Tidal heating of black holes in Kerr spacetime
For any system of gravitating bodies treated beyond a point particle description, tidal effects may take part in its energetics due to the extended nature of physical bodies involved. Within the domain of Newtonian gravity, tidal forces can perform work on a celestial body which can in turn be converted into heat energy through dissipative processes. In the case of a black hole subjected to time-varying tidal forces, general relativity predicts an increase in its surface area, which in accordance with the first law of black hole thermodynamics, implies changes to its mass and angular momentum parameters. The rates of change of a small black hole's parameters as it orbits a spinning black hole of much greater mass in a circular fashion are calculated for the first time to leading order in the system's mass ratio. Applying these results to idealised astrophysical scenarios, we investigate whether these effects could have any impact on gravitational wave signals detectable by LISA .