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Dispersion relations in finite-boost DSR
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Dispersion relations in finite-boost DSR
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We find finite-boost transformations DSR theories in first order of the Planck length $l_p$, by solving differential equations for the modified generators. We obtain corresponding dispersion relations for these transformations, which help us classify the DSR theories via four types. The final type of our classification has the same special relativistic dispersion relation but the transformations are not Lorentz. In DSR theories, the velocity of photons is generally different from the ordinary speed c and possess time delay, however in this new DSR light has the same special relativistic speed with no delay. A special case demonstrates that any search for quantum gravity effects in observations which gives a special relativistic dispersion relation is consistent with DSR.
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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