Abstract
In this article, we focus on constructing a new family of spatially anisotropic Lifshitz spacetimes with arbitrary dynamical exponent z and constant negative curvature in \(d + 1\) dimensions within the framework of the Einstein–Proca theory with a single vector field. So far, this kind of anisotropic spaces has been constructed with the aid of a set of vector fields. We also consider the spatially isotropic case as a particular limit. The constructed metric tensor depends on the spacetime dimensionality, the critical exponent and the Lifshitz radius; while, the curvature scalar depends just on the number of dimensions. We also obtain a novel spectrum with negative squared mass; we compute the corresponding Breitenlohner–Freedman bound and observe that the found family of spatially anisotropic Lifshitz spaces respects this bound. Hence, these new solutions are stable and can be useful within the gravity/condensed matter theory holographic duality, since the spectrum with negative squared mass is complementary to the positive ones already known in the literature. We also examine the null energy condition and show that it is essentially satisfied along all the boundary directions, i.e., along all directions, except the r one, of our Lifshitz spacetime with the corresponding consistency conditions imposed on the scaling exponents.
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Notes
It is important to note that there is no gauge invariance of the action (10).
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Acknowledgements
The work of AHA was completed at the Aspen Center for Physics, which is supported by National Science Foundation Grant PHY-1607611 and a Simons Foundation Grant as well. He expresses his gratitude to the ACP for providing an inspiring and encouraging atmosphere for conducting part of this research. All authors thank E. Ayón-Beato and U. Nucamendi for fruitful and illuminating discussions. RCF and AHA acknowledge a VIEP-BUAP Grant. RCF, AHA and JMR thank SNI for support. VMZ acknowledges a CONACYT PhD fellowship. UN acknowledges a fellowship granted by PROMEP-SEP and is grateful to SNI-CONACYT for a research assistant Grant. RCF, AHA, VMZ and UN acknowledgments support by a CONACYT Grant No. A1-S-38041.
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Cartas-Fuentevilla, R., Herrera-Aguilar, A., Matlalcuatzi-Zamora, V. et al. Anisotropic Lifshitz holography in Einstein–Proca theory with stable negative mass spectrum. Eur. Phys. J. Plus 135, 155 (2020). https://doi.org/10.1140/epjp/s13360-019-00091-2
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DOI: https://doi.org/10.1140/epjp/s13360-019-00091-2