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The cosmological constant was originally introduced in Einstein's 1917 paper entitled “The cosmological considerations in the General Theory of Reality”. [2] 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 ...
The Einstein field equations (EFE) may be written in the form: [5] [1] + = EFE on a wall in Leiden, Netherlands. where is the Einstein tensor, is the metric tensor, is the stress–energy tensor, is the cosmological constant and is the Einstein gravitational constant.
The second is: ¨ = (+) + which is derived from the first together with the trace of Einstein's field equations (the dimension of the two equations is time −2). a is the scale factor , G , Λ , and c are universal constants ( G is the Newtonian constant of gravitation , Λ is the cosmological constant with dimension length −2 , and c is the ...
where is the Einstein tensor, is the cosmological constant (sometimes taken to be zero for simplicity), is the metric tensor, is a constant, and is the stress–energy tensor. The Einstein field equations relate the Einstein tensor to the stress–energy tensor, which represents the distribution of energy, momentum and stress in the spacetime ...
Einstein's field equations are not used in deriving the general form for the metric: it follows from the geometric properties of homogeneity and isotropy. However, determining the time evolution of a ( t ) {\displaystyle a(t)} does require Einstein's field equations together with a way of calculating the density, ρ ( t ) , {\displaystyle \rho ...
Our results show that about 69% of our universe’s energy is dark energy.They also demonstrate, once again, that Einstein’s simplest form of dark energy – the cosmological constant – agrees ...
In Einstein's theory of general relativity, the Schwarzschild metric (also known as the Schwarzschild solution) is an exact solution to the Einstein field equations that describes the gravitational field outside a spherical mass, on the assumption that the electric charge of the mass, angular momentum of the mass, and universal cosmological constant are all zero.
The de Sitter space is the simplest solution of Einstein's equation with a positive cosmological constant. It is spherically symmetric and it has a cosmological horizon surrounding any observer, and describes an inflating universe. The Schwarzschild solution is the simplest spherically symmetric solution of the Einstein equations with zero ...