If the energy–momentum tensor T μν is that of an electromagnetic field in free space, i.e. if the electromagnetic stress–energy tensor = (+) is used, then the Einstein field equations are called the Einstein–Maxwell equations (with cosmological constant Λ, taken to be zero in conventional relativity theory): + = (+).
了解详细信息：If the energy–momentum tensor T μν is that of an electromagnetic field in free space, i.e. if the electromagnetic stress–energy tensor = (+) is used, then the Einstein field equations are called the Einstein–Maxwell equations (with cosmological constant Λ, taken to be zero in conventional relativity theory): + = (+).
en.wikipedia.org/wiki/Einstein_field_equationsThe cosmological constant term in the Einstein field equations (Λg µν) allows us to incorporate things like dark energy into our models of gravity and cosmology.
profoundphysics.com/derivation-of-einstein-field-eq…You can solve the Einstein Field Equations for an expanding universe with no cosmological constant which are $$R_{μν}- \frac{1}{2}g_{μν}R = \frac{8πG}{c^4}T_{μν}$$ Where T_μν is the stress-energy tensor i was talking about.
physics.stackexchange.com/questions/484339/fiel…In cosmology, the cosmological constant (usually denoted by the Greek capital letter lambda: Λ), alternatively called Einstein's cosmological constant, is a coefficient that Albert Einstein initially added to his field equations of general relativity.
en.wikipedia.org/wiki/Cosmological_constantEinstein modi ed his Field equation in order to provide a static universe. He introduced the term as cosmological constant G + g = 8ˇT (31) A nonzero value of no longer results in the vanishing of G in vacuum. I will not elaborate on the cosmological constant, but give an (simple) application of the Einstein equations in cosmology.
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If the energy–momentum tensor Tμν is that of an electromagnetic field in free space, i.e. if the electromagnetic stress–energy tensor $${\displaystyle T^{\alpha \beta }=\,-{\frac {1}{\mu _{0}}}\left({F^{\alpha }}^{\psi }{F_{\psi }}^{\beta }+{\tfrac {1}{4}}g^{\alpha \beta }F_{\psi \tau }F^{\psi \tau }\right)}$$ is used, then the Einstein … 展开
In the general theory of relativity, the Einstein field equations (EFE; also known as Einstein's equations) relate the geometry of spacetime to the distribution of matter within it.
The equations were … 展开The Einstein field equations (EFE) may be written in the form:
$${\displaystyle G_{\mu \nu }+\Lambda g_{\mu \nu }=\kappa T_{\mu \nu }}$$
where $${\displaystyle G_{\mu \nu }}$$ is the Einstein tensor, $${\displaystyle g_{\mu \nu }}$$ 展开If the energy–momentum tensor Tμν is zero in the region under consideration, then the field equations are also referred to as the vacuum field equations. By setting Tμν = 0 in the trace … 展开
Despite the EFE as written containing the inverse of the metric tensor, they can be arranged in a form that contains the metric tensor in polynomial form … 展开
In the Einstein field equations $${\displaystyle G_{\mu \nu }+\Lambda g_{\mu \nu }=\kappa T_{\mu \nu }\,,}$$ the term containing the cosmological constant Λ was absent from the … 展开
The nonlinearity of the EFE makes finding exact solutions difficult. One way of solving the field equations is to make an approximation, namely, … 展开
CC-BY-SA 许可证中的维基百科文本 Einstein Field Equations: A Step-By-Step Derivation …
The cosmological constant term in the Einstein field equations (Λg µν) allows us to incorporate things like dark energy into our models of gravity and cosmology.
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general relativity - Field equations with cosmological constant ...
2019年6月5日 · You can solve the Einstein Field Equations for an expanding universe with no cosmological constant which are $$R_{μν}- \frac{1}{2}g_{μν}R = \frac{8πG}{c^4}T_{μν}$$ …
Cosmological constant - Wikipedia
The cosmological constant was originally introduced in Einstein's 1917 paper entitled “The cosmological considerations in the General Theory of Reality”. Einstein included the cosmological constant as a term in his field equations for general relativity because he was dissatisfied that otherwise his equations did not allow for a static universe: gravity would cause a universe that was initially non-expanding to contract. To counteract this possibility, Einstein added the cosmologic…
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Einstein modi ed his Field equation in order to provide a static universe. He introduced the term as cosmological constant G + g = 8ˇT (31) A nonzero value of no longer results in the vanishing …
All About the Einstein Field Equations - Physics Forums
2024年2月26日 · The Einstein Field Equations (EFE) are a set of ten interrelated differential equations that form the core of Einstein’s general theory of relativity. These equations describe …
Einstein’s solution was to modify what we call the Einstein eld equations | the equations that describe how gravitational elds, in the form of spacetime curvature, are created by matter. He …
Einstein's Field Equations | Core Concepts, Applications …
2024年5月28日 · Λ is the cosmological constant, which Einstein introduced to account for a static universe, and g μν is the metric tensor describing the geometry of spacetime. G and c stand for Newton’s gravitational constant and …
Einstein Field Equations – Gaurav Tiwari
2023年1月8日 · Mathematical form of the Einstein field equations. We can write the Einstein field equations in the following form: G μν + Λg μν = κT μν. Here, G μν is the Einstein tensor, Λ is the cosmological constant, g μν is the metric …
4.1.2 The Cosmological Constant We motivated the Einstein-Hilbert action as the simplest term we could write down. While it’s true that it’s the simplest term that results in interesting …
Einstein Field Equation with or without Cosmological Constant …