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Results tagged with general-relativity
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user 228781
A theory that describes how matter interacts dynamically with the geometry of space and time. It was first published by Einstein in 1915 and is currently used to study the structure and evolution of the universe, as well as having practical applications like GPS.
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Confused about the gauge transformation of the amplitude tensor for gravitational waves
Far away from the field sources, where the energy-momentum tensor $$T_{mn}=0 \tag{m,n=0,1,2,3}$$
The linearized EFE becomes $$\Box \bar h_{mn}=0 \tag{1}$$
where $\bar h_{mn}$ is the trace-reverse ten …
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Action & Energy-Momentum Tensor for Matter Fields
Pg 163 of "Tensors, Relativity and Cosmology"
The action integral of a given matter distribution can be written in the form $$I_K=-c\int_\Omega\frac{\rho}{\sqrt{-g}}\frac{ds}{dt}\sqrt{-g} d\Om …
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Schwarzschild Black Holes
Page $190$ of “Tensors, Relativity, and Cosmology”:
Consider a particle falling radially into a black hole with a radial velocity $u^1=dr/ds$. As the particle is falling radially, we have $u^2=u^3 …
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Ricci Curvature Tensor in a static gravitational field (non-relativistic)
Pg 171 of "Tensors, Relativity and Cosmology"
The non-relativistic limit of the metric in a static gravitational field is defined as $$ds^2=\left(1+\frac{2 \phi}{c^2}\right)(dx^0)^2+g_{\alpha \bet …
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What is the name of the formula?
It's called Einstein Field Equation for gravitational fields.
The LHS term $G_{\mu v}$ is the Einstein Tensor
$$G_{\mu v}=R_{\mu v}+\frac{1}{2}g_{\mu v}R$$
which gives information about how the ge …
- 1,047
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Derivation of the geodesic equations
Pg 79 of "Tensors, Relativity and Cosmology"
In order to construct the geodesic equations which define the curve with a stationary arc length, we may choose the arc length itself as the action int …
- 213k
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Christoffel's Symbol's relation to the Metric Tensor
In chapter 9.2 of "Tensors, Relativity and Cosmology", the contracted Christoffel symbol of the second kind as a function of the metric tensor was defined as: $$\Gamma_{nm}^m=\frac{1}{2}\left(g^{mk}\f …
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