Self-force via Green functions and worldline integration

A compact object moving in curved spacetime interacts with its own gravitational field. This leads to both dissipative and conservative corrections to the motion, which can be interpreted as a self-force acting on the object. The original formalism describing this self-force relied heavily on the Green function of the linear differential operator that governs gravitational perturbations. However, because the global calculation of Green functions in non-trivial black hole spacetimes has been an open problem until recently, alternative methods were established to calculate self-force effects using sophisticated regularization techniques that avoid the computation of the global Green function. We present a method for calculating the self-force that employs the global Green function and is therefore closely modeled after the original self-force expressions. Our quantitative method involves two stages: (i) numerical approximation of the retarded Green function in the background spacetime; (ii) evaluation of convolution integrals along the worldline of the object. This novel approach can be used along arbitrary worldlines, including those currently inaccessible to more established computational techniques. Furthermore, it yields geometrical insight into the contributions to self-interaction from curved geometry (back-scattering) and trapping of null geodesics. We demonstrate the method on the motion of a scalar charge in Schwarzschild spacetime. This toy model retains the physical history-dependence of the self-force but avoids gauge issues and allows us to focus on basic principles. We compute the self-field and self-force for many worldlines including accelerated circular orbits, eccentric orbits at the separatrix, and radial infall. This method, closely modeled after the original formalism, provides a promising complementary approach to the self-force problem.Comment: 18 pages, 9 figure

Charge and mass effects on the evaporation of higher-dimensional rotating black holes

To study the dynamics of discharge of a brane black hole in TeV gravity scenarios, we obtain the approximate electromagnetic field due to the charged black hole, by solving Maxwell's equations perturbatively on the brane. In addition, arguments are given for brane metric corrections due to backreaction. We couple brane scalar and brane fermion fields with non-zero mass and charge to the background, and study the Hawking radiation process using well known low energy approximations as well as a WKB approximation in the high energy limit. We argue that contrary to common claims, the initial evaporation is not dominated by fast Schwinger discharge.Comment: Published version. Minor typos corrected. 29 pages, 5 figure