Related papers: Monstrous Moonshine over Z?
It is surprising that we hardly know only 5% of the universe. Rest of the universe is made up of 70% of dark-energy and 25% of dark-matter. Dark-energy is responsible for acceleration of the expanding universe; whereas dark-matter is said…
In this paper, we investigate the recently proposed relativistic theory for MOND using the phase space analysis. Unlike its precedent theory, namely TeVeS, this theory is claimed to agree with the observed Cosmic Microwave Background and…
Over the last few years, several close orbiting ($\sim 0.05$ AU) large mass planets ($M \sim M_{Jupiter}$) of nearby stars have been discovered. Their existence has been inferred from tiny doppler shifts in the light from the star. We…
General relativity (GR) passed many astronomical tests but in majority of them GR predictions have been tested in a weak gravitational field approximation. Around 50 years ago a shadow has been introduced by J. Bardeen as a purely…
We conjecture that for a strongly minimal theory T in a finite signature satisfying the Zilber Trichotomy, there are only three possibilities for the recursive spectrum of T: all countable models of T are recursively presentable; none of…
The composition of the dark universe although hypothesised, remains one of the biggest mysteries in modern physics. On smaller scales, there are various solar puzzling phenomena which known physics cannot explain like the coronal heating…
Equivalent conditions that make the normal cone maximal monotone are investigated in the general settings of locally convex spaces. Some consequences such as Bishop Phelps and sum representability results are presented in the last part.
The hypothetical existence of a good theory of mixed motives predicts many deep phenomena related to algebraic cycles. One of these, a generalization of Bloch's conjecture says that "small Hodge diamonds" go with "small Chow groups".…
One component of a massive black hole binary (MBHB) might capture a small third body, and then a hierarchical, inclined triple system would be formed. With the post-Newtonian approximation including radiation reaction, we analyzed the…
Pulsar wind nebulae are now well established as important probes both of neutron stars' relativistic winds and of the surrounding interstellar medium. Amongst this diverse group of objects, pulsar bow shocks have long been regarded as an…
We show that Newton's gravitational potential, augmented by a logarithmic term, partly or wholly mitigates the need for dark matter. As a bonus, it also explains why MOND seems to work at galactic scales. We speculate on the origin of such…
We discuss various recent advances on weak forms of the Twin Prime Conjecture.
We review some modified gravity models which describe the gravitational dark energy and the possibility of cosmic speed-up. The new consistent version of such theory which contains inverse and HD curvature terms as well as new type of…
Variable active galactic nuclei showing periodic light curves have been proposed as massive black hole binary (MBHB) candidates. In such scenarios the periodicity can be due to relativistic Doppler-boosting of the emitted light. This…
I discuss open theoretical questions pertaining to the modified dynamics (MOND)--a proposed alternative to dark matter, which posits a breakdown of Newtonian dynamics in the limit of small accelerations. In particular, I point the reasons…
We exposit the construction of Rademacher sums in arbitrary weights and describe their relationship to mock modular forms. We introduce the notion of Rademacher series and describe several applications, including the determination of…
Despite the failure of the integral Hodge conjecture, we show that the rational Hodge conjecture implies an integral version (modulo torsion) of the absolute Hodge conjecture.
We generalise our still-wide-open $q$-rious positivity conjecture from 2011 to a $q$-rious unimodality conjecture.
We give a new proof of Carlitz-Wan's conjecture, previously proved by Lenstra (1995).Our proofs are natural and intuitive, and shed new insights into the study of exceptional polynomials.
In this article we address the mystery of dark matter. We expound the various evidences, astrophysical and cosmological, leading to hypothesize the existence of an invisible form of matter, whose attempts at detecting it have so far all…