wheeler, J. Craig. (2007). Cosmic catastrophes. Cambridge University Press.


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