I'm Continuing my Set about Universe : Universe

An artistic design of an accretion disk of hot plasma orbiting a black hole (Picture From $NASA$)

To Start We need know what a black hole, So our first question is: What is Black Hole?

According to the general theory of relativity, a black hole is a region of space from which nothing, not even moving objects at the speed of light, can escape. This is the result of the deformation of spacetime caused after the gravitational collapse of a star by a massive astronomically matter and at the same time, infinitely compact and, soon after, disappears giving rise to what physics calls the Singularity, the heart of a black hole, where time and space for longer exists. A black hole starts from a surface called event horizon that marks the region from which one can not return. The adjective black on black hole is because this does not reflect any portion of the light will reach the event horizon, thus acting like a perfect black body in thermodynamics. It was also believed based on quantum mechanics, black holes that emit thermal radiation, in the same way as the thermodynamics of the blackbodies finite temperatures. This temperature, however, is inversely proportional to the mass of the black hole, so observe the thermal radiation from these objects becomes difficult when they have masses comparable to the stars. Although black holes are virtually invisible, these can be detected through interaction with matter in its vicinity. A black hole can, for example, be located by observing the motion of stars in a given region of space. Another possibility of locating black holes with respect to the detection of the large amount of radiation emitted when matter from a companion star is spiraling into the black hole, heating to high temperatures. Although the concept of black hole has appeared on theoretical grounds, astronomers have identified numerous stellar black hole candidates and also evidence of the existence of super massive black holes at the center of massive galaxies. There are indications that in the Via Lactea own center, in the vicinity of Sagittarius A *, there must be a black hole with over $2$ million solar masses.

*Relativity * : In $1915$, Albert Einstein developed the theory of general relativity, having always shown that gravity can influence the movement of light. Shortly thereafter, Karl Schwarzschild made ​​a system of units: Schwarzschild metric system for the Einstein field equations, which describes the gravitational field of a point mass and a spherical mass. A few months after Schwarzschild, Johannes Droste, a student of Hendrik Lorentz, independently gave the same solution for the point mass and wrote more extensively about its properties. This solution has a function which is called the Schwarzschild radius, becoming mathematical singularity, which means that some of the terms in the Einstein equations are endless. The nature of this surface was not well understood at the time. In $1924$ , Arthur Eddington showed that the singularity disappeared after a change of coordinates, although it took until $1933$ for Georges Lemaître to realize that this meant the singularity at the Schwarzschild radius, and it was not a physical property but mathematics from the discovery of mathematical singularity. In $1931$ , Subrahmanyan Chandrasekhar calculated, using special relativity, that a non-rotating body of electron degenerate matter above a certain mass limit (now called the Chandrasekhar limit of $1.4$ solar masses) has no stable solutions. His arguments suffered opposition from many of his contemporaries like Eddington and Lev Landau, who argued that some yet unknown mechanism would stop the collapse. They were partly correct: a white dwarf with slightly above the Chandrasekhar mass will collapse into a neutron star, which is itself stable because of the Pauli exclusion principle. But in $1939$, Robert Oppenheimer and others predicted that neutron stars above approximately three solar masses (the Tolman-Oppenheimer limit-Volkoff) would collapse into black for the reasons presented by Chandrasekhar holes, concluding that no law of physics was likely to intervene and stop at least some stars from collapsing to black holes.

Formation and Structure

• Formation : black hole forms when a super massive star runs out of fuel, which makes its core decrease until reduced to a fraction of its original size. When this happens, the gravity produced by it gets out of control and starts sucking everything it encounters. He begins to suck the mass of the star, doing it so fast that it chokes and blows huge torrents of energy. She is so strong that just sticking the star and jets releasing more energy. Gravity does not support this energy and the star finally explodes (this is called supernova explosion). In just a second explosion is able to generate $100$ times more energy than our Sun will produce in its entire existence. What remains in the center is the black hole. This explosion is also known as eruption gamma or gamma-ray burst. Most stars of class W (Wolf-Rayet stars or, in Portuguese, Wolf-Rayet stars) dies in deadly explosions that would have the effect of $100000$ times the atomic arsenal of the world.

• Oppenheimer-Snyder collapse : The collapse of this model describes a sphere "of" dust (dust used the concept of relativity) that inexorably collide to form a black hole. This is an exact solution to the equations of general relativistic field. The stages of collapse are:

$I)$ stationary phase before the collapse. The star could be immersed in a sphere of perfect spherical symmetry fluid. The momentum tensor:

$T = (\rho + p)uiuk + pgik$

Where $\rho$, $p$, and $gik$ are density, pressure and metric, respectively.

$II )$ End of "burning" nuclear (nuclear fusion reactions) and the beginning of the collapse, the pressure breaks $(p = 0)$ . then:

$T= puiuk$

The ball is at rest for a moment.

