Lorentz Symmetric Aether and Its Accretion Onto Black Holes

Finding a consistent formulation of Lorentz-invariant massive gravity, with the right number of five degrees of freedom has been a long-standing problem in theoretical physics. A two-parameter family of candidate models has been recently proposed by de Rham, Gabadadze, and Tolley who provided considerable evidence for the absence of any extra degree of freedom. Meanwhile, it has been shown that massive gravity can be thought of as a generally covariant theory of a medium described by four scalar fields -- the aether . In the first part of the thesis, I study this theory of four scalar fields and show that de Rham-Gabadadze-Tolley massive gravity is the unique theory in which one of the scalar fields remains non-dynamical, and the full gravitational theory propagates five degrees of freedom, thereby proving the conjecture.;The second part of the thesis deals with black holes in massive electrodynamics and massive gravity. In particular, the sense in which black hole solutions approach their counterparts in massless theories as the photon (graviton) mass is taken to zero. I will introduce and calculate the discharge mode for a Schwarzschild black hole in massive electrodynamics. For small photon mass, the discharge mode describes the decay of the electric field of a charged star collapsing into a black hole. I will then argue that a similar ``discharge of mass'' occurs in massive gravity and leads to a process of black hole disappearance. The zero-mass limit is, nevertheless, smooth in that the discharge (disappearance) rate vanishes in the limit: it scales as m2rg where m is the photon (graviton) mass and rg is the Schwarzschild radius of the black hole.