QED energy–momentum trace as a force in astrophysics

Abstract

We study the properties of the trace T of the QED energy-momentum tensor in the presence of quasi-constant external electromagnetic fields. We exhibit the origin of T in the quantum nonlinearity of the electromagnetic theory. We obtain the quantum vacuum fluctuation-induced interaction of a particle with the field of a strongly magnetized compact stellar object.

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“…We will discuss why it is necessary to consider energy-momentum conservation explicitly in deriving the effective electromagnetic force and obtain a general formula for the leading terms in the force valid in the leading order in the expansion of the nonlinear effective potential. This corrects our earlier presentation in theoretical detail [7], though the magnitude of the effects remains.…”

“…| H p | a few mG according to estimates and models of accreting plasmas [15]. Putting in the numbers shows that the nonlinear electromagnetic force dominates gravity for | B e |/| B c | 10 −7 , confirming the previous analysis [7]. We estimate the pressure P in the plasma from the ideal gas law and compare it to the interaction energy density, which is essentially the force derived here without the gradients.…”

“…(6), we recognize the first three terms in brackets as an expanded expression of the divergence of −H µν . Note that ∂ µ F µν vanishes according to the homogeneous Maxwell equation (7). From Eq.…”

A Smarr formula for charged black holes in nonlinear electrodynamics

“…It has been proposed in Refs. [56,57] that the effects of trace of the energymomentum tensor in nonlinear electrodynamics are analogous to those that produces a cosmological constant. The idea is to separate the energy-momentum tensor into two parts, that is T µν = T µν + g µν T /4, where the bar denotes the traceless remainder.…”

QED trace anomaly, non-local Lagrangians and quantum equivalence principle violations

“…This construction constitutes a fundamental ingredient if one wants to consider the effects of the anomaly on various gravitational phenomena beyond the linear approximation. Over the years, multiple authors have investigated the effects of anomalies on different phenomena ranging from cosmology and astrophysics [32][33][34][35][36][37] to black holes [38,39]. We will continue the discussion of the covariant form of the effective action in [21].…”