A single complex optical seed built from expansion and twist organizes stationary Kerr-Schild geometries, reconstructs the congruence, and encodes the zeroth-copy data that generates both the gravitational profile and the single-copy gauge field.
The Kerr-Schild ansatz revised
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abstract
Kerr-Schild metrics have been introduced as a linear superposition of the flat spacetime metric and a squared null vector field, say $\boldsymbol{k}$, multiplied by some scalar function, say $H$. The basic assumption which led to Kerr solution was that $\boldsymbol{k}$ be both geodesic and shearfree. This condition is relaxed here and Kerr-Schild ansatz is revised by treating Kerr-Schild metrics as {\it exact linear perturbations} of Minkowski spacetime. The scalar function $H$ is taken as the perturbing function, so that Einstein's field equations are solved order by order in powers of $H$. It turns out that the congruence must be geodesic and shearfree as a consequence of third and second order equations, leading to an alternative derivation of Kerr solution.
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Deformation parameters α, β, σ in a quintessence AdS black hole shift the temperature minimum, enlarge the cooling region, raise inversion temperature, and alter heat-engine efficiency.
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Untwisting the double copy: the zeroth copy as an optical seed
A single complex optical seed built from expansion and twist organizes stationary Kerr-Schild geometries, reconstructs the congruence, and encodes the zeroth-copy data that generates both the gravitational profile and the single-copy gauge field.
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Joule-Thomson effect and Efficiency of deformed AdS-Schwarzschild black hole in presence of quintessence
Deformation parameters α, β, σ in a quintessence AdS black hole shift the temperature minimum, enlarge the cooling region, raise inversion temperature, and alter heat-engine efficiency.