Information entropy for static spherically symmetric black holes

By using the new equation of state density derived from the generalized uncertainty relation, the number of the quantum states near event horizon is obtained, with which then the information entropy of static spherically symmetric black holes has been discussed. It is found that the divergent integral of quantum states near the event horizon can be naturally avoided if using the new equation of state density without introducing the ultraviolet cut-off. The information entropy of black holes can be obtained precisely by the residue theorem, which is shown to be proportional to the horizon area. The information entropy of black holes obtained agrees with the Bechenstein-Hawking entropy when the suitable cutoff factor is adopted.

Geometric Aspects of Extremal Kerr Black Hole Entropy

Extreme Black Holes is an important theoretical laboratory for exploring the nature of entropy. We suggest that this unusual nature of the extremal limit could explain the entropy of extremal Kerr black holes. The time-independence of the extremal black hole, the zero surface gravity, the zero entropy and the absence of a bifurcate Killing horizon are all related properties that define and reduce to one single unique feature of the extremal Kerr spacetime. We suggest the presence of a true geometric discontinuity as the underlying cause of a vanishing entropy.

Entropy of Causal Horizons

We analyze spacetimes with horizons and study the thermodynamic aspects of causal horizons, suggesting that the resemblance between gravitational and thermodynamic systems has a deeper quantum mechanical origin. We find that the observer dependence of such horizons is a direct consequence of associating a temperature and entropy to a spacetime. The geometrical picture of a horizon acting as a one-way membrane for information flow can be accepted as a natural interpretation of assigning a quantum field theory to a spacetime with boundary, ultimately leading to a close connection with thermodynamics.

Generalized Newton’s Theory of Universal Gravitation and Black Holes

The Newton’s theory of universal gravitation is generalized. Significantly strong at short distances central interaction of bodies and particles is established in comparison with Newtonian. A connection is found with Black Holes, with the horizon of events. Possibility of systematization of all Black Holes is shown. An illustration is given on the example of Black Hole SgrA*.

Entanglement Entropy of Reissner–Nordstrm Black Hole and Quantum Isolated Horizon

Based on the work of Ghosh and Pereze, who view the black hole entropy as the logarithm of the number of quantum states on the Quantum Isolated Horizon(QIH)§ the entropy of Reissner–Nordstr¨om black hole is studied.According to the Unruh temperature, the statistical entropy of quantum fields under the background of Reissner–Nordstr¨om spacetime is calculated by means of quantum statistics. In the calculations we take the integral from the position of QIH to infinity, so the obtained entropy is the entanglement entropy outside the QIH. In Reissner–Nordstr¨om spacetime it is shown that if only the position of QIH is properly chosen the leading term of logarithm of the number of quantum states on the QIH is equal to the leading term of the entanglement entropy outside the black hole horizon, and both are the Bekenstein–Hawking entropy. The results reveal the relation between the entanglement entropy of black hole and the logarithm of the number of quantum states.

The information entropy of a static dilaton black hole

In accordance with holographic principle, by calculating the statistical entropy of the quantum field just at the event horizon of the Garfinkle-Horowitz-Strominger dilaton black hole, the information entropy of the black hole was investigated and the Bekenstein-Hawking formula was obtained. The results show that black hole entropy is identical with the statistical entropy of the quantum field at the horizon. Using the generalized uncertainty relation, the divergence of the state density near the event horizon in usual quantum field theory was removed, and the cutoffs and the little mass approximation in the heat gas method of black hole entropy were avoided. Thus, the microstates of the massive scalar field just at the event horizon of the static dilaton black hole were studied directly and a description on holograph principle was presented. By using residue theorem, the integral difficulty in the calculation was overcome, and the information entropy and the Bekenstein-Hawking formula were obtained quantitatively. Compared with the black hole entropy from the loop quantum gravity, the consistency of methods and results of calculating black hole entropy in non-commutative quantum field theory and loop quantum gravity was investigated. By this, the gravity correction constant in the generalized uncertainty relation was suggested and the sense of holographic principle was discussed.

Identifying the Spatial Structure of Black Hole and Tropical Cyclone Based on a Theoretical Analysis of Orthogonal Interaction

Black holes are recognized by Newton’s gravitational theory and Einstein’s general relativity, but there is still a lack of understanding the spatial structure of events, especially the nature of event horizon. In this paper, a theoretical analysis is used to compare the structures of tropical cyclone in the atmosphere and black hole in the astronomy so that five results are: 1) Both of them share the similar spatial structure, with tropical cyclone and black hole having the outflow cloud shield and the horizon sphere in the central part, respectively, while four spiral material bands exist in the rotating plane around them;2) In theoretically, the energy density formed by the orthogonal interaction of the four spiral material bands is as times as the total kinetic energy of the head-on interaction;3) This region of high energy density can lead to the conversion from mass to energy and the creation of new physical states of matter, which is a black hole event;4) The outer horizon of a black hole is the outermost interface of events, or the orthogonal interaction interface of particles;5) High-speed plasma jets extended at the poles of the black hole are directly associated with the shear stress of orthogonal interaction.

