Schwinger--Keldysh worldline effective field theory for quantum black holes: dissipation, noise and decoherence

Abstract

We formulate a Schwinger--Keldysh worldline effective field theory for quantum black holes that treats dissipation, fluctuations, and decoherence within one real-time influence functional. The reduced dynamics is encoded in causal response and symmetric noise kernels. Their spectra obey positivity constraints, while thermal Kubo--Martin--Schwinger symmetry relates them through the fluctuation--dissipation relation. A Hubbard--Stratonovich representation turns the noise kernel into a Gaussian source driving the resolved metric and worldline. For a leading post-Newtonian Schwarzschild binary, direct and metric-mediated stochastic forces combine into the complete relative-acceleration noise at this order, preserve center-of-mass momentum balance, and remain Planck suppressed. The same noise kernel gives the quadrupolar decoherence functional for a supported spatial superposition and reproduces the Danielson--Satishchandran--Wald horizon-induced scaling after absorptive matching. Away from thermal equilibrium, response and noise remain independent matching data. We discuss extensions to microscopic quantum structure in the worldline kernels, matching to spatially extended coarse-grained descriptions, and gravitational splitting.