Relativity Seminar

We consider the effective theory of perturbative quantum gravity coupled to a point particle, quantizing fluctuations of both the gravitational field and the particle's position around flat space. Using a recent relational approach to construct gauge-invariant observables, we compute one-loop graviton corrections to the invariant metric perturbation, whose time-time component gives the Newtonian gravitational potential. The resulting quantum correction consists of two parts: the first stems from graviton loops and agrees with the correction derived by other methods, while the second one is sourced by the quantum fluctuations of the particle's position and energy-momentum, and may be viewed as an analog of a ``Zitterbewegung''. As a check on the computation, we also recover classical corrections which agree with the perturbative expansion of the Schwarzschild metric.

If two particles collide near a rotating black hole, their energy in the center of mass frame E_c.m. can become unbounded under certain conditions. This is the Banados-Silk-West (BSW) effect. We give a brief review and general physical explanation from the geometric and kinematic viewpoints. In doing so, the Killing energy E of debris at infinity remains, in general, restricted. If E is also unbounded, this is called the super-Penrose process. We elucidate when such a process is possible and give full classification of corresponding relativistic objects for rotating space-times. In particular, we show that it is possible for rotating wormholes. The key role in consideration is played by the Wald inequalities. We also discuss briefly the case of a pure electric super-Penrose process near black holes and singularities. It is valid even in the flat space-time.