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.

FRACTIONAL LAGRANGIAN FORMULATION OF GENERAL RELATIVITY AND EMERGENCE OF COMPLEX, SPINORIAL AND NONCOMMUTATIVE GRAVITY

2009 ◽  
Vol 06 (01) ◽  
pp. 25-76 ◽  
Author(s):  
AHMAD RAMI EL-NABULSI
Keyword(s):  
General Relativity ◽  
High Energy Physics ◽  
Differential Operators ◽  
Directional Derivative ◽  
High Energy ◽  
Real Space ◽  
Lagrangian Formulation ◽  
Einstein’S Field Equations ◽  
Field Equations ◽  
Einstein's Field Equations

Fractional calculus of variations and in particular the Fractional Action-Like Variational Approach has recently gained importance in studying nonconservative and weak decaying dynamical systems. Until now, in high-energy physics including cosmology and quantum field theories the derivative and integral operators have only been used in integer steps. In this work, we develop the fractional Lagrangian formulation of General Relativity based on the Cresson's fractional differential operators that generalize the differential operators of conventional Einstein's General Relativity but that reduces to the standard formalism in the integer limit. Our main aim is to build the multi-dimensional setting for the Einstein's field equations. The presence of a complex number in the Cresson's fractional derivatives forces the field equations to be complex and even noncommutative. An immediate consequence of this is that all gravitational and curvature fields are complexified and as a result may be decomposed into real part and complex parts. We have also indications that the fractional Einstein's field equations in the real space behave differently from those in the complex plane. Furthermore, we show how the generalization of the fractional Cresson's fractional derivative to the directional derivative at an arbitrary orientation θ leads to a spinor-like gravitational field equation in the sense of Penrose.

scholarly journals The dynamics of brane-world cosmological models

2005 ◽  
Vol 83 (5) ◽  
pp. 475-525 ◽  
Author(s):  
A A Coley
Keyword(s):  
General Relativity ◽  
Gravitational Field ◽  
Initial Conditions ◽  
High Energy ◽  
Cosmological Models ◽  
Brane World ◽  
Initial Singularity ◽  
Field Equations ◽  
Cosmological Singularity ◽  
Spatially Homogeneous

Brane-world cosmology is motivated by recent developments in string/M-theory and offers a new perspective on the hierarchy problem. In the brane-world scenario, our Universe is a four-dimensional subspace or brane embedded in a higher-dimensional bulk spacetime. Ordinary matter fields are confined to the brane while the gravitational field can also propagate in the bulk, and it is not necessary for the extra dimensions to be small, or even compact, leading to modifications of Einstein's theory of general relativity at high energies. In particular, the Randall–Sundrum-type models are relatively simple phenomenological models that capture some of the essential features of the dimensional reduction of eleven-dimensional supergravity introduced by Hořava and Witten. These curved (or warped) models are self-consistent and simple and allow for an investigation of the essential nonlinear gravitational dynamics. The governing field equations induced on the brane differ from the general relativistic equations in that there are nonlocal effects from the free gravitational field in the bulk, transmitted via the projection of the bulk Weyl tensor, and the local quadratic energy-momentum corrections, which are significant in the high-energy regime close to the initial singularity. In this review, we investigate the dynamics of the five-dimensional warped Randall–Sundrum brane worlds and their generalizations, with particular emphasis on whether the currently observed high degree of homogeneity and isotropy can be explained. In particular, we discuss the asymptotic dynamical evolution of spatially homogeneous brane-world cosmological models containing both a perfect fluid and a scalar field close to the initial singularity. Using dynamical systems techniques, it is found that, for models with a physically relevant equation of state, an isotropic singularity is a past-attractor in all orthogonal spatially homogeneous models (including Bianchi type IX models). In addition, we describe the dynamics in a class of inhomogeneous brane-world models, and show that these models also have an isotropic initial singularity. These results provide support for the conjecture that typically the initial cosmological singularity is isotropic in brane-world cosmology. Consequently, we argue that, unlike the situation in general relativity, brane-world cosmological models may offer a plausible solution to the initial conditions problem in cosmology. PACS Nos.: 98.89.Cq/Jk, 04.20–q

scholarly journals Estimations of the Optical Equivalence Theorem for Opto-Mechanical Systems for Investigation in General Relativity and High-Energy Physics

