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Results tagged with general-relativity
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user 226902
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.
2
votes
Is special relativity a special case of general relativity, qualitatively?
Imagine you have a surface, and locally you approximate the surface by the tangent plane. The surface may be curved, but locally you may think it is flat (if you are a small animal walking on the surf …
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1
vote
What is "special" and what is "general" in Relativity?
I see three main points for why SR is "special" (i.e., less general) than GR.
1 - SR can be seen as a special case of GR, where you have a fixed (i.e. non-dynamical) and flat spacetime. This is slight …
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1
vote
Accepted
Axially symmetric metric
The article Axially symmetric spacetimes: numerical and analytical perspectives is a very nice reference and treats axially symmetric spacetimes in generality, showing how to construct the "cylindrica …
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4
votes
$F = ma$ In General Relativity
Newton's law $F = m a$ is valid only when one is in an inertial frame of reference. In a non-inertial frame you have $F = m (a+a_{fr})$, where $-m a_{fr}$ is a "fictitious force" and $F$ is a "genuin …
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2
votes
Accepted
What is the source of the perturbation $h_{\mu\nu}$ in linearized Einstein field equations i...
1 - What exactly is the $T_{\mu \nu}$ here; is it the energy-momentum tensor of the source (say a neutron star which is emitting gravitational waves)?
Yes.
2 - Now if $T_{\mu \nu}=0$, then does that m …
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1
vote
Is simultaneity well-defined in general relativity?
"Simultaneity" has a well-defined technical meaning in SR, as well as in GR.
What I am referring to is the "Einstein’s convention for the definition of simultaneity", namely the set of events that are …
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3
votes
Stress-energy tensor components for a perfect fluid
Consider your stress-energy tensor:
$$
T_{\mu\nu}=(\rho+p)U_{\mu}U_{\nu}-p g_{\mu\nu}
$$
This is a legit tensor written in terms of other tensors (the scalar fields $\rho$ and $p$, the metric and the …
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0
votes
Question on Tolman-Oppenheimer-Volkoff (TOV) equation for time-dependent spacetimes
The TOV equations apply when you have a static, spherically symmetric spacetime (they describe the hydrostatic equilibrium): they are derived from the Einstein equations under the assumption of static …
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2
votes
Einstein's field equations in (1+1) spacetime?
Note: present answers are already very good, here I complement them with some references. See also the question General relativity (gravitation) in time and one spatial dimension and Einstein tensor …
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17
votes
Accepted
Do the Einstein Field Equations force the metric to be Lorentzian?
The Einstein equations alone do not enforce any particular signature. For example, in the derivation of the Schwarzschild metric you require that the metric is asymptotically flat... but not just any …
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