期刊
GEOMETRIC SCIENCE OF INFORMATION (GSI 2021)
卷 12829, 期 -, 页码 448-455出版社
SPRINGER INTERNATIONAL PUBLISHING AG
DOI: 10.1007/978-3-030-80209-7_49
关键词
Newton-Cartan geometry; Torsion
类别
资金
- Dutch organization FOM/NWO
In this article, the non-relativistic limits of general relativity are discussed, focusing on a special finely tuned limit inspired by string theory. This limit involves adding the kinetic term of a one-form gauge field to the Einstein-Hilbert action, resulting in a finite invariant non-relativistic gravity action. This action allows for an underlying torsional Newton-Cartan geometry, but lacks the Poisson equation for the Newton potential. Extensions to include this equation are mentioned for further research.
We discuss non-relativistic limits of general relativity. In particular, we define a special fine-tuned non-relativistic limit, inspired by string theory, where the Einstein-Hilbert action has been supplemented by the kinetic term of a one-form gauge field. Taking the limit, a crucial cancellation takes place, in an expansion of the action in terms of powers of the velocity of light, between a leading divergence coming from the spin-connection squared term and another infinity that originates from the kinetic term of the one-form gauge field such that the finite invariant non-relativistic gravity action is given by the next sub-leading term. This non-relativistic action allows an underlying torsional Newton-Cartan geometry as opposed to the zero torsion Newton-Cartan geometry that follows from a more standard limit of General Relativity but it lacks the Poisson equation for the Newton potential. We will mention extensions of the model to include this Poisson equation.
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