$III)$ Stage collapse. Since there is no pressure the ball will begin to shrink. To dust is expected contraction and subsequent collapse resulting in a black hole. Obviously no dust reflects the chemical complexity of the material of the stars that form the black hole.

• Non-spherical collapse

Early studies of non-spherical collapse began in the $1960$. These studies showed that disturbances around the spherical symmetry does not prevent the formation of a black hole. And who, when reached steady state, there is an exact spherical symmetry of the horizon. The problem for large deviations from spherical symmetry was answered quite differently by Werner Israel in $1967$. Without much modern appliances managed to establish a theorem:

"A static black hole, and in vacuum with a regular event horizon must be the Schwarzschild solution."

This was a solid basis for the development of many subsequent theorems culminating in Theorem baldness :

"Black holes can be characterized only by mass, angular momentum and electric charge."

The Schwarzschild black hole

Karl Schwarzschild in $1916$, found the solution to the theory of relativity is that the black hole as having a spherical shape. He showed that if the mass of a star is concentrated in a sufficiently small region, it will generate such a large gravitational field on the surface of the star which not even light will escape him. This is called the black hole. Einstein and many physicists did not believe that such a phenomenon could happen in the real universe. However, it was proved that this phenomenon actually happens. Considering a spherical gravitational field in vacuum, the solution to the Einstein equation has the following form:

(1.1)

** $G$ is the constant of gravitation.

An important property of this solution is that it is independent of time $t$. The solution is determined simply by the parameter $M$ , which is the total mass of the source which produces the field. The interpretation of this parameter arises immediately from the asymptotic form of the metric. Away from the center of gravity, spacetime approaches the flat space-time with Minkowski metric:

(1.2)

And the gravitational field can be described using the weak field approximation. Buying this approach and the metric $(1.1)$ we have that $M$ is the mass of the system is gravitating.

The fall in the black hole and the quantum nature

If we could observe a real drop an object into a black hole, according to the virtual simulations, we would see this move more and more slowly as they approached the solid core. According to Einstein, there is a red shift, and this is also dependent on the gravitational intensity. This is because, from the point of corpuscular view of light is a quantum package with mass and occupies space therefore has a particular must escape velocity. At the same time, this wave packet is of electromagnetic nature and it propagates in free space. It is known that far from intense gravitational field, the transmitted frequency tends to the upper end (in the case of visible light, violet). As the gravitational field starts acting on the particle (light), this will increase its wavelength, then jumps to the red. Due to the duality raw energy is not possible to analyze the particle as matter and energy at the same time: or sees from the point of view vibratory or corpuscular

• The light and the uniqueness : In simulations in virtual space, it was found that near massive fields occupying natural places, the gravitational pull is so strong that it can stop the oscillatory motion in the case of light enxergada as wavelength, this literally goes off. In the case of light as enxergada object that has a velocity that the exhaust is drawn back to the region where it was generated, since the exhaust speed should be equal to the speed of propagation, both being equal, the material is drawn back light. Therefore, the radiation being drawn back, goes into gravitational collapse along the mass that created it, falling over herself ..

• Computer simulation : ou can simulate on a computer the physical conditions that lead to formation of a black hole as a result of gravitational collapse of a supergiant star, or supernova. For this, the theoretical astrophysicists implement complex programs that recreate the physical conditions of matter and space-time during the implosion of the stars, which exhaust their nuclear fuel and collapse, with the passage of time, due to its gravitational weight forming an object of infinite density and curvature of space-time. These objects, nothing --- not even light can escape. The result is the formation of a gravitational singularity contained in a Schwarzschild black hole. A method for computer simulation of a black hole is the Monte Carlo method. In this method it is possible to simulate a microscopic black hole. The event generator Monte Carlo this method is the CATFISH (Collider Gravitational Field Simulator for black Holes), developed at the University of Mississippi.

Thermodynamics

• Thermodynamics of a classical black hole

A black hole, physically, is a place where not even light can escape. A precise mathematical description of it is given by asymptotically flat spacetime. The boundary of a black hole is called the event horizon. Schoen and Yau formulated in 1983 that a surface within a trap may be formed provided that a sufficient amount of dough is sufficiently confined in a small space. Then it follows from theorems of general relativity (Hawking and Hellis $(1973)$ that a singularity of spacetime should emerge. From these great discoveries followed several important conclusions as the solution of the Einstein-Maxwell equation independent of time showing that black holes can be described by three simple parameters (mass, charge and angular momentum). Furthermore, it was shown that energy can be extracted from stationary black holes that are rotating or charged (Hawking effect). But it was the discovery of a mathematical analogy between black holes and ordinary thermodynamics the biggest advance these investigations (Bardeen et al, $1973$). In this analogy the mass plays the role of energy and surface gravity of the black hole plays the role of temperature and the area of ​​the horizon entropy. The analogy between black holes and thermodynamics can be extended beyond the formal, mathematical similarity can be found in the fact that quantities of pairs of analogues are indeed physically similar. According to general relativity the total mass of the black hole has the same amount of their total energy. This analogy is broken in the Classical Theory, which considers the temperature of a black hole equal to the absolute zero

• Entropy : Entropy is a measure that characterizes the number of internal states of a black hole. The formula for the entropy was developed in 1974 by British physicist Stephen Hawking.

