scholarly journals On Kottler's path: Origin and evolution of the premetric program in gravity and in electrodynamics

2016 ◽  
Vol 25 (11) ◽  
pp. 1640016 ◽  
Author(s):  
Friedrich W. Hehl ◽  
Yakov Itin ◽  
Yuri N. Obukhov
Keyword(s):  
General Relativity ◽  
Gravitational Potential ◽  
Linear Response ◽  
Maxwell Equations ◽  
Constitutive Law ◽  
Classical Electrodynamics ◽  
Field Equations ◽  
Origin And Evolution ◽  
Fundamental Equations

In 1922, Kottler put forward the program to remove the gravitational potential, the metric of spacetime, from the fundamental equations in physics as far as possible. He successfully applied this idea to Newton’s gravitostatics and to Maxwell’s electrodynamics, where Kottler recast the field equations in premetric form and specified a metric-dependent constitutive law. We will discuss the basics of the premetric approach and some of its beautiful consequences, like the division of universal constants into two classes. We show that classical electrodynamics can be developed without a metric quite straightforwardly: the Maxwell equations, together with a local and linear response law for electromagnetic media, admit a consistent premetric formulation. Kottler’s program succeeds here without provisos. In Kottler’s approach to gravity, making the theory relativistic, two premetric quasi-Maxwellian field equations arise, but their field variables, if interpreted in terms of general relativity, do depend on the metric. However, one can hope to bring the Kottler idea to work by using the teleparallelism equivalent of general relativity, where the gravitational potential, the coframe, can be chosen in a premetric way.

The Einstein field equations

2019 ◽  
pp. 52-58
Author(s):  
Steven Carlip
Keyword(s):  
General Relativity ◽  
Conservation Laws ◽  
Newtonian Gravity ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Noether’S Theorem ◽  
Geodesic Deviation ◽  
Fundamental Equations ◽  
Hilbert Action ◽  
Qualitative Discussion

The Einstein field equations are the fundamental equations of general relativity. After a brief qualitative discussion of geodesic deviation and Newtonian gravity, this chapter derives the field equations from the Einstein-Hilbert action. The chapter contains a derivation of Noether’s theorem and the consequent conservation laws, and a brief discussion of generalizations of the Einstein-Hilbert action.

scholarly journals Variation of the Gravitational Constant in the Radiation-Dominated Universe

2012 ◽  
Vol 2012 ◽  
pp. 1-4
Author(s):  
L. L. Williams
Keyword(s):  
General Relativity ◽  
Scalar Field ◽  
Gravitational Constant ◽  
Flat Space ◽  
Scale Factor ◽  
Early History ◽  
Classical Electrodynamics ◽  
Field Equations ◽  
Walker Metric ◽  
History Of

The unification of classical electrodynamics and general relativity within the context of five-dimensional general relativity (Kaluza, 1921, and Thiry, 1948) contains a scalar field which may be identified with the gravitational constant, G. The field equations of this theory are solved under conditions of the Robertson-Walker metric for flat space, for a radiation-dominated universe—a model appropriate for the early history of our universe. This leads to a cosmology wherein G is inversely proportional to the Robertson-Walker scale factor. This result is discussed in the context of the Dirac large number hypothesis and in the context of an expression for G in terms of atomic constants.

scholarly journals The Geometrization of Maxwell’s Equations and the Emergence of Gravity

2021 ◽  
Author(s):  
Raymond Beach
Keyword(s):  
General Relativity ◽  
Dark Matter ◽  
Dark Energy ◽  
Curvature Tensor ◽  
Maxwell Equations ◽  
Classical Field Theory ◽  
Field Equations ◽  
Gravitational Fields ◽  
All Solutions ◽  
Maxwell Tensor

