The Einstein field equation of general relativity

2004 ◽  
pp. 190-208
Keyword(s):  
General Relativity ◽  
Field Equation ◽  
Einstein Field Equation

General Relativity

2017 ◽  
Author(s):  
Nicholas Manton ◽  
Nicholas Mee
Keyword(s):  
Black Holes ◽  
General Relativity ◽  
Field Equation ◽  
Einstein Field Equation ◽  
Kerr Metric ◽  
Gravitational Lenses ◽  
Field Equations ◽  
Spacetime Geometry ◽  
Tests Of General Relativity ◽  
Rotating Black Holes

This chapter presents the physical motivation for general relativity, derives the Einstein field equation and gives concise derivations of the main results of the theory. It begins with the equivalence principle, tidal forces in Newtonian gravity and their connection to curved spacetime geometry. This leads to a derivation of the field equation. Tests of general relativity are considered: Mercury’s perihelion advance, gravitational redshift, the deflection of starlight and gravitational lenses. The exterior and interior Schwarzschild solutions are discussed. Eddington–Finkelstein coordinates are used to describe objects falling into non-rotating black holes. The Kerr metric is used to describe rotating black holes and their astrophysical consequences. Gravitational waves are described and used to explain the orbital decay of binary neutron stars. Their recent detection by LIGO and the beginning of a new era of gravitational wave astronomy is discussed. Finally, the gravitational field equations are derived from the Einstein–Hilbert action.

scholarly journals Newman-Janis Ansatz for rotating wormholes

2021 ◽  
Vol 2081 (1) ◽  
pp. 012005
Author(s):  
A C Gutiérrez-Piñeres ◽  
N H Beltrán ◽  
C S López-Monsalvo
Keyword(s):  
General Relativity ◽  
Black Hole ◽  
Field Equation ◽  
Einstein Equation ◽  
Open Problem ◽  
Einstein Field Equation ◽  
Kerr Black Hole ◽  
Rotating Fluids ◽  
Anisotropic Pressures ◽  
Interior Solutions

Abstract A central problem in General Relativity is obtaining a solution to describe the source’s interior counterpart for Kerr black hole. Besides, determining a method to match the interior and exterior solutions through a surface free of predefined coordinates remains an open problem. In this work, we present the ansatz formulated by the Newman-Janis to generate solutions to the Einstein field equation inspired by the mention problems. We present a collection of independent classes of exact interior solutions of the Einstein equation describing rotating fluids with anisotropic pressures. Furthermore, we will elaborate on some obtained solutions by alluding to rotating wormholes.

scholarly journals New Gravity Field Equation is derived by Einstein Field Equation in General Relativity Theory

2021 ◽  
Author(s):  
Sangwha Yi
Keyword(s):  
General Relativity ◽  
Field Equation ◽  
Gravity Field ◽  
Order Term ◽  
Einstein Field Equation ◽  
Einstein Gravity ◽  
Cosmological Term ◽  
Relativity Theory ◽  
General Relativity Theory ◽  
Curvature Term

We found the 4-order curvature term satisfied the co-variant derivative. Einstein gravity fieldequation is consist of 2-order curvature terms. Hence, the 4-order curvature term and 2-order curvature termsmake new gravity field equation. In this point, Einstein’s gravity field equation can be modified by new 4-order curvature term because gravity field equation’s term doesn’t have to be 2-order term. Indeed, Einsteinhimself was like that, 0-order term, the cosmological term. Therefore, our theory is based on legitimate facts.

scholarly journals A Review on Black hole solutions in General Relativity

2021 ◽  
Vol 16 (3) ◽  
Author(s):  
Monika Sati ◽  
K.C. Petwal
Keyword(s):  
Black Holes ◽  
General Relativity ◽  
Black Hole ◽  
Field Equation ◽  
Einstein Field Equation ◽  
Schwarzschild Solution ◽  
Penrose Diagram ◽  
Static Solutions ◽  
Spherical Mass ◽  
Black Hole Solutions

In the present manuscript, we endeavour to review and develop the black hole solutions in general relativity. We emphasize here the Schwarzschild solution in Einstein’s field equation, which describes the gravitational field outside a spherical mass. The paper aims to obtain certain results, including the description of the Einstein field equation with stationary and static solutions and components of the metric that turns out to be time independent, some experiments on the Schwarzschild - Penrose diagram, the Kerr-Newman solution for rotating black holes, and the Reissner- Nordstrom solution for static and charged black holes.

