Exact Stress Tensor Flows in Causal Electrodynamics: Courant-Hilbert Approach
Abstract
It has been shown that for theories whose Courant-Hilbert function depends on a single dimensionful coupling, the energy-momentum tensor is controlled by the two combinations τℓ̇ and ℓ−τℓ̇, so that the quadratic invariants X=TμνTμν and Y=(Tμμ)2 depend on a single auxiliary variable. Eliminating this variable in favour of Y/X yields the exact autonomous flow ∂λℒ=X ℱ(Y/X), with no explicit dependence on the coupling, the electromagnetic invariants or the CH parameter, on every branch where the map is invertible. The expansion of ℱ in powers of √(Y/X) shows which flows are built from integer powers of X and Y and which require half-integer powers. In this paper, we work out four examples in closed form, each with its analytic structure and physical interpretation: the generalized Born-Infeld theory, whose flow is quadratic in the stress tensor; the q-deformed family, in which the odd coefficients of the expansion vanish at q=1/2 and are nonzero otherwise; the no-τ-maximum theory; and the causal Russo-Townsend logarithmic theory, whose flow involves the lower real branch of the Lambert W function and reproduces the known perturbative result. The singular points of ℱ are related to the critical fields, energy conditions, and strong-field behavior of each theory.
Related
- Exact Stress Tensor Flows in Causal Electrodynamics: Auxiliary Field Formalism
- A gravitational realization of Courant--Hilbert deformations
- Charged regular AdS3 black holes in a scalar-vector-tensor theory coupled to Born-Infeld electrodynamics
- Spiral galaxy spacetime in extended scalar-tensor-Gauss-Bonnet gravity coupled to nonlinear electrodynamics
- Novel topological subclasses of a magnetic black hole in causal nonlinear electrodynamics
BibTeX
@misc{pezhman2026exact,
title = {{Exact Stress Tensor Flows in Causal Electrodynamics: Courant-Hilbert Approach}},
author = {Zahra Pezhman and Komeil Babaei Velni and H. Babaei-Aghbolagh},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.33887},
eprint = {2610.33887},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.33887},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Exact Stress Tensor Flows in Causal Electrodynamics: Courant-Hilbert Approach
AU - Zahra Pezhman
AU - Komeil Babaei Velni
AU - H. Babaei-Aghbolagh
PY - 2026
DA - 2026/10/24
PB - arXiv
DO - 10.48550/arxiv.2610.33887
UR - https://arxiv.org/abs/2610.33887
AB - It has been shown that for theories whose Courant-Hilbert function depends on a single dimensionful coupling, the energy-momentum tensor is controlled by the two combinations τℓ̇ and ℓ−τℓ̇, so that the quadratic invariants X=T_μνT^μν and Y=(T^μ_μ)^2 depend on a single auxiliary variable. Eliminating this variable in favour of Y/X yields the exact autonomous flow ∂_λℒ=X ℱ(Y/X), with no explicit dependence on the coupling, the electromagnetic invariants or the CH parameter, on every branch where the map is invertible. The expansion of ℱ in powers of √(Y/X) shows which flows are built from integer powers of X and Y and which require half-integer powers. In this paper, we work out four examples in closed form, each with its analytic structure and physical interpretation: the generalized Born-Infeld theory, whose flow is quadratic in the stress tensor; the q-deformed family, in which the odd coefficients of the expansion vanish at q=1/2 and are nonzero otherwise; the no-τ-maximum theory; and the causal Russo-Townsend logarithmic theory, whose flow involves the lower real branch of the Lambert W function and reproduces the known perturbative result. The singular points of ℱ are related to the critical fields, energy conditions, and strong-field behavior of each theory.
ER -