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Fluid interpretation, Hawking-Ellis classification, and energy conditions of the proper kinetic gravity braiding stress tensor

László Árpád Gergely*

  • *Contact author: gergely.laszlo@wigner.hu
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Phys. Rev. D 114, 064064 – Published 16 September, 2026

DOI: https://doi.org/10.1103/wgtj-h9bd

Abstract

We investigate the fluid interpretation of the proper kinetic gravity braiding contribution to the stress tensor of minimally coupled scalar fields for timelike, spacelike, and open-region null scalar gradients. Using a 2+1+1 decomposition adapted to the causal character of the gradient, we derive the effective fluid variables associated with the proper kinetic gravity braiding contribution to the energy-momentum tensor. Unlike k-essence, where timelike scalar gradients generate perfect fluids while spacelike gradients lead to a simpler imperfect-fluid description, the braiding interaction introduces additional heat fluxes and pressure anisotropies. For timelike gradients, these consist of radial and tangential heat fluxes, whereas for spacelike gradients they become a radial heat flux together with mixed radial-tangential pressure anisotropies. These quantities are shown to depend exclusively on the normal fundamental scalars and the two-dimensional accelerations of the decomposition, despite the appearance of the full set of embedding and kinematic variables in the intermediate calculations. For open-region null gradients, the proper kinetic gravity braiding stress tensor has null-dust form. We further determine the Hawking-Ellis algebraic type of the effective stress tensor for all causal classes of the scalar field gradient, obtaining a complete geometrical classification of the effective matter content generated by proper kinetic gravity braiding. The timelike sector is of Type I for positive discriminant, Type II on the nontrivial discriminant hypersurface, and Type IV for negative discriminant. The spacelike sector has the same generic branches but, when the squared radial heat flux equals the squared mixed anisotropy, it also contains additional Type II and Type III degeneracies. The open-region null sector is of Type II for nonvanishing null-dust density, with the zero-density case reducing to the trivial vanishing stress tensor. Finally, the null, weak, dominant, and strong energy conditions further restrict the Type I and generic Type II sectors. The null energy condition already eliminates the Type III and Type IV branches and, in the spacelike gradient sector, every nonzero radial heat flux or mixed radial-tangential anisotropy. Thus, the standard energy conditions require the spacelike proper-braiding stress tensor to be diagonal, while in the timelike sector they bound the total heat flux.

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Phys. Rev. D 114, 064064– Published 16 September, 2026
  • Received 26 April 2021
  • Revised 15 July 2026
  • Accepted 14 August 2026
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