scholarly journals Entropy of Reissner–Nordström 3D Black Hole in Roegenian Economics

Entropy ◽  
2019 ◽  
Vol 21 (5) ◽  
pp. 509
Author(s):  
Constantin Udriste ◽  
Massimiliano Ferrara ◽  
Ionel Tevy ◽  
Dorel Zugravescu ◽  
Florin Munteanu
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
National Income ◽  
Political Stability ◽  
Rindler Coordinates ◽  
Total Investment ◽  
The Subject ◽  
3D Black Hole

The subject of this paper is to analyse the Mathematical Principia of Economic 3D Black Holes in Roegenian economics. In detail, we study two main problems: (i) mathematical origin of economic 3D black holes; and (ii) entropy and internal political stability depending on national income and the total investment, for economic Reissner–Nordström (RN) 3D black hole. To solve these problems, it was necessary to jump from macroeconomic side to microeconomic side (a substantial approach as they are so different), to complete the thermodynamics–economics dictionary with new entities, and to introduce the flow between two macroeconomic systems. The main contribution is about introducing and studying the Schwarzschild-type metric on an economic 4D system, together with Rindler coordinates, Einstein 4D partial differential equations (PDEs), and economic RN 3D black holes. In addition, we introduce some economic Ricci type flows or waves, for further research.

scholarly journals Entropy of Reissner-Nordström 3D Hole in Roegenian Economics

2019 ◽  
Author(s):  
Constantin Udriste ◽  
Massimiliano Ferrara ◽  
Ionel Tevy ◽  
Dorel Zugravescu ◽  
Florin Munteanu
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
National Income ◽  
Political Stability ◽  
Related Literature ◽  
Metric Properties ◽  
Rindler Coordinates ◽  
Total Investment ◽  
The Subject ◽  
3D Black Hole

The subject of this paper is to analyse the Math Principia of Economic 3D Black Holes in Roegenian economics. This idea is totally new in the related literature, excepting our papers. In details, we study two special problems: (i) math origin of economic 3D black holes, (ii) entropy and internal political stability depending on national income and the total investment, for economic RN 3D black hole. To solve these problems, it was necessary to jump from macroeconomic side to microeconomic side (a substantial approach so different), to complete the thermodynamics-economics dictionary with new entities, to introduce the flow between two macroeconomic systems, to study the Schwarzschild type metric properties on an economic 4D system, together with Rindler coordinates, Einstein 4D PDEs, and economic RN 3D black hole. In addition, we introduce some economic Ricci type flows or waves, for further research.

Probability

1936 ◽  
Vol 29 (7) ◽  
pp. 319-329
Author(s):  
Albert A. Bennett
Keyword(s):  
Monte Carlo ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Old Age ◽  
Life Insurance ◽  
First Principles ◽  
Mathematical Physics ◽  
Quadratic Equation ◽  
Education Economics ◽  
The Subject

The subject of probability reminds one of that Australian curiosity enjoying the orotund and circus-stirring name of “ornithorhyncus Paradoxus or duck-billed Platypus”—is it fish or fowl or beast?” Like the sacred cod of Boston this strange animal lives in the water; like the royal swans of his Britannic majesty, it has a flat bill, web-feet, and lays white shell-encased eggs; like the tiger of Kipling's Jungle Tales it has soft fur and suckles its young. And beside all this the male has spurs like a rooster. In a somewhat analogous way, probability, like the quadratic equation, or the removal of parentheses, is a subject in textbooks on algebra. Along with partial differential equations it is one of the advanced topics in mathematical physics. In connection with statistics it comes under education, economics, psychology, biology, or mathematics. It is studied in the theory of manufacturing practice, and in describing the operation of genetic inheritance. It proves absorbing to the dissolute gambler, while the philosopher treats it as an abstruse item of theoretical logic. It is invoked in casual comments about the weather, explained in treatises on practical surveying, and constitutes one of the first principles in the rational discussion of old age pensions, and of business cyles. Is it not strange that to explain how heat causes water to boil, one may well consider first the effect of tossing coins? Where else in algebra is any such economic prudence as that of life insurance brought home to the student, and where else is he asked to contemplate games of dice, gambling at Monte Carlo, and luck in drawing cards for poker?

