Myrzakulov gravity in vielbein formalism: A study in Weitzenböck spacetime

The quest to understand the nature of gravity and its role in shaping the universe has led to the exploration of modified gravity theories. One of the pioneering contributions in this field is the Myrzakulov gravity theory, which incorporates both curvature and torsion. In this work, we investigate the effects of torsion within the framework of $f(R,T)$-gravity, a modification of General Relativity that incorporates both curvature and torsion.

We present this theory in the Vielbein formalism, a covariant approach that provides a more flexible and geometric perspective on gravity, ensuring the theory's consistency under general coordinate transformations. This formalism is particularly powerful in the context of Weitzenböck spacetime, where torsion plays a significant role in the description of gravitational interactions. By studying $f(R,T)$-gravity in Vielbein formalism, we aim to extend the applicability of Myrzakulov's theory, providing a deeper understanding of its cosmological and astrophysical implications.

We examine the profound effects of this theory on various astrophysical phenomena, including black holes, gravitational waves, and compact objects like neutron stars. By exploring how torsion modifies the behavior of these extreme systems, we uncover new avenues for testing gravity in the strong-field regime. Our results suggest that torsion could lead to observable deviations in black hole thermodynamics, gravitational wave propagation, and the structure of dense matter.

The modifications we uncover have the potential to provide unprecedented insights into the nature of spacetime and gravity, offering a novel perspective on the fundamental forces that govern the cosmos. This work paves the way for future observational and theoretical studies that could reveal the deeper, hidden aspects of gravity, possibly rewriting our understanding of the universe's most enigmatic phenomena. Through both observational data and theoretical advancements, we present a compelling case for the exploration of $f(R,T)$-gravity as a powerful tool in the search for new physics beyond General Relativity.