The quantum nonthermal radiation and horizon surface gravity of an arbitrarily accelerating black hole with electric charge and magnetic charge

Using a new tortoise coordinate transformation,we discuss the quantum nonthermal radiation characteristics near an event horizon by studying the Hamilton-Jacobi equation of a scalar particle in curved space-time,and obtain the event horizon surface gravity and the Hawking temperature on that event horizon.The results show that there is a crossing of particle energy near the event horizon.We derive the maximum overlap of the positive and negative energy levels.It is also found that the Hawking temperature of a black hole depends not only on the time,but also on the angle.There is a problem of dimension in the usual tortoise coordinate,so the present results obtained by using a correct-dimension new tortoise coordinate transformation may be more reasonable.

Hawking radiation from the charged and magnetized BTZ black hole via covariant anomaly

This paper discusses Hawking radiation from the charged and magnetized Bafiados-Teitelboim-Zanelli （BTZ） black hole from the viewpoint of anomaly, initiated by Robinson and Wilczek recently. It reconstructs the electromagnetic field tensor and the Lagrangian of the field corresponding to the source with electric and magnetic charges to redefine an equivalent charge and gauge potential. It employs the covariant anomaly cancellation method to determine the compensating fluxes of charge flow and energy-momentum tensor, which are shown to match with those of the 2- dimensional blackbody radiation at the Hawking temperature exactly.

Redefining the Event Horizon

Presented herein is a new and independent derivation of equation for the radius of Black Holes, i.e. the event horizon of black holes. The equation has been derived by formulating the relativistic equation of escape velocity derived from the relativistic equations for gravitational potential and kinetic energy. Based upon that, it is now shown that the actual size of a black hole, as determined by its event horizon, is exactly half the value predicted by the escape velocity equation used in the Newtonian mechanics. It proves that the actual radius of a black hole is exactly one half of the Schwarzschild radius.

Growing a Kerr Black Hole

Growth of a black hole requires the participation of a near-by accretion disk if it is to occur at a significant rate. The Kerr solution of Einstein’s equation is a vacuum solution, but the center of a realistic Kerr black hole is not a vacuum, so the predicted disk singularity does not exist. Instead, the center of a black hole is occupied by an ultra-dense, spheroidal core whose diameter is greater than that of the theoretical disk singularity. The surface of a black hole’s core is continually bombarded by energetic particles from the external universe. Hence the cold remnant of a gravitationally-collapsed star that has often been assumed to be present at the center of a black hole must be replaced conceptually by a quark-gluon plasma whose temperature is of the order of 1012 K or more. The gravitational potential well of a black hole is extremely deep (TeV), but the number of discrete energy levels below the infinite-red-shift surface is finite. Information can be conveyed to observers in the external universe by thermally-excited fermions that escape from levels near the top of a black hole potential well.

What Connects Dark Matter and Black Holes?

Dark matter is a major component of the universe, about six times more abundant than ordinary visible matter. We measure the effects of its mass, but it escapes the telescopes. It has the particularity of emitting no radiation and interacting only by the action of gravity. The main purpose of this article is to try to answer what dark matter is: we conjecture that it is composed of magnetically charged neutrinos, true magnetic monopoles. But that requires a huge conceptual leap: Maxwell’s laws must be inverted and the electric charge becomes a magnetic charge. Asymmetric “reversed” Maxwell’s laws would provide the “dark” magnetic charge that would replace the electric charge. The very form of the Dirac equation, which imposed on ordinary matter that the particle carries an electric charge and obeys the principal properties of the electron, would impose in the dark matter that the “dark” particle obeys the main properties of a neutrino associated with a magnetic charge. The second aim of the article is to show that dark matter is derived from black holes, mainly from active supermassive black holes. This requires a second conceptual leap: the horizon of the black hole undergoes a high temperature and an intense pressure of magnetic fields which cause a blackout and a phase transition (or broken symmetry) when the matter crosses the horizon. The result is a reversal of Maxwell’s laws: a magnetic charge is substituted for the electric charge, and the electric current becomes a tributary of the magnetic current. A third important conceptual leap follows: sterile magnetic neutrinos created inside the black hole would cross the horizon to the outside to constitute dark matter.