Geometry of Black Holes

2020 ◽  
Author(s):  
Piotr T. Chruściel
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Einstein Equations ◽  
De Sitter ◽  
Black Hole Spacetimes ◽  
Local Coordinates ◽  
The Subject ◽  
Basic Facts ◽  
Kaluza Klein

There exists a large scientific literature on black holes, including many excellent textbooks of various levels of difficulty. However, most of these prefer physical intuition to mathematical rigour. The object of this book is to fill this gap and present a detailed, mathematically oriented, extended introduction to the subject. The first part of the book starts with a presentation, in Chapter 1, of some basic facts about Lorentzian manifolds. Chapter 2 develops those elements of Lorentzian causality theory which are key to the understanding of black-hole spacetimes. We present some applications of the causality theory in Chapter 3, as relevant for the study of black holes. Chapter 4, which opens the second part of the book, constitutes an introduction to the theory of black holes, including a review of experimental evidence, a presentation of the basic notions, and a study of the flagship black holes: the Schwarzschild, Reissner–Nordström, Kerr, and Majumdar–Papapetrou solutions of the Einstein, or Einstein–Maxwell, equations. Chapter 5 presents some further important solutions: the Kerr–Newman–(anti-)de Sitter black holes, the Emperan–Reall black rings, the Kaluza–Klein solutions of Rasheed, and the Birmingham family of metrics. Chapters 6 and 7 present the construction of conformal and projective diagrams, which play a key role in understanding the global structure of spacetimes obtained by piecing together metrics which, initially, are expressed in local coordinates. Chapter 8 presents an overview of known dynamical black-hole solutions of the vacuum Einstein equations.

Black holes as QCD laboratories

2015 ◽  
Vol 24 (09) ◽  
pp. 1542017 ◽  
Author(s):  
Antonino Flachi
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Chiral Symmetry Breaking ◽  
Gap Effect ◽  
Precise Description ◽  
Black Hole Evaporation ◽  
Gravitational Fields ◽  
Quantitative Understanding ◽  
The Subject ◽  
Strong Gravitational Fields

A precise description of black hole evaporation requires a quantitative understanding of chiral symmetry breaking and confinement in the presence of strong gravitational fields. In this paper, we present a brief review of our recent work on the subject and explain our results in terms of the recently discussed chiral gap effect.

On the reality of Hawking radiation

2019 ◽  
Vol 28 (16) ◽  
pp. 2040001
Author(s):  
Asghar Qadir
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Quantum Theory ◽  
Hawking Radiation ◽  
Black Hole Thermodynamics ◽  
The Public ◽  
Roger Penrose ◽  
The Subject

Hawking radiation caught the imagination of the public and physicists alike, because it seemed so counter-intuitive. By their very definition, black holes were supposed to endlessly absorb, but never emit, matter and energy. Yet, Hawking argued that taking Quantum Theory into account, they would radiate. The further belief was that Bekenstein and Hawking had developed the field of Black Hole Thermodynamics. Here I want to correct this impression and give due credit to Roger Penrose for founding the subject. Further, I discuss the question of whether Hawking radiation should be expected to really exist, arguing that there is reason to doubt it.

On the calculus of symbols.—Fifth memoir. With application to linear partial differential equations, and the calculus of functions

1864 ◽  
Vol 13 ◽  
pp. 432-442
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Functional Equations ◽  
Partial Differential ◽  
Independent Variables ◽  
Partial Differentiation ◽  
Linear Partial Differential Equations ◽  
Constant Coefficients ◽  
Extensive Class ◽  
The Subject

In applying the calculus of symbols to partial differential equations, we find an extensive class with coefficients involving the independent variables which may in fact, like differential equations with constant coefficients, be solved by the rules which apply to ordinary algebraical equations; for there are certain functions of the symbols of partial differentiation which combine with certain functions of the independent variables according to the laws of combination of common algebraical quantities. In the first part of this memoir I have investigated the nature of these symbols, and applied them to the solution of partial differential equations. In the second part I have applied the calculus of symbols to the solution of functional equations. For this purpose I have given some cases of symbolical division on a modified type, so that the symbols may embrace a greater range. I have then shown how certain functional equations may be expressed in a symbolical form, and have solved them by methods analogous to those already explained. Since ( x d/dy - y d/dx ) ( x 2 + y 2 ) = 0, we shall have ( x d/dy - y d/dx ) ( x 2 + y 2 ) μ = ( x 2 + y 2 ) ( x d/dy - y d/dx ) u , or, omitting the subject, ( x d/dy - y d/dx ) ( x 2 + y 2 ) = ( x 2 + y 2 ) ( x d/dy - y d/dx ), also x d/dy - y d/dx + x 2 + y 2 = x 2 + y 2 + x d/dy - y d/dx ; therefore the symbols x d/dy - y d/dx and x 2 + y 2 combine according to the laws of ordinary algebraical symbols, and consequently partial differential equations, which can be put in a form involving these functions exclusively, an be solved like algebraical equations. We shall give some instances of this.

