What are the limitations of the Einstein field equation?

In summary, the Einstein field equation is a theory of gravitation that is not limited to specific types of matter or non-gravitational fields in a spacetime model. This is seen as both a strength, as it allows for a general theory of gravitation, and a weakness, as it can also allow for solutions that may not align with our current understanding of the universe. To address this, the EFE is often supplemented with energy conditions to restrict the range of possible solutions.
  • #1
aditya23456
114
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what does this statement mean..?actually complete statement is--
" Einstein field equation is not very choosy about what kinds of states of matter or nongravitational fields are admissible in a spacetime model. This is both a strength, since a good general theory of gravitation should be maximally independent of any assumptions concerning nongravitational physics, and a weakness, because without some further criterion, the Einstein field equation admits putative solutions with properties most physicists regard as unphysical, i.e. too weird to resemble anything in the real universe even approximately"
Can anyone please explain it physically
 
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  • #2


Basically, the EFE allows systems of matter which we have never observed. For instance, the EFE are perfectly happy with negative energy density, but since mass has energy that would imply particles with negative mass. Since we have never seen such particles most scientists think that such solutions to the EFE are non-physical.

To avoid this problem, the EFE are usually supplemented with one or more energy conditions which constrain the set of admissible solutions to a set which are more reasonable given the types of matter systems that we know about:

http://en.wikipedia.org/wiki/Energy_condition
 

FAQ: What are the limitations of the Einstein field equation?

What is EFE and how does it relate to gravitational fields?

EFE stands for Einstein's field equations, which are a set of equations that describe the relationship between matter and the curvature of spacetime. In simpler terms, EFE explains how gravity is related to the curvature of spacetime caused by the presence of matter.

Why is EFE not choosy about nongravitational fields?

EFE does not differentiate between gravitational and nongravitational fields because it is a general theory of relativity. This means that it accounts for all types of fields and their effects on spacetime, not just gravity.

What does it mean for a field to be admissible in a spacetime model?

An admissible field in a spacetime model is a field that can be incorporated into the EFE to accurately describe the curvature of spacetime. This includes both gravitational and non-gravitational fields.

Can non-gravitational fields affect the curvature of spacetime?

Yes, according to EFE, all types of fields can affect the curvature of spacetime. This means that the presence of nongravitational fields, such as electromagnetic fields, can also cause spacetime to curve.

How does EFE account for the presence of nongravitational fields in a spacetime model?

EFE includes additional terms in the equations to account for the presence of nongravitational fields, such as the electromagnetic field tensor. These terms allow for a more comprehensive understanding of the relationship between matter, fields, and the curvature of spacetime.

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