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Static spherically symmetric Kundt vacuum solutions of higher-derivative gravities

Breno L. Giacchini1,*, Ivan Kolář1,†, Vojtěch Pravda2,‡, and Alena Pravdová2,§

  • *Contact author: breno.giacchini@matfyz.cuni.cz
  • †Contact author: ivan.kolar@matfyz.cuni.cz
  • ‡Contact author: pravda@math.cas.cz
  • §Contact author: pravdova@math.cas.cz
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Phys. Rev. D 114, 084036 – Published 14 October, 2026

DOI: https://doi.org/10.1103/zjk9-vxqd

Abstract

We study static spherically symmetric Kundt solutions to the vacuum field equations of quadratic gravity with a cosmological constant, as well as specific models of six-derivative gravity. In quadratic gravity, we identify all solutions for coupling constants satisfying α≠3β, while the case α=3β is studied using the Frobenius method, where we derive the recurrence relations for the power series. In contrast, in six-derivative gravity, we focus on selected models to illustrate the variety of closed-form solutions; we also analyze possible indicial families of Frobenius solutions. For all solutions, we analyze curvature singularities and their accessibility to geodesic observers. We then construct exact gravitational-wave solutions propagating on some of these backgrounds in quadratic and six-derivative gravity. It is known that in Einstein gravity, gravitational waves on the Nariai background unavoidably contain singularities, which are interpreted as physical sources generating these gravitational waves. In contrast, in addition to singular solutions, for appropriate values of the coupling constants, higher-order gravities allow for globally smooth solutions representing gravitational waves.

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See Also

Black holes and other spherical solutions in quadratic gravity with a cosmological constant

V. Pravda, A. Pravdová, J. Podolský, and R. Švarc
Phys. Rev. D 103, 064049 (2021)

Article Text

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Information

Phys. Rev. D 114, 084036– Published 14 October, 2026
  • Received 18 May 2026
  • Accepted 16 September 2026
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