Viscosity, entanglement, and acceleration

The Minkowski vacuum in an accelerated frame behaves like a fluid that has not only a finite temperature due to the Unruh effect, but also a finite shear viscosity. Moreover, the ratio of this viscosity to the entropy density exactly satisfies the Kovtun-Son-Starinets bound, inspired by the string theory <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>η</a:mi><a:mo>/</a:mo><a:mi>s</a:mi><a:mo>=</a:mo><a:mn>1</a:mn><a:mo>/</a:mo><a:mn>4</a:mn><a:mi>π</a:mi></a:math>. The origin of this viscosity is purely kinematical and is believed to be related to entanglement introduced by the Rindler horizon. We directly calculate the viscosity, entropy density, and their ratio for massless fields with spins <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mrow><c:mn>1</c:mn><c:mo>/</c:mo><c:mn>2</c:mn></c:mrow></c:math> and 1. We show that locally the ratio of viscosity to entropy density can be below the limiting value <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mn>1</e:mn><e:mo>/</e:mo><e:mn>4</e:mn><e:mi>π</e:mi></e:math> at distances of the order of the thickness of the membrane corresponding to the stretched horizon, and is described by the universal function for different spins. In particular, on the membrane surface <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi>η</g:mi><g:mo>/</g:mo><g:mi>s</g:mi><g:mo>=</g:mo><g:mn>1</g:mn><g:mo>/</g:mo><g:mn>8</g:mn><g:mi>π</g:mi></g:math>.