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Beyond Special Relativity at second order
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Beyond Special Relativity at second order
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The study of generic, non-linear, deformations of Special Relativity parametrized by a high-energy scale $M$, which was carried out at first order in $M$ in Phys.Rev. D86, 084032 (2012), is extended to second order. This can be done systematically through a ('generalized') change of variables from momentum variables that transform linearly. We discuss the different perspectives on the meaning of the change of variables, obtain the coefficients of modified composition laws and Lorentz transformations at second order, and work out how $\kappa$-Poincar\'e, the most commonly used example in the literature, is reproduced as a particular case of the generic framework exposed here.
Forward citations
Cited by 2 Pith papers
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A winding number analysis of Schwarzschild black hole stability in light of Planck-scale modified kinematics
Cubic entropy corrections from the MDR ηE³/E_P leave Schwarzschild black holes with a single physical branch of winding number W=−1; the would-be stable root is unphysical.
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A winding number analysis of Schwarzschild black hole stability in light of Planck-scale modified kinematics
For the cubic entropy correction S=πr_h²−αr_h³ arising from a Planck-scale modified dispersion relation, all physically allowed Schwarzschild-like branches have winding number w=−1, so no stable phase appears.
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