Particle Motion with Ho\v{r}ava -- Lifshitz type Dispersion Relations

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Rama, S. Kalyana
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Abstract
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Using super Hamiltonian formalism, we study the motion of particles whose dispersion relations are modified to incorporate Ho\v{r}ava -- Lifshitz type anisotropic scaling symmetry. We find the following as consequences of this modified dispersion relation: (i) The speed of a charged particle under a constant electric field grows without bound and diverges. (ii) The speed of a particle falling towards the horizon also grows without bound and diverges as the particle approaches the horizon. (iii) This particle reaches the horizon in a finite coordinate time, in contrast to the standard case where it requires infinite time.
Comment: 16 pages. Version 2: A reference added
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High Energy Physics - Theory, Astrophysics - Cosmology and Nongalactic Astrophysics, General Relativity and Quantum Cosmology
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