ON A PERFECT FLUID K¨ AHLER SPACETIME

2016 ◽  
Vol 12 (3) ◽  
pp. 4350-4355
Author(s):  
VIBHA SRIVASTAVA ◽  
P. N. PANDEY
Keyword(s):  
Field Equation ◽  
Perfect Fluid ◽  
Sectional Curvature ◽  
Einstein Field Equation ◽  
Cosmological Term ◽  
Conformal Killing ◽  
Killing Vectors ◽  
Projectively Flat ◽  
Conformal Killing Vectors

The object of the present paper is to study a perfect fluid K¨ahlerspacetime. A perfect fluid K¨ahler spacetime satisfying the Einstein field equation with a cosmological term has been studied and the existence of killingand conformal killing vectors have been discussed. Certain results related to sectional curvature for pseudo projectively flat perfect fluid K¨ahler spacetime have been obtained. Dust model for perfect fluid K¨ahler spacetime has also been studied.

scholarly journals Rainbow Gravity Corrections to the Entropic Force

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Zhong-Wen Feng ◽  
Shu-Zheng Yang
Keyword(s):  
Black Hole ◽  
Field Equation ◽  
Quantum Gravity ◽  
Gravity Model ◽  
Einstein Field Equation ◽  
Friedmann Equation ◽  
Quantum Corrections ◽  
Entropic Force ◽  
Planck Length ◽  
Multifunctional Properties

The entropic force attracts a lot of interest for its multifunctional properties. For instance, Einstein’s field equation, Newton’s law of gravitation, and the Friedmann equation can be derived from the entropic force. In this paper, utilizing a new kind of rainbow gravity model that was proposed by Magueijo and Smolin, we explore the quantum gravity corrections to the entropic force. First, we derive the modified thermodynamics of a rainbow black hole via its surface gravity. Then, according to Verlinde’s theory, the quantum corrections to the entropic force are obtained. The result shows that the modified entropic force is related not only to the properties of the black hole but also to the Planck length lp and the rainbow parameter γ. Furthermore, based on the rainbow gravity corrected entropic force, the modified Einstein field equation and the modified Friedmann equation are also derived.

ON GRAVITO-ELECTROMAGNETIC DUALITY IN GENERAL RELATIVITY

1999 ◽  
Vol 14 (12) ◽  
pp. 759-763 ◽  
Author(s):  
NARESH DADHICH
Keyword(s):  
General Relativity ◽  
Field Equation ◽  
Gravitational Constant ◽  
Electromagnetic Theory ◽  
Vacuum Field ◽  
Vacuum Equation ◽  
Riemann Curvature ◽  
Duality Transformation ◽  
Duality Symmetry ◽  
Vacuum Field Equation

In analogy with the electromagnetic theory, we resolve the Riemann curvature into electric and magnetic parts and consider the analogous duality transformation which keeps the Einstein action for vacuum invariant. It is remarkable that the duality symmetry of the action also leads to the vacuum field equation without cosmological constant. Further invariance of the vacuum equation and the action under the gravito-electric duality require gravitational constant to change sign.

scholarly journals Einstein’s Notational Equation of Electro-Magnetic Field Equation in Rindler spacetime

2021 ◽  
Author(s):  
Sangwha Yi
Keyword(s):  
Magnetic Field ◽  
General Relativity ◽  
Field Equation ◽  
Electromagnetic Fields ◽  
Space Time ◽  
Relativity Theory ◽  
General Relativity Theory ◽  
Electro Magnetic Field ◽  
Rindler Space ◽  
Electro Magnetic

We find Einstein’s notational equation of the electro-magnetic field equation and the electromagneticfield in Rindler space-time. Because, electromagnetic fields of the accelerated frame include in general relativity theory.

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