Abstract
We generalize the worldline EFT formalism developed in [4–9] to calculate the non-conservative tidal effects on spinning black holes in a long wavelength approximation that is valid to all orders in the magnitude of the spin. We present results for the rate of change of mass and angular momentum in a background field and find agreement with previous calculations obtained by different techniques. We also present new results for both the non-conservative equations of motion and power loss/gain for a binary inspiral, which start at 5PN and 2.5PN order respectively and manifest the Penrose process.
Highlights
Long wavelength dissipative effects due to the internal structure is attributed to the existence of gapless modes localized on the worldline which absorb energy as well as linear and angular momentum from the external environment
In the case of a composite object, the momentum pa(X) and spin Sab(X) are interpreted as ‘composite operators’ which account for the possibility that excitations or de-excitations of the internal modes X can contribute to changes in the linear and angular momenta measured by asymptotic observers
For the torque induced on the black hole by the tidal background, we find from eq (2.20), (3.40)
Summary
We consider how dissipative processes affect the motion of a spinning compact object moving through a fixed background spacetime. We work in the limit R R where object’s radius is R and R is the typical length scale over which the background metric varies (the curvature radius) In this limit, the object may be described by worldline effective field theory [4, 5], with finite size effects encapsulated by local, curvature dependent terms in a generalized point-particle Lagrangian. In order to account for dissipative effects while retaining a point particle description, we employ the framework introduced in [4, 5] and further developed in [6,7,8,9] In this approach, long wavelength dissipative effects due to the internal structure (finite size effects) is attributed to the existence of gapless modes localized on the worldline which absorb energy as well as linear and angular momentum from the external environment. The rotation of the particle relative to fixed inertial frames is encoded in the angular velocity
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