Anisotropic Domain Walls and Cosmologies

Abstract

We investigate anisotropic domain wall and cosmological solutions in D-dimensional gravitational theories of arbitrary spacetime signature coupled to scalar fields with a scalar potential. We identify a class of scalar potentials for which the second-order equations of motion admit a first-order formulation. The associated bosonic flows allow non-trivial Ricci-flat worldvolumes, while their Killing-spinor realization further requires the worldvolume to admit a non-vanishing parallel spinor. Five-dimensional cal N=2 gauged supergravity provides a concrete realization of this construction, with the worldvolume geometry determined by its signature and giving rise to pp-wave, hyper-Kähler, and hypersymplectic geometries. We further construct a general class of anisotropic solutions depending on a single variable, with the anisotropy encoded in a constant traceless matrix. A particular branch arises when a subset of scalar fields contribute through their kinetic terms but do not enter the scalar potential; these fields follow geodesics on the scalar manifold. As an explicit application, we recover the Kasner-dilaton-AdS solutions and show that, in the appropriate limit, they satisfy the first-order flow equations.

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BibTeX RIS

BibTeX

@misc{sabra2026anisotropic,
  title = {{Anisotropic Domain Walls and Cosmologies}},
  author = {W. A. Sabra},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.03397},
  eprint = {2610.03397},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.03397},
  note = {CC BY 4.0},
}

RIS

TY  - UNPB
TI  - Anisotropic Domain Walls and Cosmologies
AU  - W. A. Sabra
PY  - 2026
DA  - 2026/10/02
PB  - arXiv
DO  - 10.48550/arxiv.2610.03397
UR  - https://arxiv.org/abs/2610.03397
AB  - We investigate anisotropic domain wall and cosmological solutions in D-dimensional gravitational theories of arbitrary spacetime signature coupled to scalar fields with a scalar potential. We identify a class of scalar potentials for which the second-order equations of motion admit a first-order formulation. The associated bosonic flows allow non-trivial Ricci-flat worldvolumes, while their Killing-spinor realization further requires the worldvolume to admit a non-vanishing parallel spinor. Five-dimensional cal N=2 gauged supergravity provides a concrete realization of this construction, with the worldvolume geometry determined by its signature and giving rise to pp-wave, hyper-Kähler, and hypersymplectic geometries. We further construct a general class of anisotropic solutions depending on a single variable, with the anisotropy encoded in a constant traceless matrix. A particular branch arises when a subset of scalar fields contribute through their kinetic terms but do not enter the scalar potential; these fields follow geodesics on the scalar manifold. As an explicit application, we recover the Kasner-dilaton-AdS solutions and show that, in the appropriate limit, they satisfy the first-order flow equations.
ER  -

Abstract

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