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Register a new userA Simple Determination of the Thermodynamical Characteristics of the Weakly Charged, Very Thin Black Ring
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In our previous work we suggested a very simple, approximate formalism for description of some basic (especially thermodynamical) characteristics of a non-charged, rotating, very thin black ring. Here, in our new work, generalizing our previous results, we suggest a very simple, approximate description of some basic (especially thermodynamical) characteristics of a weakly charged, rotating, very thin black ring. (Our formalism is not theoretically dubious, since, at it is not hard to see, it can represent an extreme simplification of a more accurate, e.g. Copeland-Lahiri, string formalism for the black hole description.) Even if suggested formalism is, generally speaking, phenomenological and rough, obtained final results, unexpectedly, are non-trivial. Concretely, given formalism reproduces exactly Bekenstein-Hawking entropy, Bekenstein quantization of the entropy or horizon area and Hawking temperature of a weakly charged, rotating, very thin black ring originally obtained earlier using more accurate analysis by Emparan, Aestefanesei, Radu etc. (Conceptually it is similar to situation in Bohrs atomic model where energy levels are determined practically exactly even if electron motion is described roughly.) Our formalism is physically based on the assumption that circumference of the horizon tube holds the natural (integer) number of corresponding reduced Comptons wave length. (It is conceptually similar to Bohrs quantization postulate in Bohrs atomic model interpreted by de Broglie relation.) Also, we use, mathematically, practically only simple algebraic equations.
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In this work we suggest a very simple, approximate formalism for description of some basic (especially thermodynamical) characteristics of a rotating, very thin black ring. (In fact, our formalism is not theoretically dubious, since, at it is not hard to see, it can correspond to an extreme simplification of a more accurate, Copeland-Lahiri string formalism for the black hole description.) Even if suggested formalism is, generally speaking, phenomenological and rough, obtained final results, unexpectedly, are non-trivial. Concretely, given formalism reproduces exactly Bekenstein-Hawking entropy, Bekenstein quantization of the entropy or horizon area and Hawking temperature of a rotating, very thin black ring obtained earlier using more accurate analysis by Reall, Emparan, Elvang, Virmani etc. (Conceptually it is similar to situation in Bohrs atomic model where energy levels are determined practically exactly even if electron motion is described roughly.) Our formalism, according to suggestions in our previous works, is physically based on the assumption that circumference of the horizon tube holds the natural (integer) number of corresponding reduced Comptons wave length. (It is conceptually similar to Bohrs quantization postulate in Bohrs atomic model interpreted by de Broglie relation.) Also, we use, mathematically, practically only simple algebraic equations (by determination of Hawking temperature we use additionally only simple differentiation of Smarr relation).
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.)
In this work, starting by simple, approximate (quasi-classical) methods presented in our previous works, we reproduce effectively and generalize final results of Herdeiro and Rebelo on the basic thermodynamical characteristics (entropy and temperature) of two interacting Kerr black holes (in touching limit) obtained recently by accurate analysis. Like as it has been done in our previous works, we simply suppose that circumference of the horizon of total black hole (that includes two or, generally, a crystal lattice of many interacting Kerr black holes in touching limit, without angular momentum) holds integer number of reduced Compton wave lengths corresponding to mass spectrum of a small quantum system captured at horizon. (Obviously it is conceptually analogous to Bohr quantization postulate interpreted by de Broglie relation in Old, Bohr-Sommerfeld, quantum theory.) It, by simple mathematical methods, first neighbour approximation of the black holes interaction and first thermodynamical law, implies mentioned basic thermodinamical characteristic of the total black hole as well as any its part, i.e. single black hole. Especially, it is shown that, in limit of increasing number of the black holes, entropy and horizon surface of the total black hole stand observables of the discrete spectrum while entropy and horizon surface of the single black hole tends toward observables of the continuous spectrum.
We study the motion of a charged particle around a weakly magnetized rotating black hole. We classify the fate of a charged particle kicked out from the innermost stable circular orbit. We find that the final fate of the charged particle depends mostly on the energy of the particle and the radius of the orbit. The energy and the radius in turn depend on the initial velocity, the black hole spin, and the magnitude of the magnetic field. We also find possible evidence for the existence of bound motion in the vicinity of the equatorial plane.
In this work, starting by simple, approximate (quasi-classical) methods presented in our previous works, we suggest a simple determination of the (logarithmic) corrections of (Schwarzschild) black hole entropy without knowing the details of quantum gravity(Fursaev). Namely, in our previous works we demonstrated that all well-known important thermodynamical characteristics of the black hole (Bekenstein-Hawking entropy, Bekenstein entropy/surface quantization and Hawking temperature) can be effectively reproduced starting by simple supposition that black hole horizon circumference holds integer number of reduced Compton wave lengths corresponding to mass (energy) spectrum of a small quantum system. (Obviously it is conceptually analogous to Bohr quantization postulate interpreted by de Broglie relation in Old, Bohr-Sommerfeld, quantum theory.) Especially, black hole entropy can be presented as the quotient of the black hole mass and the minimal mass of small quantum system in ground mass (energy) state. Now, we suppose that black hole mass correction is simply equivalent to negative classical potential energy of the gravitational interaction between black hole and small quantum system in ground mass (energy) state. As it is not hard to see absolute value of the classical potential energy of gravitational interaction is identical to black hole temperature. All this, according to first thermodynamical law, implies that first order entropy correction holds form of the logarithm of the surface with coefficient -0.5. Our result, obtained practically quasi-classically, without knowing the details of quantum gravity, is equivalent to result obtained by loop quantum gravity and other quantum gravity methods for macroscopic black holes.
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