• Corpus ID: 253761495

Teleparallel Newton--Cartan gravity

@inproceedings{Schwartz2022TeleparallelNG,
  title={Teleparallel Newton--Cartan gravity},
  author={Philip K Schwartz},
  year={2022}
}
We discuss a teleparallel version of Newton–Cartan gravity. This theory arises as a formal large-speed-of-light limit of the teleparallel equivalent of general relativity ( TEGR ). Thus, it provides a geometric formulation of the Newtonian limit of TEGR , similar to standard Newton–Cartan gravity being the Newtonian limit of general relativity. We show how by a certain gauge-fixing the standard formulation of Newtonian gravity can be recovered. 
1 Citations

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References

SHOWING 1-10 OF 29 REFERENCES

The teleparallel equivalent of Newton–Cartan gravity

We construct a notion of teleparallelization for Newton–Cartan theory, and show that the teleparallel equivalent of this theory is Newtonian gravity; furthermore, we show that this result is

Covariant formulation of the post-1-Newtonian approximation to general relativity

We derive a coordinate-independent formulation of the post-1-Newtonian approximation to general relativity. This formulation is a generalization of the Newton-Cartan geometric formulation of

Bargmann structures and Newton-Cartan theory.

It is shown that Newton-Cartan theory of gravitation can best be formulated on a five-dimensional extended space-time carrying a Lorentz metric together with a null parallel vector field. The

‘Stringy’ Newton–Cartan gravity

We construct a ‘stringy’ version of Newton–Cartan gravity in which the concept of a Galilean observer plays a central role. We present both the geodesic equations of motion for a fundamental string

Minimal gravitational coupling in the Newtonian theory and the covariant Schrödinger equation

The role of the Bargmann group (11-dimensional extended Galilei group) in nonrelativistic gravitation theory is investigated. The generalized Newtonian gravitation theory (Newton-Cartan theory)

Newtonian gravity and the Bargmann algebra

We show how the Newton–Cartan formulation of Newtonian gravity can be obtained from gauging the Bargmann algebra, i.e. the centrally extended Galilean algebra. In this gauging procedure several

Post-Newtonian extension of the Newton - Cartan theory

The theory obtained as a singular limit of general relativity, if the reciprocal velocity of light is assumed to tend to zero, is known to be not exactly the Newton - Cartan theory, but a slight

An Exactly soluble sector of quantum gravity

Cartan's spacetime reformulation of the Newtonian theory of gravity is a generally-covariant Galilean-relativistic limit-form of Einstein's theory of gravity known as the Newton-Cartan theory.

Newton-Cartan Geometry and the Quantum Hall Effect

We construct an effective field theory for quantum Hall states, guided by the requirements of nonrelativistic general coordinate invariance and regularity of the zero mass limit. We propose

Non-relativistic gravity and its coupling to matter

We study the non-relativistic expansion of general relativity coupled to matter. This is done by expanding the metric and matter fields analytically in powers of 1 /c 2 where c is the speed of light.