Abstract:

Parallel to the great revolution in science witnessed in the first decades of the 20th century in view of the discovery of quantum mechanics, Einstein’s theory of General Relativity emerges as a big breakthrough in the history of physics. This theory made a remarkable change in the basic physical concepts with respect to space, time and matter. It attributed a geometrical meaning to the gravitational phenomena, or in other words gave spacetime geometry a physical signification by identifying the gravitational field with the space curvature described in terms of Riemannian geometry and presented in tensorial form. This situation with Einstein’s theory makes it isolated from the mainstream of physical laws by being not amenable to unification with other field theories or sharing common grounds with the wellestablished quantum theory. The predictions of general relativity were tested to be successful when applied to weakfield gravity, viz, of the solar system whereas its predictions with the large scales of the Universe where gravity is strong leads to a bizarre description. This description is realized in the reckoned gravitational collapse of massive stars due to which black hole exotics thought to be created, that still need to be verified, in addition to certain cosmological problems that need to be solved. On the other hand beside these setbacks of this theory in the macroscopic scales it suffers from defectiveness in the microscopic domains of atomic and subatomic dimensions where again gravity is assumed to be strong and hence quantum effects are believed to be dominant. In view of these difficulties mostly all efforts towards rectifying this theory run to acute mathematical complications and eventually led to no significant success.
In this thesis we contribute to these efforts with the aim of achieving improved results through the replacement of Einstein’s equations of the 2nd differential order by generalized Lagrangianbased 4th order differential equations of gravitation. These generalized equations have been thoroughly investigated and studied both analytically and computationally. Treating these equations by utilizing a Lagrangian density quadratic in the scalar curvature R as well as employing a complex spacetime metric yields a wellbehaved nonsingular solution that may elucidate the enigmatic irregular behavior within the subtle features of strong gravity which is inexplicable in the framework of Einstein’s model. Thus, besides preventing the occurrence of singular behavior inherent in General Relativity the obtained solutions hopefully reveal ideas paving the route to a classically comprehensive theory of gravitation and indicating towards its long sought quantized formulation at strong field gravity. 