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General Relativity and Quantum Cosmology

Title: Quantum gravity corrections to white dwarf dynamics

Abstract: We study the invariant Planck scale correction to the white dwarf dynamics. We have considered the modified dispersion relation and the cut-off to the maximum possible momentum/energy of the non-interacting Fermi gas particles as a signal of appearance of the effects of Quantum Gravity phenomena. With such a modification the expression for the degenerate pressure of white dwarf gets modified accordingly and so does the Chandrasekhar mass limit. The mass-radius M-R plot shows that the modified/ corrected radius of the white dwarf can be greater than, equal to and smaller than the usual special relativity (SR) value for particular masses. We found that the Chandrasekhar mass limit gets a positive correction i.e, the maximum possible mass for white dwarf increases in this formalism. The correction is purely perturbative in the SR limit which is quite unusual for a theory having an ultraviolet energy cut-off. Therefore this correction is solely because of the modified dispersion relation. The value of the obtained degenerate pressure for a given mass is found to be greater than, equal to and smaller than the usual special relativity (SR) value for particular masses as expected. It is shown by Mishra et al. that the Stefan-Boltzmann law gets a correction in such a theory with an ultraviolet cut-off. Using this result we have calculated the luminosity of the white dwarf by taking the model of partially degenerate gas and considering the modified radiative envelope equation. In such an analysis we observe that the pressure for a given mass and temperature value is less than that predicted by the usual SR theory. The luminosity also gets a negative correction. The correction to luminosity is nonperturbative as expected for such a theory.
Comments: 31 pages, 4 figures
Subjects: General Relativity and Quantum Cosmology (gr-qc)
Cite as: arXiv:1803.06640 [gr-qc]
  (or arXiv:1803.06640v1 [gr-qc] for this version)

Submission history

From: Dheeraj Kumar Mishra [view email]
[v1] Sun, 18 Mar 2018 10:52:36 GMT (191kb)