520 citations · 1.8k across the 29 of their papers we have counts for
29 papers
Generating Spherically Symmetric Static Anisotropic Fluid Solutions of Einstein's Equations from Hydrostatic Equilibrium
M M Akbar, R Solanki
For static fluid spheres, the condition of hydrostatic equilibrium is given by the generalized Tolman--Oppenheimer--Volkoff (TOV) equation, a Riccati equation in the radial pressur…
Algorithms for Generating All Static Spherically Symmetric (An)isotropic Fluid Solutions of Einstein's Equations
M M Akbar, R Solanki
We study the Einstein equations of the static spherically symmetric anisotropic fluid system in curvature coordinates to find algorithms that generate all solutions and all solutio…
Embedding FLRW Geometries in Pseudo-Euclidean and Anti-de Sitter Spaces
M. M. Akbar
Contrary to the general consensus in the literature that Friedmann--Lemaître--Robertson--Walker (FLRW) geometries are of embedding class one (i.e.,\ embeddable in one higher dimens…
Spherical Spacelike Geometries in Static Spherically Symmetric Spacetimes: Generalized Painlevè-Gullstrand Coordinates, Foliation, and Embedding
M. M. Akbar
It is well known that static spherically symmetric spacetimes can admit foliations by flat spacelike hypersurfaces, which are best described in terms of the Painlevè--Gullstrand co…
Static Axisymmetric Einstein Equations in Vacuum: Symmetry, New Solutions and Ricci Solitons
M. M. Akbar, M. A. H. MacCallum
An explicit one-parameter Lie point symmetry of the four-dimensional vacuum Einstein equations with two commuting hypersurface-orthogonal Killing vector fields is presented. The pa…
Pseudo-Riemannian Ricci-flat and Flat Warped Geometries and New Coordinates for the Minkowski metric
M. M. Akbar
It is well-known that the Einstein condition on warpedgeometries requires the fibres to be necessarily Einstein. However, exact warped solutions have often been obtained using one-…