Non-relativistic limit of the Mielke–Baekler gravity theory

Patrick Concha; Nelson Merino; Evelyn Rodríguez

doi:10.1140/epjc/s10052-024-12787-6

2023 Impact factor 4.2

Particles and Fields

Open Access

Eur. Phys. J. C (2024) 84: 407
https://doi.org/10.1140/epjc/s10052-024-12787-6

Regular Article - Theoretical Physics

Non-relativistic limit of the Mielke–Baekler gravity theory

Patrick Concha¹^,2^a, Nelson Merino³^,4 and Evelyn Rodríguez¹^,2

¹ Departamento de Matemática y Física Aplicadas, Universidad Católica de la Santísima Concepción, Alonso de Ribera 2850, Concepción, Chile
² Grupo de Investigación en Física Teórica, GIFT, Concepción, Chile
³ Instituto de Ciencias Exactas y Naturales, Universidad Arturo Prat, Playa Brava 3265, 1111346, Iquique, Chile
⁴ Facultad de Ciencias, Universidad Arturo Prat, Avenida Arturo Prat Chacón 2120, 1110939, Iquique, Chile

^a patrick.concha@ucsc.cl

Received: 13 September 2023
Accepted: 10 April 2024
Published online: 21 April 2024

Abstract

In this paper, we present a generalized non-relativistic Chern–Simons gravity model in three spacetime dimensions. We first study the non-relativistic limit of the Mielke–Baekler gravity through a contraction process. The resulting non-relativistic theory contains a source for the spatial component of the torsion and the curvature measured in terms of two parameters, denoted by p and q. We then extend our results by defining a Newtonian version of the Mielke–Baekler gravity theory, based on a Newtonian like algebra which is obtained from the non-relativistic limit of an enhanced and enlarged relativistic algebra. Remarkably, in both cases, different known non-relativistic and Newtonian gravity theories can be derived by fixing the $(p, q)$ $\left( p,q\right)$ parameters. In particular, torsionless models are recovered for $q = 0$ $$q=0$$ .

© The Author(s) 2024

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