Spacetimes dressed with stealth electromagnetic fields

Abstract

Stealth field configurations by definition have a vanishing energy-momentum tensor, and 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.

Massive stealth scalar fields from deformation method

“…Also, in a similar spirit but in absence of scalar fields, we can consider redefinitions of gauge fields to produce deformation of gauge theories with non-trivial propagating degrees of freedom, in spite of which they will not feedback the gravitational background. Indeed, non-linear electrodynamics can produce stealth configurations [8]. In this direction, an example of a field redefinition approach was found in 2 `1 dimensions [16], where it was shown that the correspondent (deformed) gauge theory contains self-dual fields in 2 `1 dimensions [17] which are stealth.…”

“…However, it seems mathematically possible the existence of non-trivial matter-field configurations with vanishing energy-momentum tensor, such that the first statement will not be always truth. Indeed, there are examples of systems where this happens [1][2][3][4][5][6][7][8][9]. In these references the authors impose separately the vanishing Einstein tensor equation, the vanishing energy-momentum tensor equation (obtained from some scalar theory), and the matter-field equations of motion.…”

“…It has been shown by many authors [1][2][3][4][5][6][7][8][9][10][11][12][13][14] that scalar matter fields may not always curve the spacetime, in spite of their non-trivial degrees of freedom. Similar results were obtained also in the context of massive gauge theories in three dimensions [15].…”

Schwarzschild spacetime immersed in test nonlinear electromagnetic fields

“…The niche of NLE models has been heavily populated over the last three decades, based on various choices of NLE Lagrangian functions [20][21][22][23][24][25][26][27]. Large part of the motivation for this line of research comes from the quest for regular black hole solutions [28][29][30][31][32][33][34][35].…”

Universal p-form black holes in generalized theories of gravity

“…It is well-known that non-trivial stealth electromagnetic p-form fields are not possible in the standard Maxwell theory in any ddimensional Lorentzian space (simply because T μν u μ u ν > 0 for any timelike u, unless F = 0[58]). See[59] for a discussion of stealth fields in non-linear electrodynamics in four dimensions.…”