A class of interior solutions corresponding to a (2+1)(2+1) dimensional asymptotically anti-de Sitter spacetime

Lower dimensional gravity has the potential of providing non-trivial and valuable insight into some of the conceptual issues arising in four dimensional relativistic gravitational analysis. The asymptotically anti-de Sitter (2+1) dimensional spacetime described by Ba$\tilde{n}$ados, Teitelboim and Zanelli (BTZ) which admits a black hole solution, has become a source of fascination for theoretical physicists in recent years. By suitably choosing the form of the mass function $m(r)$, we derive a new class of solutions for the interior of an isotropic star corresponding to the exterior (2+1) asymptotically anti-de Sitter BTZ spacetime. The solution obtained satisfies all the regularity conditions and its simple analytical form helps us to study the physical parameters of the configuration in a simple manner.Comment: 5 pages, 5 figures. Accepted for publication in Phys. Lett. B, some typos are correcte

Anisotropic generalization of well-known solutions describing relativistic self-gravitating fluid systems: An algorithm

We present an algorithm to generalize a plethora of well-known solutions to Einstein field equations describing spherically symmetric relativistic fluid spheres by relaxing the pressure isotropy condition on the system. By suitably fixing the model parameters in our formulation, we generate closed-form solutions which may be treated as anisotropic generalization of a large class of solutions describing isotropic fluid spheres. From the resultant solutions, a particular solution is taken up to show its physical acceptability. Making use of the current estimate of mass and radius of a known pulsar, the effects of anisotropic stress on the gross physical behaviour of a relativistic compact star is also highlighted.Comment: To appear in Eur. Phys. J.

Atomistic study on the effect of the size of diamond abrasive particle during polishing of stainless steel

Nanofinishing or polishing helps to reduce surface roughness, which further improves both the optical and chemical properties of engineering materials. During the polishing of any engineering material, the size of abrasive particles plays a significant role in efficient polishing. In this paper, stainless steel 304 (or SS304) is selected for polishing through diamond abrasives with varying particle sizes using molecular dynamics simulations (MDS). It is found that the diamond abrasive particle initially causes elastic deformation due to the attractive force between the abrasive particle and the workpiece surface. As the size of the abrasive particle increases, plastic deformation occurs by spreading the dislocations on the surface only, which helps to annihilate the dislocations after polishing. It is revealed that the smaller abrasive particles (<3 nm) get trapped due to strong chemical bonding with the surface of the workpiece, and the abrasive particles start depositing on the workpiece instead of material removal. In this paper, it is proposed that an optimum size of abrasive particles is required for a given set of polishing parameters to achieve efficient material removal and minimum surface and subsurface defects. Thus, the present study is worthwhile for efficient polishing or nanocutting of stainless steel through monocrystalline diamond