Abstract:
This article analyses the nature of classical Newtonian gravity beginning with Galileo's experiments and the paradox that ensues from Aristotle's law of falling bodies, delving on the notions of inertial and gravitational masses. Arguing that Newton's gravity law is inconsistent with relativity, it briefly describes Einstein's relativistic theory of gravity, pointing out the importance of weak equivalence principle in the formulation of general theory of relativity. It also provides a short discussion on an important prediction of general relativity, namely, the existence of gravitational waves and the attempts to detect them. Finally, the article touches on the current challenges facing the gravity researchers.

Abstract:
This article provides a brief introduction to the basics of stars, galaxies and Quasi-stellar objects (QSOs). In stars, the central pressure and temperature must be high in order to halt the stellar gravitational collapse. High temperature leads to thermonuclear fusion in the stellar core, releasing thereby enormous amount of nuclear energy, making the star shine brilliantly. On the other hand, the QSOs are very bright nuclei lying in the centres of some galaxies. Many of these active galactic nuclei, which appear star-like when observed through a telescope and whose power output are more than 1011 times that of the Sun, exhibit rapid time variability in their X-ray emissions. Rapid variability along with the existence of a maximum speed limit, c, provide a strong argument in favour of a compact central engine model for QSOs in which a thick disc of hot gas going around a supermassive blackhole is what makes a QSO appear like a bright point source. Hence, unlike stars, QSOs are powered by gravitational potential energy.

Abstract:
We study the effect of a (3+1)-dimensional Chern-Simons electrodynamics on the equations governing the dynamics of magnetized plasma and fields. In this model, the Chern-Simons (CS) part consists of a dynamical pseudo-scalar field whose space-time derivatives couple with the electromagnetic field. We explore the CS corrections to the evolution equation for the magnetic field in a plasma with non-zero electrical resistivity. We revisit Cowling's theorem in this context and observe that the CS corrections lead to possibly small but non-zero source terms for axisymmetric magnetic field. The scalar product of electric and magnetic fields play the role of source of the pseudo-scalar field, and therefore, pulsars and magnetars are likely astrophysical candidates to generate propagating pseudo-scalar waves. Although aligned electric field gets shorted out by flowing charges in large parts of the magnetosphere, there are vacuum gaps in the vicinity of pulsars where strong $\vec E. \vec B$ is expected to be present. We derive a wave solution for the pseudo-scalar field generated by the time-varying $\vec E. \vec B$ associated with a pulsar.

Abstract:
We consider the dynamics of a four-form field $\tilde {w} $, treating it as a distinct physical degree of freedom, independent of the metric. The equations of motion are derived from an action which, besides having the standard Hilbert-Einstein term and the matter part, consists of a new action for $\tilde {w} $. The evolution of $\tilde {w} $ in a flat FRW universe is studied, and it is shown that the parameters of the theory admit solutions wherein it is possible to have an equation of state $p_\phi \approx -\epsilon_\phi $, so that it leads to an accelerating universe. We also put forward electromagnetic as well as gravitational `Chern-Simons' like terms that arise naturally in 4D, entailing a modified Einstein-Maxwell equation and an enlarged system of Einstein equation involving a Cotton tensor. We demonstrate that the scalar-density associated with $\tilde {w} $ can be employed to construct a generalized exterior derivative that converts a p-form density to a (p+1)-form density of identical weight.

Abstract:
This is a concise review, addressed to undergraduate students, of S. Chandrasekhar's oeuvre in astrophysics, ranging from his early studies on white dwarfs using relativistic quantum statistics to topics as diverse as dynamical friction, negative hydrogen ion, fluid dynamical instabilities, black holes and gravitational waves. The exposition is based on simple physical explanations in the context of observational astronomy. Black holes and their role as central engines of active, compact, high energy sources have been discussed.

Abstract:
Propagation of weak gravitational waves, when a dynamical four-form is around, has been investigated. Exact, self-consistent solutions corresponding to plane, monochromatic gravitational waves have been studied.

Abstract:
The 2011 Nobel prize in physics has been awarded to S. Perlmutter, A. Riess and B. Schmidt for their path breaking discovery that the rate of expansion of the universe is increasing with time. The trio used Type Ia supernovae (SNe Ia) as standard candles to estimate their luminosity-distances. To appreciate some of the far reaching implications of their work, I have provided an elementary exposition of general theory of relativity, accelerated expansion of the universe, luminosity-distance, SNe Ia and the cosmological constant problem.

Abstract:
The Indo-aryans of ancient India observed stars and constellations for ascertaining auspicious times in order to conduct sacrificial rites ordained by vedas. It is but natural that they would have recounted in the vedic texts about comets. In Rigveda ($\sim $ 1700 - 1500 BC) and Atharvaveda ($\sim $ 1150 BC), there are references to dhumaketus and ketus, which stand for comets in Sanskrit. Rigveda mentions a fig tree with roots held up in the sky (Parpola 2009, 2010). Could it have been inspired by the hirsute appearance of a comet's tail? Similarly, could `Ketu' (the torso or the tail part of Rahu) be a Dravidian loan word, since `kottu', an old Tamil word, is associated with scorpion's sting and top tuft of hair? Varahamihira in 550 AD and Ballal Sena ($\sim $ 1100 - 1200 AD) have described a large number of comets recorded by ancient seers such as Parashara, Vriddha Garga, Narada, Garga, etc. In this article, I conjecture that an episode narrated in Mahabharata of a radiant king, Nahusha, ruling the heavens, and later turning into a serpent after he had kicked the seer Agastya (also the star Canopus), is a mythological retelling of a cometary event.

Abstract:
Mathematical tradition in India is deep rooted. Indian (and of Indian origin) mathematicians have continued to do seminal work till present times, culminating in Manjul Bhargava receiving the Fields Medal last year. In such fabulous times, a non-mathematician ponders about the nature of mathematics, and revisits the question: why are fundamental laws of Nature inherently mathematical?

Abstract:
Graphene's honeycomb lattice structure is quite remarkable in the sense that it leads, in the long wavelength limit, to a massless Dirac equation description of nonrelativistic quasiparticles associated with electrons and holes present in the two dimensional crystallite. In the case of cold bosonic atoms trapped in a honeycomb optical lattice, Haddad and Carr (2009) have recently shown, by taking into account binary contact interactions, that the dynamics of these Bose-Einstein condensates is governed by a nonlinear Dirac equation (NLDE). In this paper, we study exact stationary solutions of such a NLDE. After proving that the energy eigenvalues are real, we show that the sum of orbital angular momentum and pseudospin angular momentum normal to the crystal commutes with the nonlinear Hamiltonian whenever magnitudes of the pseudospin components do not depend on the polar angle $\phi $. We obtain some exact stationary and localized solutions of the NLDE.