Vanishing Energy Momentum Tensor Research Articles

Spacetimes dressed with stealth electromagnetic fields

Stealth field configurations by definition have a vanishing energy-momentum tensor, thus do not contribute to the gravitational field equations. While only trivial fields can be stealth in Maxwell's electrodynamics, nontrivial stealth fields appear in some nonlinear models of electromagnetism. We find the necessary and sufficient conditions for the electromagnetic fields to be stealth and analyse which models admit such configurations. Furthermore, we present some concrete exact solutions, featuring a class of black holes dressed with the stealth electromagnetic hair, closely related to force-free solutions. Stealth hair does not alter the generalized Smarr formula, but may contribute to the Komar charges.

On symmetry inheritance of nonminimally coupled scalar fields

We present the first symmetry inheritance analysis of fields non-minimally coupled to gravity. In this work we are focused on the real scalar field ϕ with nonminimal coupling of the form . Possible cases of symmetry noninheriting fields are constrained by the properties of the Ricci tensor and the scalar potential. Examples of such spacetimes can be found among those which are ‘dressed’ with the stealth scalar field, a nontrivial scalar field configuration with the vanishing energy–momentum tensor. We classify the scalar field potentials which allow symmetry noninheriting stealth field configurations on top of the exact solutions of the Einstein’s gravitational field equation with the cosmological constant.

On classical and semiclassical properties of the Liouville theory with defects

The Lagrangian of the Liouville theory with topological defects is analyzed in detail and general solution of the corresponding defect equations of motion is found. We study the heavy and light semiclassical limits of the defect two-point function found before via the bootstrap program. We show that the heavy asymptotic limit is given by the exponential of the Liouville action with defects, evaluated on the solutions with two singular points. We demonstrate that the light asymptotic limit is given by the finite-dimensional path integral over solutions of the defect equations of motion with a vanishing energy–momentum tensor.

Spherically symmetric self-dual Yang-Mills instantons on curved backgrounds in all even dimensions

We present several different classes of self-dual Yang-Mills instantons in all even $d$-dimensional backgrounds with Euclidean signature. In $d=4p+2$ the only solutions we found are on constant curvature dS (de Sitter) and AdS (anti\char21{}de Sitter) backgrounds and are evaluated in closed form. In $d=4p$ an interesting class of instantons are given on black hole backgrounds. One class of solutions are (Euclidean) time-independent and spherically symmetric in $d\ensuremath{-}1$ dimensions, and the other class are spherically symmetric in all $d$ dimensions. Some of the solutions in the former class are evaluated numerically, all the rest being given in closed form. Analytic proofs of existence covering all numerically evaluated solutions are given. All instantons studied have finite action and vanishing energy momentum tensor and do not disturb the geometry.

PHANTOM FIELD FROM CONFORMAL INVARIANCE

We establish a correspondence between a conformally invariant complex scalar field action (with a conformal self-interaction potential) and the action of a phantom scalar field minimally coupled to gravity (with a cosmological constant). In this correspondence, the module of the complex scalar field is used to relate conformally the metrics of both systems while its phase is identified with the phantom scalar field. At the level of the equations, the correspondence allows to map solution of the conformally nonlinear Klein–Gordon equation with vanishing energy–momentum tensor to solution of a phantom scalar field minimally coupled to gravity with cosmological constant satisfying a massless Klein–Gordon equation. The converse is also valid with the advantage that it offers more possibilities owing to the freedom of rewriting a metric as the conformal transformation of another metric. In three dimensions, the coupling of this matter action to conformal gravity is put in equivalence with topologically massive gravity with a cosmological constant and with a phantom source. Finally, we provide some examples of this correspondence.

Neutrinos in a Robertson-Walker universe

A solution to the Einstein-Dirac system of equations in a Robertson-Walker spacetime is presented using the separation of variables method. With an axially symmetric and a non-axially symmetric boundary conditions, we find that there are no solutions for the massless fermions and only null or `ghost' solutions for the massive fermions. The `ghost' solutions carry a current but have a vanishing energy-momentum tensor and correspond to the special case when the Robertson-Walker spacetime reduces to flat spacetime.

Free ghost gauge fields

Singularity-free non-Abelian solutions of the classical free Yang-Mills equations are shown to exist, which have a vanishing energymomentum tensor density. Their internal holonomy group is found to be noncompact.