Energy, stars, and black holes in Einstein-aether theory

Abstract

In recent years there have been hints of Lorentz violation in various approaches to quantum gravity. Lorentz violating physics has also been proposed as an explanation for unexpected observational anomalies such as atmospheric cosmic rays apparently observed above the GZK cutoff, the flatness of galactic rotation curves and the accelerating expansion of the universe. In this dissertation we will consider an alternative theory of gravity that exhibits Lorentz violation. This ``Einstein-aether" theory is a four parameter class of theories where a dynamical unit timelike vector field (the ``aether") is coupled to gravity. We will focus particularly on energy, stars, and black holes in the theory. First, using pseudotensor methods we find expressions for the Einstein-aether energy. These are then applied to find the energy in both linear and non-linear regimes. Enforcing the energy positivity of linearized wave modes yields an important constraint on the four parameters. An expression for the energy of an asymptotically flat spacetime is also obtained, but a complete positive energy theorem remains elusive. Next, we study in detail non-linear spherically symmetric solutions in the theory. The time independent asymptotically flat solutions fall into two classes depending on whether the aether is aligned with the timelike Killing vector. ``Static" solutions aligned with the Killing vector describe the interior and vacuum regions of fluid stars. We characterize properties such as maximum masses and surface redshifts for candidate neutron star equations of state. Only tentative observational constraints on the theory are currently possible due to uncertainties in neutron star physics. Black hole solutions, which must be non-static, are shown to exist in a class of Einstein-aether theories using numerical integration. The geometry outside the horizon is very similar to the Schwarzschild solution of General Relativity, but there are qualitative differences inside. Finally, we investigate classical two-dimensional Einstein-aether theory as a toy model that could be used to study the Hawking effect and quantization in a Lorentz violating setting. We conclude by examining directions for future research.