A recently proposed classical field theory in which Maxwell’s equations are replaced by an equation that couples the Maxwell tensor to the Riemann-Christoffel curvature tensor in a fundamentally new way is reviewed and extended. This proposed geometrization of the Maxwell tensor provides a succinct framework for the classical Maxwell equations which are left intact as a derivable consequence. Beyond providing a basis for the classical Maxwell equations, the coupling of the Riemann-Christoffel curvature tensor to the Maxwell tensor leads to the emergence of gravity, with all solutions of the proposed theory also being solutions of Einstein’s equation of General Relativity augmented by a term that can mimic the properties of dark matter and/or dark energy. Both electromagnetic and gravitational phenomena are put an equal footing with both being tied to the curvature of space-time. Using specific solutions to the proposed theory, the unification brought to electromagnetic and gravitational phenomena as well as the consistency of solutions with those of the classical Maxwell and Einstein field equations is emphasized throughout. Unique to the proposed theory and based on specific solutions are the emergence of antimatter and its behavior in gravitational fields, the emergence of dark matter and dark energy mimicking terms in the context of General Relativity, an underlying relationship between electromagnetic and gravitational radiation, and the impossibility of negative mass solutions that would generate repulsive gravitational fields or antigravity. Finally, a method for quantizing the charge, mass, and angular momentum of particle-like solutions as well as the possibility of superluminal transport of specific curvature related quantities is conjectured.

Electromagnetic Radiation

2019 ◽  
Author(s):  
Richard R. Freeman ◽  
James A. King ◽  
Gregory P. Lafyatis
Keyword(s):  
Electromagnetic Radiation ◽  
Energy Transport ◽  
Radiation Reaction ◽  
Classical Electrodynamics ◽  
X Rays ◽  
Field Equations ◽  
Radio Frequency Radiation ◽  
Relativistic Treatment ◽  
Time Variations ◽  
Radiation Science

Electromagnetic Radiation is a graduate level book on classical electrodynamics with a strong emphasis on radiation. This book is meant to quickly and efficiently introduce students to the electromagnetic radiation science essential to a practicing physicist. While a major focus is on light and its interactions, topics in radio frequency radiation, x-rays, and beyond are also treated. Special emphasis is placed on applications, with many exercises and homework problems. The format of the book is designed to convey the basic concepts of a topic in the main central text in the book in a mathematically rigorous manner, but with detailed derivations routinely relegated to the accompanying side notes or end of chapter “Discussions.” The book is composed of four parts: Part I is a review of basic E&M, and assumes the reader has a had a good upper division undergraduate course, and while it offers a concise review of topics covered in such a course, it does not treat any given topic in detail; specifically electro- and magnetostatics. Part II addresses the origins of radiation in terms of time variations of charge and current densities within the source, and presents Jefimenko’s field equations as derived from retarded potentials. Part III introduces special relativity and its deep connection to Maxwell’s equations, together with an introduction to relativistic field theory, as well as the relativistic treatment of radiation from an arbitrarily accelerating charge. A highlight of this part is a chapter on the still partially unresolved problem of radiation reaction on an accelerating charge. Part IV treats the practical problems of electromagnetic radiation interacting with matter, with chapters on energy transport, scattering, diffraction and finally an illuminating, application-oriented treatment of fields in confined environments.

General Relativity

2019 ◽  
Author(s):  
Steven Carlip
Keyword(s):  
General Relativity ◽  
High Energy Physics ◽  
Hamiltonian Formulation ◽  
Experimental Tests ◽  
High Energy ◽  
Gravitational Energy ◽  
Field Equations ◽  
Physics First ◽  
Condensed Matter Theory ◽  
Introductory Textbooks

This work is a short textbook on general relativity and gravitation, aimed at readers with a broad range of interests in physics, from cosmology to gravitational radiation to high energy physics to condensed matter theory. It is an introductory text, but it has also been written as a jumping-off point for readers who plan to study more specialized topics. As a textbook, it is designed to be usable in a one-quarter course (about 25 hours of instruction), and should be suitable for both graduate students and advanced undergraduates. The pedagogical approach is “physics first”: readers move very quickly to the calculation of observational predictions, and only return to the mathematical foundations after the physics is established. The book is mathematically correct—even nonspecialists need to know some differential geometry to be able to read papers—but informal. In addition to the “standard” topics covered by most introductory textbooks, it contains short introductions to more advanced topics: for instance, why field equations are second order, how to treat gravitational energy, what is required for a Hamiltonian formulation of general relativity. A concluding chapter discusses directions for further study, from mathematical relativity to experimental tests to quantum gravity.

scholarly journals Does general relativity highlight necessary connections in nature?

