Exact solutions of general relativity derived from 5‐D ‘‘black hole’’ solutions of Kaluza–Klein theory

1992 ◽  
Vol 33 (11) ◽  
pp. 3888-3891 ◽  
Author(s):  
Hongya Liu ◽  
P. S. Wesson
Keyword(s):  
General Relativity ◽  
Black Hole ◽  
Exact Solutions ◽  
Klein Theory ◽  
Black Hole Solutions ◽  
Kaluza Klein

On the Correspondence between Exact Solutions in Kaluza–Klein Theory and in Scalar–Tensor Theories

1997 ◽  
Vol 12 (28) ◽  
pp. 2121-2132 ◽  
Author(s):  
Andrew Billyard ◽  
Alan Coley
Keyword(s):  
General Relativity ◽  
Exact Solutions ◽  
The Other ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Formal Equivalence ◽  
Higher Dimensional ◽  
Klein Theory ◽  
Dimensional Version ◽  
Kaluza Klein

Using the formal equivalences between Kaluza–Klein gravity, Brans–Dicke theory and general relativity coupled to a massless scalar field, exact solutions obtained in one theory will correspond to analogous solutions in the other two theories. Often exact solutions in one theory are "rediscovered" since theory are not recognized as analogs of the corresponding solutions in one of the other theories. We review here a number of exact solutions in each of the theories, with an emphasis on identifying and presenting the higher-dimensional version of the solutions. We also briefly comment upon the formal equivalence between Kaluza–Klein theory and scalar–tensor theories in general.

scholarly journals Constructing black hole solutions in supergravity theories

2019 ◽  
Vol 34 (35) ◽  
pp. 1930017 ◽  
Author(s):  
Antonio Gallerati
Keyword(s):  
Black Holes ◽  
General Relativity ◽  
Black Hole ◽  
Supergravity Models ◽  
Detailed Analysis ◽  
Black Hole Solution ◽  
Explicit Construction ◽  
General Introduction ◽  
Supersymmetric Theories ◽  
Black Hole Solutions

We perform a detailed analysis of black hole solutions in supergravity models. After a general introduction on black holes in general relativity and supersymmetric theories, we provide a detailed description of ungauged extended supergravities and their dualities. Therefore, we analyze the general form of black hole configurations for these models, their near-horizon behavior and characteristic of the solution. An explicit construction of a black hole solution with its physical implications is given for the STU-model. The second part of this review is dedicated to gauged supergravity theories. We describe a step-by-step gauging procedure involving the embedding tensor formalism to be used to obtain a gauged model starting from an ungauged one. Finally, we analyze general black hole solutions in gauged models, providing an explicit example for the [Formula: see text], [Formula: see text] case. A brief review on special geometry is also provided, with explicit results and relations for supersymmetric black hole solutions.

EXACT SOLUTIONS OF DILATON GRAVITY WITH (ANTI)-DE SITTER ASYMPTOTICS

2014 ◽  
Vol 29 (02) ◽  
pp. 1450010 ◽  
Author(s):  
S. MIGNEMI
Keyword(s):  
Black Hole ◽  
Exact Solutions ◽  
Maxwell Field ◽  
Spherically Symmetric ◽  
Dilaton Gravity ◽  
De Sitter ◽  
Asymptotically Flat ◽  
Black Hole Solutions

We present a technique for obtaining exact spherically symmetric asymptotically de Sitter (dS) or anti-de Sitter (adS) black hole solutions of dilaton gravity with generic coupling to Maxwell field, starting from asymptotically flat solutions and adding a suitable dilaton potential to the action.

scholarly journals A SLOWLY ROTATING CHARGED BLACK HOLE IN FIVE DIMENSIONS

2006 ◽  
Vol 21 (09) ◽  
pp. 751-757 ◽  
Author(s):  
A. N. ALIEV
Keyword(s):  
General Relativity ◽  
Black Hole ◽  
System Of Equations ◽  
Maxwell System ◽  
Five Dimensions ◽  
Four Dimensions ◽  
Higher Dimensional ◽  
Long Time ◽  
Electrically Charged ◽  
Black Hole Solutions

