Radial stress in rotating ACKN/KSZ continuations of Einstein-cluster dark matter halos
Abstract
Einstein-cluster dark matter halos have zero radial pressure in the ideal static model. I test whether this property survives the exact finite-spin ACKN/KSZ rotating continuation, whose geodesic and scalar-wave equations are separable. Using the full metric, I require p r = 0 at every polar angle. The condition factorizes and leaves only flat or Schwarzschild seeds. Their rotating members are flat space or Kerr. Thus, a nonvacuum Einstein-cluster seed cannot remain radially pressureless in this class. If the same nonvacuum seed is kept, the rotating metric instead generates a negative radial principal stress, with leading behavior O ( a 2 ). For a relativistic Hernquist halo, I evaluate the ratio | p r |/ ρ h exactly at r = 10 M and a / M = 0.3 . The three published benchmarks give 2.36 × 10 − 3 , 2.27 × 10 − 2 , and 1.23 × 10 − 1 . The weak-halo estimate underpredicts the first two values by about 50%. Therefore, in the ACKN/KSZ class, preserving separability does not preserve the ideal Einstein-cluster matter source.
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BibTeX
@article{fathi2026radial,
title = {{Radial stress in rotating ACKN/KSZ continuations of Einstein-cluster dark matter halos}},
author = {Mohsen Fathi},
journal = {Physics Letters B},
year = {2026},
month = oct,
doi = {10.1016/j.physletb.2026.141077},
url = {https://linkinghub.elsevier.com/retrieve/pii/S0370269326009275},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Radial stress in rotating ACKN/KSZ continuations of Einstein-cluster dark matter halos
AU - Mohsen Fathi
PY - 2026
DA - 2026/10/30
JO - Physics Letters B
DO - 10.1016/j.physletb.2026.141077
UR - https://linkinghub.elsevier.com/retrieve/pii/S0370269326009275
AB - Einstein-cluster dark matter halos have zero radial pressure in the ideal static model. I test whether this property survives the exact finite-spin ACKN/KSZ rotating continuation, whose geodesic and scalar-wave equations are separable. Using the full metric, I require p r = 0 at every polar angle. The condition factorizes and leaves only flat or Schwarzschild seeds. Their rotating members are flat space or Kerr. Thus, a nonvacuum Einstein-cluster seed cannot remain radially pressureless in this class. If the same nonvacuum seed is kept, the rotating metric instead generates a negative radial principal stress, with leading behavior O ( a 2 ). For a relativistic Hernquist halo, I evaluate the ratio | p r |/ ρ h exactly at r = 10 M and a / M = 0.3 . The three published benchmarks give 2.36 × 10 − 3 , 2.27 × 10 − 2 , and 1.23 × 10 − 1 . The weak-halo estimate underpredicts the first two values by about 50%. Therefore, in the ACKN/KSZ class, preserving separability does not preserve the ideal Einstein-cluster matter source.
SN - 0370-2693
SN - 1873-2445
ER -