The elements of General Relativity

2021 ◽  
pp. 11-26
Author(s):  
Andrew M. Steane
Keyword(s):  
General Relativity ◽  
Equivalence Principle ◽  
Geometric Interpretation ◽  
Energy Tensor ◽  
Stress Energy Tensor ◽  
Stress Energy ◽  
Basic Equations ◽  
Absolute Concept ◽  
Spacetime Interval

This chapter is a survey of central ideas and equations in general relativity. The basic equations are written down with a view to seeing where we are heading in the book, and in order to present both the field theory and the geometric interpretation of gravity. The central role of the metric is introduced, and the equivalence principle is discussed. It is emphasized that spacetime interval is both a mathematical and a physical idea. It is explained how gravity works “behind the scenes” by modifying equations which otherwise look like familiar equations of electromagnetism. The sense in which acceleration is in some respects a relative and in some respects an absolute concept is explained. It is shown why the motion of matter, not just its mass, must influence gravitation. The stress-energy tensor is introduced and defined.

scholarly journals Genesis of general relativity — A concise exposition

2016 ◽  
Vol 25 (14) ◽  
pp. 1630004
Author(s):  
Wei-Tou Ni
Keyword(s):  
General Relativity ◽  
Special Relativity ◽  
Equivalence Principle ◽  
Energy Tensor ◽  
Stress Energy Tensor ◽  
Relativistic Fluids ◽  
Schwarzschild Solution ◽  
Stress Energy ◽  
Perihelion Advance ◽  
Theory Of Gravity

This short exposition starts with a brief discussion of situation before the completion of special relativity (Le Verrier’s discovery of the Mercury perihelion advance anomaly, Michelson–Morley experiment, Eötvös experiment, Newcomb’s improved observation of Mercury perihelion advance, the proposals of various new gravity theories and the development of tensor analysis and differential geometry) and accounts for the main conceptual developments leading to the completion of the general relativity (CGR): gravity has finite velocity of propagation; energy also gravitates; Einstein proposed his equivalence principle and deduced the gravitational redshift; Minkowski formulated the special relativity in four-dimentional spacetime and derived the four-dimensional electromagnetic stress–energy tensor; Einstein derived the gravitational deflection from his equivalence principle; Laue extended Minkowski’s method of constructing electromagnetic stress-energy tensor to stressed bodies, dust and relativistic fluids; Abraham, Einstein, and Nordström proposed their versions of scalar theories of gravity in 1911–13; Einstein and Grossmann first used metric as the basic gravitational entity and proposed a “tensor” theory of gravity (the “Entwurf” theory, 1913); Einstein proposed a theory of gravity with Ricci tensor proportional to stress–energy tensor (1915); Einstein, based on 1913 Besso–Einstein collaboration, correctly derived the relativistic perihelion advance formula of his new theory which agreed with observation (1915); Hilbert discovered the Lagrangian for electromagnetic stress–energy tensor and the Lagrangian for the gravitational field (1915), and stated the Hilbert variational principle; Einstein equation of GR was proposed (1915); Einstein published his foundation paper (1916). Subsequent developments and applications in the next two years included Schwarzschild solution (1916), gravitational waves and the quadrupole formula of gravitational radiation (1916, 1918), cosmology and the proposal of cosmological constant (1917), de Sitter solution (1917), Lense–Thirring effect (1918).

scholarly journals Stress Energy Tensor Study in Fluid Mechanics

2019 ◽  
Author(s):  
Roman Baudrimont
Keyword(s):  
General Relativity ◽  
Fluid Mechanics ◽  
Space Time ◽  
Newtonian Fluids ◽  
Third Party ◽  
Energy Tensor ◽  
Stress Energy Tensor ◽  
Perfect Fluids ◽  
Stress Energy

This paper is to summarize the involvement of the stress energy tensor in the study of fluid mechanics. In the first part we will see the implication that carries the stress energy tensor in the framework of general relativity. In the second part, we will study the stress energy tensor under the mechanics of perfect fluids, allowing us to lead third party in the case of Newtonian fluids, and in the last part we will see that it is possible to define space-time as a no-Newtonian fluids.