Black hole solutions in higher dimensional Einstein and Einstein–Maxwell gravity have been discussed by Tangherlini as well as Myers and Perry a long time ago. These solutions are the generalizations of the familiar Schwarzschild, Reissner–Nordström and Kerr solutions of four-dimensional general relativity. However, higher dimensional generalization of the Kerr–Newman solution in four dimensions has not been found yet. As a first step in this direction we shall report on a new solution of the Einstein–Maxwell system of equations that describes an electrically charged and slowly rotating black hole in five dimensions.

scholarly journals ON GENERATING SOME KNOWN BLACK HOLE SOLUTIONS

2010 ◽  
Vol 25 (10) ◽  
pp. 835-842 ◽  
Author(s):  
F. RAHAMAN ◽  
MUBASHER JAMIL ◽  
A. GHOSH ◽  
K. CHAKRABORTY
Keyword(s):  
General Relativity ◽  
Black Hole ◽  
Alternative Theories Of Gravity ◽  
Dimensional Parameters ◽  
Theories Of Gravity ◽  
Alternative Theories ◽  
Black Hole Solutions

In this paper, we have presented an algorithm to generate various black hole solutions in general relativity and alternative theories of gravity. The algorithm involves few dimensional parameters that are assigned suitable values to specify the required black hole.

scholarly journals BOSONIC STRING — KALUZA–KLEIN THEORY EXACT SOLUTIONS USING 5D–6D DUALITIES

2001 ◽  
Vol 16 (01) ◽  
pp. 29-39 ◽  
Author(s):  
ALFREDO HERRERA-AGUILAR ◽  
OLEG V. KECHKIN
Keyword(s):  
String Theory ◽  
General Solution ◽  
Exact Solutions ◽  
Bosonic String ◽  
Extremal Solutions ◽  
Explicit Formulas ◽  
New Family ◽  
Klein Theory ◽  
Bosonic String Theory ◽  
Kaluza Klein

We present explicit formulas which allow one to transform a general solution of the 6D Kaluza–Klein theory compactified on a three-torus into a special solution of the 6D bosonic string theory compactified on a three-torus, as well as into the general solution of the 5D bosonic string theory compactified on a two-torus. We construct a new family of extremal solutions of the 3D chiral equation for the SL(4, R)/SO(4) coset matrix and interpret it in terms of the component fields of these three duality related theories.

scholarly journals Unification of the Maxwell-Einstein-Dirac Correspondence

2019 ◽  
Author(s):  
Wim Vegt
Keyword(s):  
Field Theory ◽  
General Relativity ◽  
String Theory ◽  
Dimensional Space ◽  
Space Time ◽  
Unified Field ◽  
S Matrix ◽  
Klein Theory ◽  
Dimensional Space Time ◽  
Kaluza Klein

Albert Einstein, Lorentz and Minkowski published in 1905 the Theory of Special Relativity and Einstein published in 1915 his field theory of general relativity based on a curved 4-dimensional space-time continuum to integrate the gravitational field and the electromagnetic field in one unified field. Since then the method of Einstein’s unifying field theory has been developed by many others in more than 4 dimensions resulting finally in the well-known 10-dimensional and 11-dimensional “string theory”. String theory is an outgrowth of S-matrix theory, a research program begun by Werner Heisenberg in 1943 (following John Archibald Wheeler‘s(3) 1937 introduction of the S-matrix), picked up and advocated by many prominent theorists starting in the late 1950’s.Theodor Franz Eduard Kaluza (1885-1954), was a German mathematician and physicist well-known for the Kaluza–Klein theory involving field equations in curved five-dimensional space. His idea that fundamental forces can be unified by introducing additional dimensions re-emerged much later in the “String Theory”.The original Kaluza-Klein theory was one of the first attempts to create an unified field theory i.e. the theory, which would unify all the forces under one fundamental law. It was published in 1921 by Theodor Kaluza and extended in 1926 by Oskar Klein. The basic idea of this theory was to postulate one extra compactified space dimension and introduce nothing but pure gravity in a new (1 + 4)-dimensional space-time. Klein suggested that the fifth dimension would be rolled up into a tiny, compact loop on the order of 10-35 [m]The presented "New Unification Theory" unifies Classical Electrodynamics with General Relativity and Quantum Physics

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