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  • Letter
  • Open Access

Causality, the Kovtun-Son-Starinets bound, and a novel sum rule for spectral densities

G. Yu. Prokhorov* and O. V. Teryaev†

  • *Contact author: prokhorov@theor.jinr.ru
  • †Contact author: teryaev@jinr.ru
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Phys. Rev. D 114, L081701 – Published 2 October, 2026

DOI: https://doi.org/10.1103/6chf-qxh5

Abstract

We directly show that the local ratio of the shear viscosity to the entropy density for Unruh radiation at a finite distance from the horizon is universal and satisfies the relation η/s=1/(4πcs2), which involves the speed of sound cs. Since cs2≤1 by causality, this establishes the close connection between the famous Kovtun-Son-Starinets bound and causality. Moreover, we show that the ratio of bulk to shear viscosity saturates another well-known bound for the bulk viscosity, predicted within holographic approach. We also show that the condition of isotropy of thermal radiation in the Rindler space leads to a novel sum rule relating the c(0)(μ) and c(2)(μ) spectral densities, generally considered as independent objects, and we explicitly demonstrate its validity for conformal field theory and free massive Dirac fields in any number of dimensions. The sum rule provides the validity of Pascal law and bears some similarity with Burkhardt-Cottingham sum rule for spin-dependent parton distributions. Our result suggests a new perspective on dissipative transport phenomena in media undergoing extreme acceleration, such as quark-gluon plasma created in relativistic heavy-ion collisions.

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Outline

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Phys. Rev. D 114, L081701– Published 2 October, 2026
  • Received 8 July 2026
  • Accepted 11 September 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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