The Bach-flat and conformally Einstein equations for Siklos spacetimes

[1] Abbena, E., Garbiero, S. and Salamon, S. (2013). Bach-Flat Lie groups in dimension 4. C. R. Math. Acad. Sci. Paris 351, 303{306. https://doi.org/10.48550/arXiv.1303.4527.

[2] Almansi, E. (1898). sull'integrazione dell'equazione di erenziale
2n = 0. Annali di Matematica, tomo II, serie III.

[3] Brinkmann, HW. (1924). Riemann spaces conformal to Einstein spaces. Math. Ann. 91, 269{278. https://doi.org/10.1007/BF01556083.

[4] Calvaruso, G. (2019). Siklos spacetimes as homogeneous Ricci solitons. Class. Quantum Grav., 36, 095011, 13pp. https://doi.org/10.1088/1361-6382/ab10f6.

[5] Calvaruso, G. (2020). Conformally  flat Siklos metrics are Ricci solitons. Axioms, 9(64). https://doi.org/10.3390/axioms9020064.

[6] Calvaruso, G. (2021). Solutions of the Ricci soliton equation for a large class of Siklos spacetimes. Int. J. Geom. Meth. Mod. Phys., 18, 2150052, 19pp. https://doi.org/10.1142/S0219887821500523.

[7] Calvino-Louzao, E., Garcia-Rio, E., Gutierrez-Rodriguez, I., and Vazquez-Lorenzo, R. (2017). Conformal geometry of non-reductive four-dimensional homogeneous spaces. Math. Nachr., 290, 1470{1490. https://doi.org/10.1002/mana.201600099.

[8] Calvino-Louzao, E., Garcia-Martinez, X., Garcia-Rio, E., Gutierrez-Rodriguez, I., and Vazquez-Lorenzo, R. (2019). Conformally Einstein and Bach-flat four-dimensional homogeneous manifolds. J. Math. Pures Appl., 130, 347{374.
https://doi.org/10.1016/j.matpur.2019.01.005.

[9] Gover, AR., and Nurowski, P. (2006). Obstructions to conformally Einstein metrics in n dimensions. Jour. Geom. Phys. 56(3), 450{484, https://doi.org/10.1016/j.geomphys.2005.03.001.

[10] Kozameh, CN., Newman, ET., and Tod, KP. (1985). Conformal Einstein spaces. Gen. Rel. Grav. 17, 343{352, https://doi.org/10.1007/BF00759678.

[11] Mohseni, M. (2018). Vacuum polarization in Siklos spacetimes. Phys. Rev. D 97, 024006, 6 pp, https://doi.org/10.1103/PhysRevD.97.024006.

[12] Ozsvath, I., Robinson, I., and Rozga, K. (1985). Plane-fronted gravitational and electromagnetic waves in spaces with cosmological constant. J. Math. Phys., 26, 1755{1761.

[13] Podolski, J. (1998). Interpretation of the Siklos solutions as exact gravitational waves in the anti-de Sitter universe. Class. Quantum Grav. 15,719{733, https://iopscience.iop.org/article/10.1088/0264-9381/15/3/019.

[14] Siklos, STC. (1985). Lobatchevski plane gravitational waves, in Galaxies, axisymmetric systems and relativity. Ed. M.A.H. MacCallum, page 247, Cambridge University Press, Cambridge.