Synthese ◽  
2021 ◽  
Author(s):  
Antonio Vassallo
Keyword(s):  
General Relativity ◽  
Laws Of Nature ◽  
Coupling Mechanism ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Bianchi Identities ◽  
Physical Role ◽  
General Relativistic ◽  
Differential Relations ◽  
Necessary Connections

AbstractThe dynamics of general relativity is encoded in a set of ten differential equations, the so-called Einstein field equations. It is usually believed that Einstein’s equations represent a physical law describing the coupling of spacetime with material fields. However, just six of these equations actually describe the coupling mechanism: the remaining four represent a set of differential relations known as Bianchi identities. The paper discusses the physical role that the Bianchi identities play in general relativity, and investigates whether these identities—qua part of a physical law—highlight some kind of a posteriori necessity in a Kripkean sense. The inquiry shows that general relativistic physics has an interesting bearing on the debate about the metaphysics of the laws of nature.

scholarly journals GENERALIZED EINSTEIN–MAXWELL FIELD EQUATIONS IN THE PALATINI FORMALISM

2013 ◽  
Vol 22 (04) ◽  
pp. 1350017 ◽  
Author(s):  
GINÉS R. PÉREZ TERUEL
Keyword(s):  
Electromagnetic Field ◽  
Algebraic Equation ◽  
Ricci Tensor ◽  
Maxwell Equations ◽  
Natural Generalization ◽  
New Method ◽  
Maxwell Field ◽  
Field Equations ◽  
Palatini Formalism

We derive a new set of field equations within the framework of the Palatini formalism. These equations are a natural generalization of the Einstein–Maxwell equations which arise by adding a function [Formula: see text], with [Formula: see text] to the Palatini Lagrangian f(R, Q). The result we obtain can be viewed as the coupling of gravity with a nonlinear extension of the electromagnetic field. In addition, a new method is introduced to solve the algebraic equation associated to the Ricci tensor.

Relativity Made Relatively Easy Volume 2

2021 ◽  
Author(s):  
Andrew M. Steane
Keyword(s):  
General Relativity ◽  
Classical Field Theory ◽  
Weak Field ◽  
Stellar Structure ◽  
Field Equations ◽  
Graduate Course ◽  
Entry Level ◽  
Introductory Course ◽  
Penrose Process ◽  
Low Amplitude

This is a textbook on general relativity and cosmology for a physics undergraduate or an entry-level graduate course. General relativity is the main subject; cosmology is also discussed in considerable detail (enough for a complete introductory course). Part 1 introduces concepts and deals with weak-field applications such as gravitation around ordinary stars, gravimagnetic effects and low-amplitude gravitational waves. The theory is derived in detail and the physical meaning explained. Sources, energy and detection of gravitational radiation are discussed. Part 2 develops the mathematics of differential geometry, along with physical applications, and discusses the exact treatment of curvature and the field equations. The electromagnetic field and fluid flow are treated, as well as geodesics, redshift, and so on. Part 3 then shows how the field equation is solved in standard cases such as Schwarzschild-Droste, Reissner-Nordstrom, Kerr, and internal stellar structure. Orbits and related phenomena are obtained. Black holes are described in detail, including horizons, wormholes, Penrose process and Hawking radiation. Part 4 covers cosmology, first in terms of metric, then dynamics, structure formation and observational methods. The meaning of cosmic expansion is explained at length. Recombination and last scattering are calculated, and the quantitative analysis of the CMB is sketched. Inflation is introduced briefly but quantitatively. Part 5 is a brief introduction to classical field theory, including spinors and the Dirac equation, proceeding as far as the Einstein-Hilbert action. Throughout the book the emphasis is on making the mathematics as clear as possible, and keeping in touch with physical observations.

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