We use the (1 + 1)-dimensional Kardar-Parisi-Zhang equation driven by a Gaussian white noise and employ the dynamic renormalization-group of Yakhot and Orszag without rescaling [J. Sci. Comput. 1, 3 (1986)]. Hence we calculate the second and third order moments of height distribution using the diagrammatic method in the large scale and long time limits. The moments so calculated lead to the value S = 0.3237 for the skewness. This value is comparable with numerical and experimental estimates.

The existence of Chandrasekhar’s limit has played various decisive roles in astronomical observations for many decades. However, various recent theoretical investigations suggest that gravitational collapse of white dwarfs is withheld for arbitrarily high masses beyond Chandrasekhar’s limit if the equation of state incorporates the effect of quantum gravity via the generalized uncertainty principle. There have been a few attempts to restore the Chandrasekhar limit but they are found to be inadequate. In this paper, we rigorously resolve this problem by analysing the dynamical instability in general relativity. We confirm the existence of Chandrasekhar’s limit as well as stable mass–radius curves that behave consistently with astronomical observations. Moreover, this stability analysis suggests gravitational collapse beyond the Chandrasekhar limit signifying the possibility of compact objects denser than white dwarfs.

Generalized uncertainty relation that carries the imprint of quantum gravity introduces a minimal length scale into the description of space-time. It effectively changes the invariant measure of the phase space through a factor (1+βp 2 ) −3 so that the equation of state for an electron gas undergoes a significant modification from the ideal case. It has been shown in the literature (Rashidi 2016) that the ideal Chandrasekhar limit ceases to exist when the modified equation of state due to the generalized uncertainty is taken into account. To assess the situation in a more complete fashion, we analyze in detail the mass-radius relation of Newtonian white dwarfs whose hydrostatic equilibria are governed by the equation of state of the degenerate relativistic electron gas subjected to the generalized uncertainty principle. As the constraint of minimal length imposes a severe restriction on the availability of high momentum states, it is speculated that the central Fermi momentum cannot have values arbitrarily higher than pmax ∼ β −1/2 . When this restriction is imposed, it is found that the system approaches limiting mass values higher than the Chandrasekhar mass upon decreasing the parameter β to a value given by a legitimate upper bound. Instead, when the more realistic restriction due to inverse β-decay is considered, it is found that the mass and radius approach the values close to 1.45 M⊙ and 600 km near the legitimate upper bound for the parameter β. On the other hand, when β is decreased sufficiently from the legitimate upper bound, the mass and radius are found to be approximately 1.46 M⊙ and 650 km near the neutronization threshold.

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Abstract. We study the fourth order normalized cumulant of height fluctuations governed by 1 + 1 dimensional Kardar-Parisi-Zhang (KPZ) equation for a growing surface. Following a diagrammatic renormalization scheme, we evaluate the kurtosis Q from the connected diagrams leading to the value Q = 0.1523 in the large-scale long-time limit.