A brief survey of general relativity

2019 ◽  
pp. 25-50
Author(s):  
Nils Andersson
Keyword(s):  
General Relativity ◽  
Geometric Theory ◽  
Einstein’S Field Equations ◽  
Curved Spacetime ◽  
Field Equations ◽  
Einstein's Field Equations ◽  
Theory Of Gravity

This chapter provides an overview of Einstein’s geometric theory of gravity – general relativity. It introduces the mathematics required to model the motion of objects in a curved spacetime and provides an intuitive derivation of Einstein’s field equations.

scholarly journals How Extra Symmetries Affect Solutions in General Relativity

Universe ◽  
2020 ◽  
Vol 6 (10) ◽  
pp. 170
Author(s):  
Aroonkumar Beesham ◽  
Fisokuhle Makhanya
Keyword(s):  
General Relativity ◽  
Exact Solutions ◽  
Einstein’S Field Equations ◽  
Field Equations ◽  
Einstein's Field Equations

To get exact solutions to Einstein’s field equations in general relativity, one has to impose some symmetry requirements. Otherwise, the equations are too difficult to solve. However, sometimes, the imposition of too much extra symmetry can cause the problem to become somewhat trivial. As a typical example to illustrate this, the effects of conharmonic flatness are studied and applied to Friedmann–Lemaitre–Robertson–Walker spacetime. Hence, we need to impose some symmetry to make the problem tractable, but not too much so as to make it too simple.

scholarly journals A MODEL PROBLEM FOR THE INITIAL-BOUNDARY VALUE FORMULATION OF EINSTEIN'S FIELD EQUATIONS

2005 ◽  
Vol 02 (02) ◽  
pp. 397-435 ◽  
Author(s):  
OSCAR REULA ◽  
OLIVIER SARBACH
Keyword(s):  
General Relativity ◽  
Boundary Conditions ◽  
Model Problem ◽  
Boundary Value ◽  
Initial Boundary ◽  
Einstein’S Field Equations ◽  
Field Equations ◽  
Einstein's Field Equations ◽  
Initial Boundary Value ◽  
Well Posed

In many numerical implementations of the Cauchy formulation of Einstein's field equations one encounters artificial boundaries which raises the issue of specifying boundary conditions. Such conditions have to be chosen carefully. In particular, they should be compatible with the constraints, yield a well posed initial-boundary value formulation and incorporate some physically desirable properties like, for instance, minimizing reflections of gravitational radiation. Motivated by the problem in General Relativity, we analyze a model problem, consisting of a formulation of Maxwell's equations on a spatially compact region of space–time with timelike boundaries. The form in which the equations are written is such that their structure is very similar to the Einstein–Christoffel symmetric hyperbolic formulations of Einstein's field equations. For this model problem, we specify a family of Sommerfeld-type constraint-preserving boundary conditions and show that the resulting initial-boundary value formulations are well posed. We expect that these results can be generalized to the Einstein–Christoffel formulations of General Relativity, at least in the case of linearizations about a stationary background.

Characteristic initial data and wavefront singularities in general relativity

1983 ◽  
Vol 385 (1789) ◽  
pp. 345-371 ◽  
Keyword(s):  
General Relativity ◽  
Initial Data ◽  
Minkowski Space ◽  
The Self ◽  
Einstein’S Field Equations ◽  
Field Equations ◽  
Null Hypersurfaces ◽  
Einstein's Field Equations ◽  
Arbitrary Space

The structure of singularities (caustics), self-intersections of wavefronts (null hypersurfaces) and wavefront families (null coordinates) in arbitrary space-times is discussed in detail and illustrated by explicit examples of stable wavefront singularities in Minkowski space. It is shown how characteristic initial data determine the caustics and the self-intersections of the characteristics of Einstein’s field equations.

scholarly journals Some pure radiation filds in general relativity

1980 ◽  
Vol 21 (4) ◽  
pp. 464-473 ◽  
Author(s):  
R. P. Akabari ◽  
U. K. Dave ◽  
L. K. Patel
Keyword(s):  
General Relativity ◽  
General Solution ◽  
Einstein’S Field Equations ◽  
Field Equations ◽  
Pure Radiation ◽  
Radiation Fields ◽  
Einstein's Field Equations

AbstractA Demianski-type metric investigated in connection with Einstein's field equations corresponding to pure radiation fields. With aid of complex vectorical formalism, a general solution of these fiel equations is obtained. The solution is algebraically spcial. A particular case of the solution is considered which includes many known solutions; among them are the raiationg versions of some of Kinnersley's solutions.

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.

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