Violation of Chandrasekhar mass-limit in noncommutative geometry: A strong possible explanation for the super-Chandrasekhar limiting mass white dwarfs Surajit Kalita, 1, ∗ Banibrata Mukhopadhyay, 1, † and T. R. Govindarajan 2, ‡ 1 Department of Physics, Indian Institute of Science, Bangalore 560012, India 2 Chennai Mathematical Institute, Kelambakkam, Chennai 603103, India One of the most celebrated discoveries of twentieth century is the existence of limiting mass of white dwarfs, which is one of the compact objects formed once nuclear burning stops inside the star. On approaching this limiting mass ∼ 1.4M⊙, called the Chandrasekhar mass-limit, a white dwarf is believed to spark oﬀ with an explosion called type Ia supernova, which is considered to be a stan- dard candle. However, observations of several over-luminous, peculiar type Ia supernovae indicate that the Chandrasekhar mass-limit to be signiﬁcantly larger. By considering noncommutativity of components of position and momentum variables, hence uncertainty in their measurements, at the quantum scales, we show that the mass of white dwarfs could be signiﬁcantly super-Chandrasekhar and thereby arrive at a new mass-limit ∼ 2.6M⊙, explaining a possible origin of over-luminous pe- culiar type Ia supernovae. The idea of noncommutativity, apart from the Heisenberg’s uncertainty principle, is there for quite sometime, without any observational proof however. Our ﬁnding oﬀers a plausible astrophysical evidence of noncommutativity, arguing for a possible second standard candle, which has many far reaching implications. 1. INTRODUCTION Einstein’s theory of general relativity (GR) and quan- tum mechanics are considered to be among the greatest discoveries in the twentieth century. GR is undoubtedly the most panoramic theory to explain the theory of grav- ity. It can easily explain a large number of phenomena where Newtonian gravity falls short. It also helps to un- derstand the stability of Chandrasekhar’s mass-limit for the white dwarf with ﬁnite radius. White dwarf is the end state of a star with mass  8M ⊙ , where the in- ward gravitational force is balanced by the force due to outward electron degeneracy pressure arising from Fermi statistics. Moreover, if the white dwarf has a binary part- ner, it starts pulling matter out oﬀ the partner due to its high gravity, resulting in the increase in the mass of the white dwarf. When it gains suﬃcient amount of mat- ter, beyond a certain mass, known as the Chandrasekhar mass-limit (currently accepted value ∼ 1.4M ⊙ [1] for a carbon-oxygen non-magnetized and non-rotating white dwarf), this pressure/force balance is no longer sustained and it sparks oﬀ to produce type Ia supernova (SNIa) [2]. The luminosity of SNIa is very important as it is used as one of the standard candles to measure the luminosity distance of various objects in cosmology. However, recent observations have questioned the com- plete validity of GR near the compact objects. For ex- ample, in the past decade, a number of peculiar over- luminous SNeIa, viz. SN 2003fg, SN 2006gz, SN 2007if, SN 2009dc [3, 4] etc. have been observed, which were inferred to be originating from white dwarfs of super- Chandrasekhar mass as high as 2.8M ⊙ . In this scenario, ∗ Email: surajitk@iisc.ac.in † Email: bm@iisc.ac.in ‡ Email: trg@imsc.res.in; trg@cmi.ac.in the Chandrasekhar mass-limit is well violated. Diﬀerent theories and models have been proposed to explain this class of the white dwarfs. Our group started exploring the signiﬁcant violation of the Chandrasekhar mass-limit based on the eﬀect of magnetic ﬁelds [5, 6]. Subsequently, there are enormous interest in re-exploring the Chan- drasekhar mass-limit by introducing various new phys- ical eﬀects in white dwarfs. Some such physics are (1) eﬀects of strong magnetic ﬁeld leading to signiﬁcantly super-Chandrasekhar mass: quantum, through Landau orbital eﬀects above the Schwinger limit 4.414 × 10 13 G, which aﬀects the equation of state (EoS) [7], and classi- cal: through the ﬁeld pressure aﬀecting the macroscopic structural properties [8–11]; (2) modiﬁed gravity eﬀect, leading to signiﬁcantly sub- and super-Chandrasekhar mass-limits [12–14]; (3) ungravity eﬀect [15]; (4) con- sequence of total lepton number violation in magnetized white dwarfs [16]; (5) charged white dwarfs leading to super-Chandrasekhar mass [17]; (6) generalized Heisen- berg uncertainty principle [18]; (7) eﬀects of momentum- momentum noncommutativity in the white dwarf mat- ter and hence the equation of state, leading to super- Chandrasekhar mass-limit [19]; and many more. In the present work, we plan to analyze the possible noncommutativity eﬀects. Many researchers earlier used the idea of noncommutativity to explain the physics of various systems [20–35]. However, unfortunately, there is no direct way to conﬁrm the natural evidence of such non- commutativity and hence it still remains as a hypothesis. Nevertheless, our observable universe abides by position- position and momentum-momentum commutative rules, which implies that two position coordinates and two mo- mentum coordinates can be measured simultaneously. However, at a very small length scale (and/or at a very high energy regime), the position and corresponding con- jugate momentum follow the Heisenberg’s uncertainty principle. Nevertheless, there are proposals that at a very high energy regime, e.g. at Planck’s scale, position- arXiv:1912.00900v1 [gr-qc] 26 Nov 2019