Warping Spacetime: A New Path to Lorentz-Violating Gravity
![For Kerr-(A)dS spacetime, the ranges of energy and rotation parameter define regions where the associated bumblebee field remains globally real or transitions to imaginary values, demarcated by critical curves and influenced by the cosmological constant [latex]\lambda=\Lambda m^{2}[/latex], with the dashed line indicating the threshold where the black hole becomes extremal.](https://arxiv.org/html/2601.16037v1/pic4.png)
Researchers have developed a novel technique to generate a family of spacetime solutions within bumblebee gravity, offering insights into how Lorentz symmetry might be broken.
![For Kerr-(A)dS spacetime, the ranges of energy and rotation parameter define regions where the associated bumblebee field remains globally real or transitions to imaginary values, demarcated by critical curves and influenced by the cosmological constant [latex]\lambda=\Lambda m^{2}[/latex], with the dashed line indicating the threshold where the black hole becomes extremal.](https://arxiv.org/html/2601.16037v1/pic4.png)
Researchers have developed a novel technique to generate a family of spacetime solutions within bumblebee gravity, offering insights into how Lorentz symmetry might be broken.
![A pronounced anomalous Hall effect is observed in valley-polarized polaritons, where strain-induced symmetry breaking generates an effective pseudomagnetic field driving a measurable drift velocity of [latex]1.69 \times 10^{5}~\mathrm{m/s}[/latex], as evidenced by the temporal evolution of valley polarization and confirmed by a two-Gaussian fit with a [latex]95\%[/latex] prediction interval.](https://arxiv.org/html/2601.15631v1/x2.png)
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![The study reveals a complex relationship between recursive parameters, demonstrating that [latex]r_n(0.5 + 14.135i)[/latex] at iteration 110, alongside its minimum [latex]r_{p_{min}}[/latex] and maximum [latex]r_{p_{max}}[/latex] values - represented in blue and magenta respectively - fluctuate around a mean [latex]\langle r_p \rangle[/latex] (black), with prime number locations highlighted to suggest an underlying mathematical structure governing the recursion.](https://arxiv.org/html/2601.16193v1/r_n.png)
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