$S= \frac{Akc}{4\hbar G}$

Caption :

$S$ : Entropy

$A$ : Area

$k$ : Boltzmann constant

$\hbar$ : Planck constant normalized

$G$ : Universal Gravitational Constant Newton

$c$ : speed of light in vacuum

This equation could be formulated taking into account the quantum theory. So, it is believed that black holes emit thermal radiation:

$T= \frac{\hbar k}{2 \pi kb}$

In the special case of the Schwarzschild metric:

$T= \frac{\hbar}{8 \pi GkM}$

The formulation of Bekenstein-Hawking obtained from the combination between the law and the fact that $dM = TdS$. In the case of Schwarzschild hole, this formulation is:

$S= \frac{k \pi R^2}{g \hbar}$

Entropy of the black hole is much larger than the entropy of the star that collapsed to him to be generated

• Evaporating Black Hole

The main limitation of the Hawking effect is that it is based on approximations. This effect is not in accordance with the principle of conservation of energy, since the radiation energy of the black hole should be counterbalanced by the decrease of its mass, the same rate of energy output. However, for macroscopic black holes temperature is very low. The luminosity of the black hole is an estimate of the life of a non-rotating black hole integrating the equation:

~

Where $\beta$ is a dimensionless constant.

And the total evaporation process requires a lot of time:

~

$mp$ is the Planck mass, as follows: $0.000022 g$

"The radiation from the black hole originates from just beyond the event horizon. Virtual particle-antiparticles form from the Casimir effect. These particle-antiparticles pop in and out of existence. These particle-antiparticles require energy to form. The bigger the particle, the larger energy requirement. When the particle-antiparticles pop out of existence the balance is restored.There is this special experiment based to show this happens. Take $2$ perfectly smooth non-conducting plates and hold them next to each other with the distance of $1$ micron $(10^{-6}m)$ held in the vacuum of space. There would be particles (such as photons) popping in and out of existence both outside and inside the plate. The particles on the outside would have a larger variety of photons as compare to inside because there is more space for a larger wavelength. Sometimes though these particles hit the plates, creating pressure. There would be higher pressure from outside, resulting in the space between the plates shortening. This has actually been measured. Furthermore, there is this experiment called the Dynamic Casimir Effect. It is just like the experiment given except one of the plates has started accelerating up and back at a fraction of the speed of light. This gives energy to convert the virtual particles into real particles. You may think that this means that you got something new for no energy but that's not right. Since the plate was moving, it required work to move, which needs energy. Now, onto black holes. Some of these particle-antiparticles can spawn just beyond a black holes origin. Both of these particles becomes real but only one of them gets ejected from the system as radiation. The other one gets sucked into the black hole. You may think about where the energy came from to convert the virtual particle-antiparticles into real particles. This can be explained from the General Theory of Relativity's Principle of Equivalence. This principle basically states that gravity and acceleration are indistinguishable. Since a black hole has an immense gravitational field, it acts in the same way to the particle-antiparticles as acceleration did. But the energy from the gravitational field isn't given here. This energy itself comes from the black hole itself. Since some of these real particles get sucked, something must be displaced for the energy. The black hole's mass. Hence how black holes evaporate." - By Sharky Kesa

• Information in Black Hole

There with the purpose of training and subsequent evaporation of the black hole a dramatic consequence: the loss of information. This issue was raised in 1976 by Stephen Hawking. It is understood that in a refined sense quantum information would be lost, which then challenge Primeria Law of Thermodynamics. The discussion was easy and persuasive and based on only tool available at the time: quantum field theory. Despite the conclusion of Hawking certainly be wrong, set in motion old ideas that have long remained stops, challenging them with a new paradigm. Quantum theory presents a serious problem when describing systems with horizons. It provides an infinite entropy density of a black hole, different from the Bekenstein-Hawking density : $\frac{c^3}{4G \hbar}$

A final opportunity to establish a logical way out of this problem the possibility of black holes was proposed not evaporate completely. Instead, live remaining stable way Planck mass that contains all the information lost. Obviously these remnants should contain a huge, perhaps infinite entropy.

~

A simulation of gravitational lensing by a black hole, distorting the background image of the Milky Way

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