Alexander A. H. Graham

Stationary black holes with time-dependent scalar fields

It has been well known since the 1970s that stationary black holes do not generically support scalar hair. Most of the no-hair theorems which support this depend crucially upon the assumption that the scalar field has no time dependence. Here we fill in this omission by ruling out the existence of stationary black hole solutions even when the scalar field may have time dependence. Our proof is fairly general, and in particular applies to noncanonical scalar fields and certain nonasymptotically flat spacetimes. It also does not rely upon the spacetime being a black hole.

General Dynamics of Varying-Alpha Universes

We introduce and study extensions of the varying alpha theory of Bekenstein-Sandvik-Barrow-Magueijo to allow for an arbitrary coupling function and self-interaction potential term in the theory. We study the full evolution equations without assuming that variations in alpha have a negligible effect on the expansion scale factor and the matter density evolution, as was assumed in earlier studies. The background FRW cosmology of this model in the cases of zero and non-zero spatial curvature is studied in detail, using dynamical systems techniques, for a wide class of potentials and coupling functions. All the asymptotic behaviours are found, together with some new solutions. We study the cases where the electromagnetic parameter, zeta, is positive and negative, corresponding to magnetic and electrostatic energy domination in the non-relativistic matter. In particular, we investigate the cases where the scalar field driving alpha variations has exponential and power-law self-interaction potentials and the behaviour of theories where the coupling constant between matter and alpha variations is no longer a constant. PACS numbers: 98.80.Es, 98.80.Bp, 98.80.Cq

On algebraically special vacuum spacetimes in five dimensions

Vacuum solutions admitting a hypersurface-orthogonal repeated principal null direction are an important class of 4D algebraically special spacetimes. We investigate the 5D analogues of such solutions: vacuum spacetimes admitting a hypersurface-orthogonal multiple Weyl aligned null direction (WAND). Such spacetimes fall into four families determined by the rank of the 3 × 3 matrix that defines the expansion and shear of the multiple WAND. The rank 3 and rank 0 cases have been studied previously. We investigate the two remaining families. We show how to define coordinates which lead to a considerable simplification of the Einstein equation with cosmological constant. The rank 2 case gives warped product and Kaluza–Klein versions of the 4D Robinson–Trautman solutions as well as some new solutions. The rank 1 case gives product, or analytically continued Schwarzschild, spacetimes.

Non-Existence of Black Holes with Non-Canonical Scalar Fields

We study the existence of stationary black holes with a non-canonical scalar field as a matter source. We prove a simple black hole no-hair theorem which rules out the existence of asymptotically flat black holes which are static or stationary and axisymmetric possessing scalar hair for a wide class of non-canonical scalar field theories. This applies to scalar field theories which are of the form of K-essence theories. In particular, we rule out the existence of such black holes in the ghost condensate model, and in large sectors of the Dirac-Born-Infeld model.

New Singularities in Unexpected Places

Spacetime singularities have been discovered which are physically much weaker than those predicted by the classical singularity theorems. Geodesics evolve through them and they only display infinities in the derivatives of their curvature invariants. So far, these singularities have appeared to require rather exotic and unphysical matter for their occurrence. Here, we show that a large class of singularities of this form can be found in a simple Friedmann cosmology containing only a scalar-field with a power-law self-interaction potential. Their existence challenges several preconceived ideas about the nature of spacetime singularities and has an impact upon the end of inflation in the early universe.

Nonexistence of black holes with noncanonical scalar fields

We study the existence of stationary black holes with a non-canonical scalar field as a matter source. We prove a simple black hole no-hair theorem which rules out the existence of asymptotically flat black holes which are static or stationary and axisymmetric possessing scalar hair for a wide class of non-canonical scalar field theories. This applies to scalar field theories which are of the form of K-essence theories. In particular, we rule out the existence of such black holes in the ghost condensate model, and in large sectors of the Dirac-Born-Infeld model.

Varying-alpha and K-essence

We introduce a model which allows the fine structure constant (alpha) to vary throughout space and time due to a coupling to a scalar field with a non-canonical kinetic structure. This provided a new extension of the Bekenstein-Sandvik-Barrow-Magueijo model of alpha variations. The background cosmology is studied in detail using dynamical systems techniques for a scalar field of ghost condensate type. We show generically that if the kinetic terms are chosen to allow an accelerated late-time attractor for the expansion scale factor then alpha will not asymptote to a constant at late times.

No-Hair Theorems in K-Essence Theories

We study the existence of stationary black holes with a non-canonical scalar field as a matter source. We prove a simple black hole no-hair theorem which rules out the existence of asymptotically flat black holes which are static or stationary and axisymmetric possessing scalar hair for a wide class of non-canonical scalar field theories. This applies to scalar field theories which are of the form of K-essence theories. In particular, we rule out the existence of such black holes in the ghost condensate model, and in large sectors of the Dirac-Born-Infeld model.

Varying-αand K-essence

We introduce a model which allows the fine structure constant (alpha) to vary throughout space and time due to a coupling to a scalar field with a non-canonical kinetic structure. This provided a new extension of the Bekenstein-Sandvik-Barrow-Magueijo model of alpha variations. The background cosmology is studied in detail using dynamical systems techniques for a scalar field of ghost condensate type. We show generically that if the kinetic terms are chosen to allow an accelerated late-time attractor for the expansion scale factor then alpha will not asymptote to a constant at late times.

Varying-α and K-essence

We introduce a model which allows the fine structure constant (alpha) to vary throughout space and time due to a coupling to a scalar field with a non-canonical kinetic structure. This provided a new extension of the Bekenstein-Sandvik-Barrow-Magueijo model of alpha variations. The background cosmology is studied in detail using dynamical systems techniques for a scalar field of ghost condensate type. We show generically that if the kinetic terms are chosen to allow an accelerated late-time attractor for the expansion scale factor then alpha will not asymptote to a constant at late times.