Computation ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 60
Author(s):  
Orchidea Maria Lecian
Keyword(s):  
General Relativity ◽  
Equivalence Principle ◽  
High Energy Physics ◽  
Mechanical Systems ◽  
Equivalence Theorem ◽  
High Energy ◽  
Laser Fields ◽  
Energy Physics

The optical equivalence principle is analyzed according to the possibility of describing unbounded states, and the suitable approximations are calculated for highly energetic phenomena. Among these possibilities, the relevance for laser fields, interferometers, and optomehcanical systems are implemented. Their suitableness for research in General Relativity, Cosmology, and High-Energy Physics are outlined.

scholarly journals PERTURBATIVE QUANTUM FIELD THEORY

2001 ◽  
Vol 16 (18) ◽  
pp. 3041-3065 ◽  
Author(s):  
GEORGE STERMAN
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Mechanics ◽  
High Energy Physics ◽  
Experimental Tests ◽  
High Energy ◽  
Quantum Field ◽  
Perturbative Quantum ◽  
Perturbative Quantum Field Theory ◽  
Energy Physics

This talk introduces perturbative quantum field on a heuristic level. It is directed at an audience familiar with elements of quantum mechanics, but not necessarily with high energy physics. It includes a discussion of the strategies behind experimental tests of fundamental theories, and of the field theory interpretations of these tests.

scholarly journals ADVANCED METHODS IN BLACK-HOLE PERTURBATION THEORY

2013 ◽  
Vol 28 (22n23) ◽  
pp. 1340018 ◽  
Author(s):  
PAOLO PANI
Keyword(s):  
Black Hole ◽  
Perturbation Theory ◽  
High Energy Physics ◽  
High Energy ◽  
Field Equations ◽  
Open Problems ◽  
Small Perturbations ◽  
Curved Space ◽  
Current State ◽  
Energy Physics

Black-hole perturbation theory is a useful tool to investigate issues in astrophysics, high-energy physics, and fundamental problems in gravity. It is often complementary to fully-fledged nonlinear evolutions and instrumental to interpret some results of numerical simulations. Several modern applications require advanced tools to investigate the linear dynamics of generic small perturbations around stationary black holes. Here, we present an overview of these applications and introduce extensions of the standard semianalytical methods to construct and solve the linearized field equations in curved space–time. Current state-of-the-art techniques are pedagogically explained and exciting open problems are presented.

scholarly journals Is gravity actually the curvature of spacetime?

2019 ◽  
Vol 28 (14) ◽  
pp. 1944021
Author(s):  
Sebastian Bahamonde ◽  
Mir Faizal
Keyword(s):  
General Relativity ◽  
Casimir Effect ◽  
Boundary Effect ◽  
Experimental Tests ◽  
Classical Field ◽  
Einstein Equations ◽  
Field Equations ◽  
Tests Of General Relativity ◽  
Boundary Terms ◽  
Theories Of Gravity

The Einstein equations, apart from being the classical field equations of General Relativity, are also the classical field equations of two other theories of gravity. As the experimental tests of General Relativity are done using the Einstein equations, we do not really know if gravity is the curvature of a torsionless spacetime or torsion of a curvatureless spacetime or if it occurs due to the nonmetricity of a curvatureless and torsionless spacetime. However, as the classical actions of all these theories differ from each other by the boundary terms, and the Casimir effect is a boundary effect, we propose that a novel gravitational Casimir effect between superconductors can be used to test which of these theories actually describe gravity.

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