Abstract
In the present work we find novel Newtonian gravity models in three space-time dimensions. We first present a Maxwellian version of the extended Newtonian gravity, which is obtained as the non-relativistic limit of a particular U(1)-enlargement of an enhanced Maxwell Chern-Simons gravity. We show that the extended Newtonian gravity appears as a particular sub-case. Then, the introduction of a cosmological constant to the Maxwellian extended Newtonian theory is also explored. To this purpose, we consider the non-relativistic limit of an enlarged symmetry. An alternative method to obtain our results is presented by applying the semigroup expansion method to the enhanced Nappi-Witten algebra. The advantages of considering the Lie algebra expansion procedure is also discussed.
Highlights
The dual version of the Maxwell symmetry, denoted as Hietarinta-Maxwell [52], allowed to recover the topological and minimal massive gravity theories. Both of these massive gravity theories appear as particular cases of a more general massive gravity arising from a spontaneous breaking of a local symmetry in a CS gravity theory invariant under the Hietarinta-Maxwell algebra [53]
We show that the new NR algebra can be seen as an enlargement of the extended Newtonian algebra [36] and reproduces the Maxwellian extended Newtonian (MENt) algebra (4.3)–(4.4) in the vanishing cosmological constant limit → ∞
In this work we have presented a Maxwellian version of the three-dimensional extended Newtonian gravity theory introduced in [36]
Summary
We briefly review the three-dimensional relativistic Maxwell CS gravity [77,78,79,80,81] and its generalization to the so-called AdS-Lorentz gravity [82,83,84]. Considering the gauge connection one-form (3.9) and the non-vanishing components of the invariant tensor (3.6) and (3.8) in the general expression of the CS action (2.6), we find the following relativistic CS action for the [enhanced Maxwell] ⊕ u (1) algebra:. The relativistic algebra seems simpler in the form of three copies of the Poincare algebra (3.13), we shall consider the basis {JA, PA, ZA, SA, TA, VA} since it allows to establish a well-defined and evident vanishing cosmological constant limit → ∞ reproducing the enhanced Maxwell algebra. Considering the gauge connection one-form for the enhanced algebra which coincides with the Maxwell one (3.9) and the non-vanishing components of the invariant tensor (3.6), (3.18), and (3.8) in the general expression of the CS action (2.6), we find the following relativistic CS action for the [enhanced AdS-L] ⊕ u (1) algebra:. The presence of the U(1) gauge fields will be essential to establish a well-defined NR limit allowing us to accommodate a cosmological constant into the Maxwellian version of the extended Newtonian gravity
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