On General Relativity with Massive Graviton.

摘要

We begin this thesis by studying the properties of horizons in the de Rham-Gabadadze-Tolley model of massive GR.;In massive gravity the generic black hole (BH) solutions on Minkowski space happen to convert horizons into a certain type of singularities. Here we explore whether these singularities can be avoided if space-time is not asymptotically Minkowskian. We find an exact analytic BH solution which evades the above problem by a transition at large scales to self-induced de Sitter (dS) space-time, with the curvature scale set by the graviton mass. The solution demonstrates that in massive GR, in the Schwarzschild coordinate system, a BH metric has to be accompanied by the Stuckelberg fields with nontrivial backgrounds to prevent the horizons to convert into the singularities. We also find an analogous solution for a Reissner-Nordstrom BH on dS space.;The second part concerns with the geometrical construction of massive gravity. Namely, the theory of gravity with an auxiliary extra dimension is known to give a ghost-free cubic completion of the Fierz-Pauli mass term in the decoupling limit. Yet, the theory propagates ghost in quartic order and beyond. Our work proposes a completion of the boundary condition in the auxiliary dimension that avoids ghosts order-by-order in the decoupling limit. Furthermore, we show that the multi-dimensional extension, with the rotationally invariant boundaries of the bulk, is equivalent to the model with a single auxiliary dimension. Therefore, all these constructions require the appropriate adjustment of the boundary condition. The other possible extension of the original model, by the Gauss-Bonnet term, is studied as well.;In the last part we analyze the models known as "gravitational Higgs theories" against instabilities. We show that these models, although seemingly different from the effective field theories of massive gravity, are in fact equivalent to them. We also show the equivalence between the non-covariant mode decomposition used in the Higgs theories, and the covariant Stuckelberg parametrization adopted in the effective field theories, thus, proving that the presence or absence of the ghost is independent of the parametrization used.