Einstein and Beyond: A Critical Perspective on General Relativity

An alternative approach to Einstein's theory of General Relativity (GR) is reviewed, which is motivated by a range of serious theoretical issues inflicting the theory, such as the cosmological constant problem, presence of non-Machian solutions, problems related with the energy-stress tensor $T^{ik}$ and unphysical solutions. The new approach emanates from a critical analysis of these problems, providing a novel insight that the matter fields, together with the ensuing gravitational field, are already present inherently in the spacetime without taking recourse to $T^{ik}$. Supported by numerous evidences, the new insight revolutionizes our views on the representation of the source of gravitation and establishes the spacetime itself as the source, which becomes crucial for understanding the unresolved issues in a unified manner. This leads to a new paradigm in GR by establishing equation $R^{ik}=0$ as the field equation of gravitation plus inertia in the very presence of matter.Comment: An invited review accepted for publication by `Universe' in its Special Issue "100 Years of Chronogeometrodynamics: the Status of the Einstein's Theory of Gravitation in Its Centennial Year

Lanczos potential of Weyl field: interpretations and applications

An attempt is made to uncover the physical meaning and significance of the obscure Lanczos tensor field which is regarded as a potential of the Weyl field. Despite being a fundamental building block of any metric theory of gravity, the Lanczos tensor has not been paid proper attention as it deserves. By providing an elucidation on this tensor field through its derivation in some particularly chosen spacetimes, we try to find its adequate interpretation. Though the Lanczos field is traditionally introduced as a gravitational analogue of the electromagnetic 4-potential field, the performed study unearths its another feature - a relativistic analogue of the Newtonian gravitational force field. A new domain of applicability of the Lanczos tensor is introduced which corroborates this new feature of the tensor.Comment: 27 pages, no figure

A Critique of Supernova Data Analysis in Cosmology

Observational astronomy has shown significant growth over the last decade and has made important contributions to cosmology. A major paradigm shift in cosmology was brought about by observations of Type Ia supernovae. The notion that the universe is accelerating has led to several theoretical challenges. Unfortunately, although high quality supernovae data-sets are being produced, their statistical analysis leaves much to be desired. Instead of using the data to directly test the model, several studies seem to concentrate on assuming the model to be correct and limiting themselves to estimating model parameters and internal errors. As shown here, the important purpose of testing a cosmological theory is thereby vitiated.Comment: v2: Revised, comments and references added; Published version [vailable at http://www.raa-journal.org/raa/index.php/raa/article/view/539