The paper claims that Wronskian determinants of closed first-order ODE systems serve as integrals of motion on Euler-Lagrange extremals, constructed via the Jacobi equation.
An atom in front of Lorentz violating Kalb-Ramond black hole background
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abstract
We investigate the role of Lorentz violation in the acceleration radiation produced when an atom falls into a Kalb-Ramond (KR) black hole and observe that the amplitude and an exponential (Planck-like) factor are both shaped by the Lorentz-violating parameter, indicating a breach of the equivalence principle and resembling characteristics observed in bumblebee gravity models. We further investigate how Lorentz violation and conformal symmetry work together to determine the thermodynamic behavior of the system and the implications for the equivalence principle by looking at the transition probabilities of a two-level atomic detector interacting with the black hole. These findings provide new information about the interaction of black hole entropy, symmetry breaking, and possible observational probes of novel physics beyond general relativity. The horizon brightening acceleration radiation (HBAR) entropy in the KR black hole spacetime is also calculated in detail. Although the corrections are very different from those in bumblebee gravity, our study demonstrates that even though Lorentz-violating events alter the entropy, it nevertheless maintains a structural resemblance to the ordinary Bekenstein-Hawking entropy.
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Integrals of motion on extremals of the equation Euler-Lagrange
The paper claims that Wronskian determinants of closed first-order ODE systems serve as integrals of motion on Euler-Lagrange extremals, constructed via the Jacobi equation.