Black holes in Einstein-aether theory

Abstract

We study black hole solutions in general relativity coupled to a unit timelike vector field dubbed the "aether". To be causally isolated a black hole interior must trap matter fields as well as all aether and metric modes. The theory possesses spin-0, spin-1, and spin-2 modes whose speeds depend on four coupling coefficients. We find that the full three-parameter family of local spherically symmetric static solutions is always regular at a metric horizon, but only a two-parameter subset is regular at a spin-0 horizon. Asymptotic flatness imposes another condition, leaving a one-parameter family of regular black holes. These solutions are compared to the Schwarzschild solution using numerical integration for a special class of coupling coefficients. They are very close to Schwarzschild outside the horizon for a wide range of couplings, and have a spacelike singularity inside, but differ inside quantitatively. Some quantities constructed from the metric and aether oscillate in the interior as the singularity is approached. The aether is at rest at spatial infinity and flows into the black hole, but differs significantly from the the 4-velocity of freely-falling geodesics.

Radiation damping in Einstein-aether theory

“…Additional tests of ae-theory can come from the study of stellar solutions and black holes, begun in [15,16], and from the "ultimate" test [7] provided by observations of binary pulsar systems. This work begins that examination with a calculation of the generation of gravityaether radiation by a nearly Newtonian source and the subsequent energy loss, or radiation damping, of the source.…”

Post-Newtonian parameters in the tensor-vector-scalar theory

“…It is also important to investigate neutron stars or black holes. In Einstein-Aether theory, these features are investigated and show interesting differences from the case in general relativity [18,19,20]. As for TeVeS, black holes have been investigated only for the cases where the scalar field diverges at the horizon [8,13] or the scalar field is constant [16].…”

“…We notice that τ αβ disappears to O(1). From (3.1), we obtain 19) to O(2). Thus, this term also disappears to O(1).…”

White holes in Einstein-aether theory

“…Einstein-aether theory contains four free parameters, c 1 , c 2 , c 3 and c 4 representing coefficients of different terms in the action. In [6] black hole solutions were found for certain ranges of the parameters; however, it was found that when c 1 was sufficiently large the method did not find black hole solutions.…”

“…For Einstein-aether theory, both of these approaches have been used. [6][7][8] The approach of [6] was to assume a static, spherically symmetric spacetime with an event horizon. These assumptions reduced the field equations of the theory to a set of coupled ordinary differential equations (for the fields as a function of the radial coordinate) which satisfied an appropriate set of boundary conditions (smoothness at the horizon and asymptotic flatness at infinity).…”