Comment on `The Stefan-Boltzmann constant in<b><i>n</i></b>-dimensional space'

Menon, V. J.; Agrawal, D. C.

doi:10.1088/0305-4470/31/3/021

Cited by 18 publications

(92 citation statements)

References 1 publication

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…There are many pdf's, and corresponding cumulative probability distribution functions (cdf's), which will satisfy Equations, (2)(3)(4)(5)(6)(7)(8), (2)(3)(4)(5)(6)(7)(8)(9), and, (2)(3)(4)(5)(6)(7)(8)(9)(10) In Equation, (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14), the quantity, , which is model dependent, i.e., specifically depends of the pdf chosen. We will soon derive an expression for it, and we will notice that it will depend on radius.…”

Section: Pilot Journal Of High Energy Physics Gravitation and Cosmentioning

confidence: 99%

On the Internal Structure of a Black Hole Utilizing a 4-D Spatial Blackbody Radiation Model

Pilot¹

2019

JHEPGC

View full text Add to dashboard Cite

A black hole is treated as a self-contained, steady state, spherically symmetric, 4-dimensional spatial ball filled with blackbody radiation, which is embedded in 3-D space. To model the interior distribution of radiation, we invoke two stellar-like equations, generalized to 4-D space, and a probability distribution function (pdf) for the actual radiative mass distribution within its interior. For our purposes, we choose a truncated Gaussian distribution, although other pdf's with support, ( ), s x γ , and interestingly, scales with a more complicated function of radius.Thus, within our framework, the black hole is a highly-ordered state, in sharp 2 0.1 R M c . This factor of 0.1 is specific to 4-D space. Keywords Black Hole, 4-D Spatial Blackbody Radiation Model, Internal Structure, Radiative Pressure * g T . See references [1] [2] [3] [4]. The black hole, being defined as a steady state ball of radiation in 4-D space, is embedded in 3-D space, much like a gas bubble within a liquid, or, a liquid droplet within a gas. However, the droplet is 4-dimensional, and, as we shall see, not of uniform density. There are three central issues regarding black holes for which we seek an answer. First, what is the nature of the event horizon? Second, what does the internal structure of a black hole look like? And third, can we calculate key thermodynamic variables within the black hole itself? As examples of ther-modynamic quantities, what are the radiative pressure, the internal energy density, the total (radiative mass) energy density, the entropy density, and the gravitational strength within the black hole as functions of, r, the 4-D radius? In the C. Pilot first paper [5], we focused on giving an answer to the first question. In this paper, we will address questions two, and three.In a previous work [5], we presented a model to answer question one. We argued that the event horizon can be thought of as a membrane, where we have a discontinuity in space, which separates the 4-D black hole from the surrounding 3-D space. Access from one space to the other is through the event horizon, which acts as flexible membrane, and which allows for zero or net radiative heat inflow, but no net outflow. The event horizon was assumed to be infinitely thin.The temperature, 1 T , just inside the event horizon in 4-D space is given strictly in terms of the black hole mass, or radius. If the temperature just outside, 2 T , equals 2.725 K, then we will assume that there is no inflow. For higher temperatures, where, 2 2.725 K T > , we will assume net inflow. The amount of radiative heat inflow, d d Q t , depends on the temperature 2 T , as well as on the size, or mass, of the black hole. It can be determined using a generalized version of the Stefan-Boltzmann equation, derived in reference [5], to take into account radiative transfers between adjoining spatial dimensions. With or without net inflow of radiative heat energy, we saw that the temperature drops precipitously upon entering the black hole. This is due to the change in the dimension...

show abstract

Section: Pilot Journal Of High Energy Physics Gravitation and Cosmentioning

confidence: 99%

On the Internal Structure of a Black Hole Utilizing a 4-D Spatial Blackbody Radiation Model

Pilot¹

2019

JHEPGC

View full text Add to dashboard Cite

show abstract

“…For a black body in an n-dimensional space, it is known [9,20,23,[32][33][34] that the distribution of modes in the interval ν to ν + dν is,…”

Section: Generalization To N Dimensionsmentioning

confidence: 99%

“…Since the works by Kaluza and Klein [7,8], many proposals about the universe's models with dimensionality different from three have been published [7,8,18,20,22,23,[32][33][34][43][44][45]. Remarkably, this has been the case for papers stemming from string, D−branes (where D is for dimensionality) and gauge theories [10][11][12][13][14]17,22].…”

Section: A Possible Simple Application To Cosmologymentioning

confidence: 99%

A Possible Cosmological Application of Some Thermodynamic Properties of the Black Body Radiation in n-Dimensional Euclidean Spaces

González-Ayala

Pérez-Oregon

Cordero

et al. 2015

Entropy

View full text Add to dashboard Cite

In this work, we present the generalization of some thermodynamic properties of the black body radiation (BBR) towards an n-dimensional Euclidean space. For this case, the Planck function and the Stefan-Boltzmann law have already been given by Landsberg and de Vos and some adjustments by Menon and Agrawal. However, since then, not much more has been done on this subject, and we believe there are some relevant aspects yet to explore. In addition to the results previously found, we calculate the thermodynamic potentials, the efficiency of the Carnot engine, the law for adiabatic processes and the heat capacity at constant volume. There is a region at which an interesting behavior of the thermodynamic potentials arises: maxima and minima appear for the n-dimensional BBR system at very high temperatures and low dimensionality, suggesting a possible application to cosmology. Finally, we propose that an optimality criterion in a thermodynamic framework could be related to the 3-dimensional nature of the universe.

show abstract

“…The n-dimensional magnetic field can be defined as the antisymmetrization of ∇A, with ∇ denoting the n-dimensional gradient operator, i.e. [5]…”

Section: Linear Gauge and Equations Of Motion In General Formmentioning

confidence: 99%

“…Another important series of papers was started by independent, but very closely related, works of Brown [3] and Zak [4] concerning a Bloch electron in a magnetic field. This paper is inspired by a comment of Menon and Agrawal [5] in which the n-dimensional magnetic field was determined. We consider a general form of the ndimensional vector potential A determining a constant and uniform magnetic field H. The equations of motion, analogous to those given by Johnson and Lipmann [2], are obtained and they lead to decomposition of the coordinates into two parts corresponding to the cyclotron and free movements, respectively.…”

Section: Introductionmentioning

confidence: 99%

Equations of Motion for a Charged Particle in n-Dimensional Magnetic Field

Florek

Thomas

2000

Acta Phys. Pol. A

View full text Add to dashboard Cite

The equation of motion for a charged particle moving in the n-dimensional constant magnetic field is obtained for any linear gauge and any metric tensor by generalization of Johnson and Lipmann's approach. It allows to consider the magnetic orbits in the n-dimensional space. It is shown that the movement of a particle can always be decomposed into a number of two-dimensional cyclotronic motions and a free particle part.

show abstract

Comment on `The Stefan-Boltzmann constant inn-dimensional space'

Cited by 18 publications

References 1 publication

On the Internal Structure of a Black Hole Utilizing a 4-D Spatial Blackbody Radiation Model

On the Internal Structure of a Black Hole Utilizing a 4-D Spatial Blackbody Radiation Model

A Possible Cosmological Application of Some Thermodynamic Properties of the Black Body Radiation in n-Dimensional Euclidean Spaces

Equations of Motion for a Charged Particle in n-Dimensional Magnetic Field

Contact Info

Product

Resources

About