Thermal radiation in curved spacetime using influence functional formalism

Generalizing to relativistic exponential scaling and using the theory of noise from quantum fluctuations, it has been shown that one vacuum (Rindler, Hartle-Hawking, or Gibbons-Hawking for the cases of the uniformly accelerated detector, black hole, and de Sitter universe, respectively) can be understood as resulting from the scaling of quantum noise in another vacuum. We explore this idea more generally to establish a flat spacetime and curved spacetime analogy. For this purpose, we start by examining noise kernels for free fields in some well-known curved spacetimes, e.g., the spacetime of a charged black hole, the spacetime of a Kerr black hole, Schwarzschild-de Sitter, Schwarzschild anti-de Sitter, and Reissner-Nordstrom de Sitter spacetimes. Here, we consider a maximal analytical extension for all these spacetimes and different vacuum states. We show that the exponential scale transformation is responsible for the thermal nature of radiation.