Tunable Unruh effect: Accelerated detectors in kappa-Rindler vacua

We study the response of an accelerated Unruh-DeWitt detector to a one-parameter family of “kappa Rindler” vacua, which generalize the standard Unruh effect. These states, parametrized by <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>κ</a:mi></a:math>, continuously interpolate between the Rindler (<c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>κ</c:mi><c:mo stretchy="false">→</c:mo><c:mn>0</c:mn></c:math>) and Minkowski (<f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"><f:mi>κ</f:mi><f:mo>=</f:mo><f:mn>1</f:mn></f:math>) vacua. We find the detector registers a perfect thermal bath at a tunable temperature <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"><h:msub><h:mi>T</h:mi><h:mi>κ</h:mi></h:msub><h:mo>=</h:mo><h:mi>κ</h:mi><h:msub><h:mi>T</h:mi><h:mi>U</h:mi></h:msub></h:math>. This result establishes a framework for environments perceived as both “hotter” (<j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"><j:mi>κ</j:mi><j:mo>&gt;</j:mo><j:mn>1</j:mn></j:math>) and “colder” (<l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"><l:mi>κ</l:mi><l:mo>&lt;</l:mo><l:mn>1</l:mn></l:math>) than the standard Unruh temperature. We establish this thermality by demonstrating the Kubo-Martin-Schwinger condition for the Wightman function and by analyzing the associated particle creation process. Furthermore, we visualize the spacetime structure of the created field quanta, revealing an intuitive link between the <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"><n:mi>κ</n:mi></n:math>-controlled symmetry of the modes and the perceived temperature. Our work provides a comprehensive framework for a modulated Unruh effect, bridging formal quantum field theory with clear visual intuition.