Quantum fields on self-similar spacetimes

Abstract We study scalar (not necessarily conformal) quantum fields on self-similar spacetimes. It is shown that in states respecting the self-similarity the expectation value of the stress tensor gives rise to a Lyapunov exponent <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>ω</mml:mi> <mml:mi>q</mml:mi> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:math> , with a leading coefficient which is state-independent and geometric. Three examples for states respecting self-similarity are presented.