Absolute Zero Occurs in Black Holes

The black hole is a region in space in which nothing can escape its pull. The two important parts of the anatomy of a stable black hole are the event horizon and gravitational singularity. The main discussion is regarding the temperature of a black hole. Absolute zero is a state which enthalpy and entropy is zero. The temperature of a black hole approaches the gravitational singularity in which space-time possibly ceases and entropy is zero producing absolute zero or possible sub- absolute zero.

The Correct Reissner-Nordstrøm, Kerr and Kerr-Newman Metrics

In a very recent article of mine I have corrected the traditional derivation of the Schwarzschild metric thus arriving to formulate a correct Schwarzschild metric different from the traditional Schwarzschild metric. In this article, starting from this correct Schwarzschild metric, I also propose corrections to the other traditional Reissner-Nordstrøm, Kerr and Kerr-Newman metrics on the basis of the fact that these metrics should be equal to the correct Schwarzschild metric in the borderline case in which they reduce to the case described by this metric. In this way, we see that, like the correct Schwarzschild metric, also the correct Reissner-Nordstrøm, Kerr and Kerr-Newman metrics do not present any event horizon (and therefore do not present any black hole) unlike the traditional Reissner-Nordstrøm, Kerr and Kerr-Newman metrics.

The Solution of the Einstein’s Equations in the Vacuum Region Surrounding a Spherically Symmetric Mass Distribution

In this article, we address the solution of the Einstein’s equations in the vacuum region surrounding a spherically symmetric mass distribution. There are two different types of mathematical solutions, depending on the value of a constant of integration. These two types of solutions are analysed from a physical point of view. The comparison with the linear theory limit is also considered. This leads to a new solution, different from the well known one. If one considers the observational data in the weak field limit this new solution is in agreement with the available data. While the traditional Schwarzschild solution is characterized by a horizon at r=2GM/c2, no horizon exists in this new solution.

The Unified Field

This is a Unified Field description based on the holographic Time Dilation Cosmology, TDC, model, which is an eternal continuum evolving forward in the forward direction of time, at the speed of light, c, at an invariant 1 s/s rate of time. This is the Fundamental Direction of Evolution, FDE. There is also an evolution down time dilation gradients, the Gravitational Direction of Evolution, GDE. These evolutions are gravity, which is the evolutionary force in time. Gravitational velocities are compensation for the difference in the rate of time, dRt, in a dilation field, and the dRtis equal to the compensatory velocity’s percentage of c, and is a measure of the force in time inducing the velocity. In applied force induced velocities, the dRt is a measure of the resistance in time to the induced velocity, which might be called “anti-gravity” or “negative gravity”. The two effects keep the continuum uniformly evolving forward at c. It is demonstrated that gravity is already a part of the electromagnetic field equations in way of the dRt element contained in the TDC velocity formula. Einstein’s energy formula is defined as a velocity formula and a modified version is used for charged elementary particle solutions. A time dilation-based derivation of the Lorentz force ties gravity directly to the electromagnetic field proving the unified field of gravity and the EMF. It is noted how we could possibly create gravity drives. This is followed by a discussion of black holes, proving supermassive objects, like massive black hole singularities, are impossible, and that black holes are massless Magnetospheric Eternally Collapsing Objects (MECOs) that are vortices in spacetime. .

<i>D’addio</i>to Blackness

It is assumed here that the energy of a strong gravitational field creates non-linear effects over enclosed masses. This idea and the rigorous rules of the General Theory of Relativity output a metric that covers strong and weak gravitational fields. The proposed metric could be correct because it included the Schwarzschild’s metric as a particular case and has no singularities. Additionally, it appears here that the massive condition of the gravitational fields has properties like the so-called Dark Matter.

四维Einstein-Gauss-Bonnet引力时空中非线性电磁场对光线偏折的影响

文章研究了含非线性电磁场的四维爱因斯坦-高斯-博内引力时空中的弱引力透镜现象。首先应用高斯-博内定理计算了含非线性电磁场的四维爱因斯坦-高斯-博内引力中的确切带电黑洞解得时空中光线的弱偏转角,并讨论了高斯-博内参数和非线性参数对偏转角的影响。此外,还利用类光测地线法计算了该黑洞的阴影半径。利用来自于事件视界望远镜的M87*黑洞观测数据限制了高斯-博内参数和磁荷,并讨论了非线性参数对观测值的影响。

Three kinds of horizon-like hypersurface of a uniformly accelerating, non-stationary charged black hole

Three kinds of horizon like hypersurface of a uniformly rectilinearly accelerating, non stationary charged black hole: event horizon, apparent horizon and time like limit surface are studied. The result is that the event horizon is apart from the time like limit surface and the apparent horizon in the case where the black hole is charged, uniformly accelerating and its mass is varying (evaporating and accreting). Some other new results are also given.