scholarly journals Stress Energy Tensor Study in Fluid Mechanics

2019 ◽  
Author(s):  
Roman Baudrimont
Keyword(s):  
General Relativity ◽  
Fluid Mechanics ◽  
Space Time ◽  
Newtonian Fluids ◽  
Third Party ◽  
Energy Tensor ◽  
Stress Energy Tensor ◽  
Perfect Fluids ◽  
Stress Energy

This paper is to summarize the involvement of the stress energy tensor in the study of fluid mechanics. In the first part we will see the implication that carries the stress energy tensor in the framework of general relativity. In the second part, we will study the stress energy tensor under the mechanics of perfect fluids, allowing us to lead third party in the case of Newtonian fluids, and in the last part we will see that it is possible to define space-time as a no-Newtonian fluids.

scholarly journals Spherically Symmetric Fluid Cosmological Model with Anisotropic Stress Tensor in General Relativity

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
D. D. Pawar ◽  
V. R. Patil ◽  
S. N. Bayaskar
Keyword(s):  
General Relativity ◽  
Cosmological Model ◽  
Generating Functions ◽  
Energy Tensor ◽  
Spherically Symmetric ◽  
Stress Energy Tensor ◽  
Anisotropic Stress ◽  
Stress Energy ◽  
Anisotropic Stress Tensor ◽  
Symmetric Spacetime

This paper deals with the cosmological models for the static spherically symmetric spacetime for perfect fluid with anisotropic stress energy tensor in general relativity by introducing the generating functions g(r) and w(r) and also discussing their physical and geometric properties.

scholarly journals THEORY OF GRAVITATION THEORIES: A NO-PROGRESS REPORT

2008 ◽  
Vol 17 (03n04) ◽  
pp. 399-423 ◽  
Author(s):  
THOMAS P. SOTIRIOU ◽  
STEFANO LIBERATI ◽  
VALERIO FARAONI
Keyword(s):  
Equivalence Principle ◽  
Progress Report ◽  
Energy Tensor ◽  
Stress Energy Tensor ◽  
Gravitational Fields ◽  
Stress Energy ◽  
Theories Of Gravity ◽  
Theory Of Gravitation ◽  
Conformal Frames ◽  
Shaky Ground

Already in the 1970s there where attempts to present a set of ground rules, sometimes referred to as a theory of gravitation theories, which theories of gravity should satisfy in order to be considered viable in principle and, therefore, interesting enough to deserve further investigation. From this perspective, an alternative title of this paper could be "Why Are We Still Unable to Write a Guide on How to Propose Viable Alternatives to General Relativity?". Attempting to answer this question, it is argued here that earlier efforts to turn qualitative statements, such as the Einstein equivalence principle, into quantitative ones, such as the metric postulates, stand on rather shaky ground — probably contrary to popular belief — as they appear to depend strongly on particular representations of the theory. This includes ambiguities in the identification of matter and gravitational fields, dependence of frequently used definitions (such as those of the stress–energy tensor or classical vacuum) on the choice of variables, etc. Various examples are discussed and possible approaches to this problem are pointed out. In the course of this study, several common misconceptions related to the various forms of the equivalence principle, the use of conformal frames and equivalence between theories are clarified.

scholarly journals CANONICAL AND GRAVITATIONAL STRESS-ENERGY TENSORS

2006 ◽  
Vol 15 (07) ◽  
pp. 959-989 ◽  
Author(s):  
M. LECLERC
Keyword(s):  
General Relativity ◽  
Matter Field ◽  
Field Energy ◽  
Energy Tensor ◽  
Maxwell System ◽  
Stress Energy Tensor ◽  
Spinor Fields ◽  
Gravitational Stress ◽  
Stress Energy ◽  
Matter Fields

We deal with the question, under which circumstances the canonical Noether stress-energy tensor is equivalent to the gravitational (Hilbert) tensor for general matter fields under the influence of gravity. In the framework of general relativity, the full equivalence is established for matter fields that do not couple to the metric derivatives. Spinor fields are included into our analysis by reformulating general relativity in terms of tetrad fields, and the case of Poincaré gauge theory, with an additional, independent Lorentz connection, is also investigated. Special attention is given to the flat limit, focusing on the expressions for the matter field energy (Hamiltonian). The Dirac–Maxwell system is investigated in detail, with special care given to the separation of free (kinetic) and interaction (or potential) energy. Moreover, the stress-energy tensor of the gravitational field itself is briefly discussed.

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