On the naturalness of Einstein's equation
نویسندگان
چکیده
We compute all 2-covariant tensors naturally constructed from a semiriemannian metric g which are divergence-free and have weight greater than −2. As a consequence, it follows a characterization of the Einstein tensor as the only, up to a constant factor, 2-covariant tensor naturally constructed from a semiriemannian metric which is divergence-free and has weight 0 (i.e., is independent of the unit of scale). Since these two conditions are also satisfied by the energy-momentum tensor of a relativistic space-time, we discuss in detail how these theorems lead to the field equation of General Relativity.
منابع مشابه
Spacetimes admitting quasi-conformal curvature tensor
The object of the present paper is to study spacetimes admitting quasi-conformal curvature tensor. At first we prove that a quasi-conformally flat spacetime is Einstein and hence it is of constant curvature and the energy momentum tensor of such a spacetime satisfying Einstein's field equation with cosmological constant is covariant constant. Next, we prove that if the perfect flui...
متن کاملNaturalness Mapping of Fereydounshahr County with Respect to Ecotourism, Using Ordered Weighted Averaging Operator
The importance of the economic aspect of tourism usually overshadow many natural tourism destinations. Fereydounshahr county in Isfahan province, with pristine mountainous landscapes and diverse natural features, has high potential to attract many tourists. However, pristineness over much of its area suggests limiting the public access based on the degree of naturalness. Hence, the aim of this ...
متن کاملبررسی دو شاخص کمی کردن الگوهای چشمانداز با استفاده از RS و GIS در منطقه حفاظت شده موته
Landscape ecology as a modern interdisciplinary science offers new concepts, theories, and methods for land evaluation and management. One main part of landscape ecology is describing patterns in the landscape and interpreting the ecological effects of these patterns on flora, fauna, flow of energy and materials. Landscape studies require methods to identify and quantify spatial patterns of lan...
متن کاملScrutiny of Einstein's Geodesic and Field Equations
Since its final version and publication in 1916, it is widely reported in several specialized textbooks and research articles that General Relativity theory reduces to Newton's theory of gravity in the limit of a weak gravitational field and slowly moving material bodies. In the present paper, the so-called reducibility of Einstein's geodesic and field equations, to Newton's equation of motion ...
متن کامل