Gravity of R^{ik}=0: A New Paradigm in GR

TL;DR

This paper proposes a new perspective on general relativity, suggesting that the curvature of spacetime can be explained without the need for the traditional energy-stress tensor, aligning with observations and resolving existing puzzles.

Contribution

It introduces a novel interpretation of the vacuum equations $R^{ ext{ik}}=0$ as the fundamental source of spacetime curvature, challenging the conventional reliance on $T^{ ext{mu nu}}$.

Findings

Aligns with all known GR phenomena without $T^{ ext{mu nu}}$

Resolves some longstanding puzzles in GR

Circumvents issues related to dark energy and dark matter

Abstract

Theory of general relativity (GR) has been scrutinized by experts for almost a century and describes accurately all gravitational phenomena ranging from the solar system to the universe. However, this success is achieved provided one admits three completely independent new components in the energy-stress tensor $T^{\mu\nu}$$-$inflaton, dark matter and dark energy, which though do not have any non-gravitational or laboratory evidence and have remained generally speculative. Moreover, the dark energy poses a serious confrontation between fundamental physics and cosmology. The present situation reminds us of Einstein's `biggest blunder' when he forced his theory to predict a static universe, perhaps guided by his religious conviction that the universe must be eternal and unchanging. It seems that we are making a similar blunder by forcing $T^{\mu\nu}$ into the field equations while the observations indicate that it is not needed. We seem to have a deep-rooted conviction that the spacetime will remain empty unless we fill it by the energy-stress tensor. However, we have been ignoring numerous evidences earnestly indicating otherwise. From a critical analysis of the present situation, we develop an entirely new insight about the source of curvature in equations $R^{\mu\nu}=0$ which, though may appear orthogonal to the usual understanding, is in striking agreement with all known phenomena in GR. Moreover, it answers some hitherto unexplained puzzles and circumvents some long-standing problems of the standard paradigm.