Black hole mass dynamics and renormalization group evolution

Understand

We examine the real-time dynamics of a system of one or more black holes interacting with long wavelength gravitational fields.

• We find that the (classical) renormalizability of the effective field theory that describes this system necessitates the introduction of a time dependent mass counterterm, and consequently the mass parameter must be promoted to a dynamical degree of freedom.
• To track the time evolution of this dynamical mass, we compute the expectation value of the energy-momentum tensor within the in-in formalism, and fix the time dependence by imposing energy-momentum conservation.
• Mass renormalization induces logarithmic ultraviolet divergences at quadratic order in the gravitational coupling, leading to a new time-dependent renormalization group (RG) equation for the mass parameter.