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.
Extended Uncertainty Principle for Rindler and cosmological horizons
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We find exact formulas for the Extended Uncertainty Principle (EUP) for the Rindler and Friedmann horizons and show that they can be expanded to obtain asymptotic forms known from the previous literature. We calculate the corrections to Hawking temperature and Bekenstein entropy of a black hole in the universe due to Rindler and Friedmann horizons. The effect of the EUP is similar to the canonical corrections of thermal fluctuations and so it rises the entropy signalling further loss of information.
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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.