Generalized uncertainty principle, black holes, and white dwarfs: a tale of two infinities

Abstract

It is often argued that quantum gravitational correction to the Heisenberg's uncertainty principle leads to, among other things, a black hole remnant with finite temperature. However, such a generalized uncertainty principle also seemingly removes the Chandrasekhar limit, i.e., it permits white dwarfs to be arbitrarily large, which is at odds with astrophysical observations. We show that this problem can be resolved if the parameter in the generalized uncertainty principle is negative. We also discuss the Planck scale physics of such a model.

A complementary third law for black hole thermodynamics

“…Such a choice of sign of α may seem unusual, but it is consistent with some quantum gravity models in which physics at the Planck scale "classicalized" and becomes deterministic (as the RHS of the GUP equation goes to zero when ∆p · c is equal to the Planck energy) [13][14][15][16]. Specifically, we have seen that a lattice "spacetime crystal" gives rise to such a GUP [13].…”

“…(1), we would find that there is no lower bound for black hole mass, so in principle the black hole can evaporate completely. However the final temperature is finite and nonzero [14,15], also see Fig. (1).…”

“…The question is: How does one make sense of a nonzero black hole temperature if the black hole has completely evaporated? A possible interpretation is that this is the temperature of the Hawking radiation at the final moment just before the black hole disappears [14]. This parallels the explanation for the α > 0 case, but instead of interpreting the temperature as energy of the remnant (since there is no radiation), one now takes it to be the temperature of the final emission of radiation (since there is no black hole).…”

“…However, in [15], a more detailed study of the evaporation process reveals that the α < 0 GUP-corrected black hole actually takes an infinite amount of time to evaporate completely, so there is no need to resort to the aforementioned interpretation; the black hole simply continues to evaporate indefinitely (indeed its heat capacity is always negative and so it interacts thermodynamically with the environment), with temperature asymptotes to a finite nonzero value. This value is T * = 1/(4π |α|) [14,15] (note the typo in [15]). Thus even though black hole mass is not bounded below, the black hole behaves effectively as a meta-stable remnant at late times.…”

Erratum: ‘Continuous gravitational wave from magnetized white dwarfs and neutron stars: possible missions for LISA, DECIGO, BBO, ET detectors’

“…Ostriker and his collaborators first showed that rotation (and also magnetic field) of the white dwarf can lead to the violation of the Chandrasekhar mass limit (Ostriker & Hartwick 1968), but they could not reveal any limiting mass. More recently, magnetic field (Das & Mukhopadhyay 2013, 2015aSubramanian & Mukhopadhyay 2015), modified theories of gravity (Das & Mukhopadhyay 2015b;Kalita & Mukhopadhyay 2018;Carvalho et al 2017), generalized Heisenberg uncertainty principle (Ong 2018) etc. have been proposed as some of the prominent possibilities to explain super-Chandrasekhar white dwarfs and also corresponding limiting mass.…”