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Register a new userGeneralized Laplace Method for Simple Determination of Kerr-Newman Black Hole Horizon Radius
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In this work we present a generalized Laplace method for a formal, simple, quasi-classical, determination of the outer and inner horizon radius of Kerr-Newman black hole. We consider classical gravitational interaction between a thin, with homogeneously distributed mass and electric charge, spherical (black) shell and a probe particle. Also, we use relativistic equivalence principle. Finally we suppose that probe particle propagates radially to shell with speed of light while tangentially it rotates in common with shell, so that total energy of a probe particle equals zero.
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In this work we present a simple, approximate method for analysis of the basic dynamical and thermodynamical characteristics of Kerr-Newman black hole. Instead of the complete dynamics of the black hole self-interaction we consider only such stable (stationary) dynamical situations determined by condition that black hole (outer) horizon circumference holds the integer number of the reduced Compton wave lengths corresponding to mass spectrum of a small quantum system (representing quant of the black hole self-interaction). Then, we show that Kerr-Newman black hole entropy represents simply the quotient of the sum of static part and rotation part of mass of black hole on the one hand and ground mass of small quantum system on the other hand. Also we show that Kerr-Newman black hole temperature represents the negative value of the classical potential energy of gravitational interaction between a part of black hole with reduced mass and small quantum system in the ground mass quantum state. Finally, we suggest a bosonic great canonical distribution of the statistical ensemble of given small quantum systems in the thermodynamical equilibrium with (macroscopic) black hole as thermal reservoir. We suggest that, practically, only ground mass quantum state is significantly degenerate while all other, excited mass quantum states are non-degenerate. Kerr-Newman black hole entropy is practically equivalent to the ground mass quantum state degeneration. Given statistical distribution admits a rough (qualitative) but simple modeling of Hawking radiation of the black hole too.
In this work, generalizing our previous results, we determine in an original and the simplest way three most important thermodynamical characteristics (Bekenstein-Hawking entropy, Bekenstein quantization of the entropy or (outer) horizon surface area and Hawking temperature) of Kerr-Newman black hole. We start physically by assumption that circumference of Kerr-Newman black hole (outer) horizon holds the natural (integer) number of corresponding reduced Comptons wave length and use mathematically, practically, only simple algebraic equations. (It is conceptually similar to Bohrs quantization postulate in Bohrs atomic model interpreted by de Broglie relation.)
This article explores the characteristics of ergoregion, horizons and circular geodesics around a Kerr-Newman-Kasuya black hole. We investigate the effect of spin and dyonic charge parameters on ergoregion, event horizon and static limit surface of the said black hole. We observed that both electric, as well as magnetic charge parameters, results in decreasing the radii of event horizon and static limit, whereas increasing the area of ergoregion. The obtained results are compared with that acquired from Kerr and Schwarzschild black holes. Moreover, we figured out the photons orbit of circular null geodesics and studied the angular velocity of a particle within ergoregion.
For the Schwarzschild black hole the Bekenstein-Hawking entropy is proportional to the area of the event horizon. For the black holes with two horizons the thermodynamics is not very clear, since the role of the inner horizons is not well established. Here we calculate the entropy of the Reissner-Nordstrom black hole and of the Kerr black hole, which have two horizons. For the spherically symmetric Reissner-Nordstrom black hole we used several different approaches. All of them give the same result for the entropy and for the corresponding temperature of the thermal Hawking radiation. The entropy is not determined by the area of the outer horizon, and it is not equal to the sum of the entropies of two horizons. It is determined by the correlations between the two horizons, due to which the total entropy of the black hole and the temperature of Hawking radiation depend only on mass $M$ of the black hole and do not depend on the black hole charge $Q$. For the Kerr and Kerr-Newman black holes it is shown that their entropy has the similar property: it depends only on mass $M$ of the black hole and does not depend on the angular momentum $J$ and charge $Q$.
We show that the Kerr-(Newman)-AdS$_4$ black hole will be shadowless if its rotation parameter is larger than a critical value $a_c$ which is not necessarily equal to the AdS radius. This is because the null hypersurface caustics (NHC) appears both inside the Cauchy horizon and outside the event horizon for the black hole with the rotation parameter beyond the critical value, and the NHC outside the event horizon scatters diffusely the light reaching it. Our studies also further confirm that whether an ultraspinning black hole is super-entropic or not is unrelated to the existence of the NHC outside the event horizon.
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