scholarly journals Growth and merging phenomena of black holes: observational, computational and theoretical efforts

2021 ◽  
pp. 56-74
Author(s):  
G. Ter-Kazarian
Keyword(s):  
Black Holes ◽  
General Relativity ◽  
Black Hole ◽  
Microscopic Theory ◽  
Considerable Change ◽  
Spontaneous Breaking ◽  
Nuclear Density ◽  
Self Consistent ◽  
The Subject ◽  
Time Continuum

We briefly review the observable signature and computational efforts of growth and merging phenomena of astrophysical black holes. We examine the meaning, and assess the validity of such properties within theoretical framework of the long-standing phenomenological model of black holes (PMBHs), being a peculiar repercussion of general relativity. We provide a discussion of some key objectives with the analysis aimed at clarifying the current situation of the subject. It is argued that such exotic hypothetical behaviors seem nowhere near true if one applies the PMBH. Refining our conviction that a complete, self-consistent gravitation theory will smear out singularities at huge energies, and give the solution known deep within the BH, we employ the microscopic theory of black hole (MTBH), which has explored the most important novel aspects expected from considerable change of properties of space-time continuum at spontaneous breaking of gravitation gauge symmetry far above nuclear density. It may shed further light upon the growth and merging phenomena of astrophysical BHs.

Construction of metric and vector potential perturbations of a Reissner–Nordström black hole

1979 ◽  
Vol 369 (1736) ◽  
pp. 67-81 ◽  
Keyword(s):  
Black Hole ◽  
Partial Differential Equations ◽  
Linear System ◽  
Differential Equations ◽  
Vector Potential ◽  
Maxwell Equations ◽  
Coupled System ◽  
System Of Equations ◽  
Partial Differential ◽  
Explicit Formulae

When an appropriate decoupling of variables in a coupled linear system of partial differential equations is obtained, a recently described procedure enables one to construct solutions to the full coupled system of equations. We employ this procedure here to generate solutions of the linearized Einstein–Maxwell equations describing perturbations of a Reissner–Nordström black hole, using Chandrasekhar’s recent decoupling of these equations. Explicit formulae are given for the metric and vector potential perturbations for each parity type.

scholarly journals Variability in Ultra-luminous X-ray Sources

2014 ◽  
Vol 31 ◽  
Author(s):  
N. A. Webb ◽  
D. Cseh ◽  
F. Kirsten
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
High Resolution ◽  
Temporal Variability ◽  
Intermediate Mass ◽  
X Ray ◽  
Open Questions ◽  
The Subject ◽  
State Changes ◽  
New Facilities

AbstractMany upcoming surveys, particularly in the radio and optical domains, are designed to probe either the temporal and/or the spatial variability of a range of astronomical objects. In the light of these high resolution surveys, we review the subject of ultra-luminous X-ray (ULX) sources, which are thought to be accreting black holes for the most part. We also discuss the sub-class of ULXs known as the hyper-luminous X-ray sources, which may be accreting intermediate mass black holes. We focus on some of the open questions that will be addressed with the new facilities, such as the mass of the black hole in ULXs, their temporal variability and the nature of the state changes, their surrounding nebulae, and the nature of the region in which ULXs reside.

XXII.—Integration of a Certain System of Linear Partial Differential Equations of Hypergeometric Type

1940 ◽  
Vol 59 ◽  
pp. 224-241 ◽  
Author(s):  
A. Erdélyi
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Singular Points ◽  
Partial Differential ◽  
Linear Partial Differential Equations ◽  
Power Series Expansions ◽  
Complete Set ◽  
Hypergeometric Type ◽  
The Subject ◽  
Singular Manifolds

1. The integration of systems of linear partial differential equations of hypergeometric type has been the subject of a great number of recent investigations (e.g. Appell, 1925; Appell-Kampé de Fériet, 1926). Especially Professor Horn (see references) and his pupils, for instance Borngässer (1933), have done much valuable work in this field.The first method that suggests itself for integrating systems of this type is to try power-series expansions of the solutions in the neighbourhood of the singular points of the system. This method, however, does not yield in general a complete set of solutions. Those singular points of the system in which more than n singular manifolds intersect, n being the number of independent variables, give rise to considerable difficulties.

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