Non-Conservative Gravitational Equations

New Black Holes Solutions in a Modified Gravity

“…Similarly, later, inspired by the foundations of the gauge theory, Mignani et al [22] apply a new methodology for the commutators algebra of covariant derivatives which is the construction of a modification of the GR and which leads to the GR in a particular case. In the same way as Camenzind [21], Mignani et al found an imposition on the theory, that is, the 4-current acts as the source of the matter content and is conserved, while the energy-momentum tensor is not.…”

“…In this paper, we will explain more clearly some basic concepts of the theory constructed by Mignani et al [22], through the original inspiration of the gauge theory and the commutator algebra of covariant derivatives [26], for a Riemannian spacetime, defined through the Levi-Civita connection. We reobtain the equations of motion of this theory, taking into account all original ingredients used by Mignani, getting a model that possesses an equation of motion different from that presented in [22].…”

“…We reobtain the equations of motion of this theory, taking into account all original ingredients used by Mignani, getting a model that possesses an equation of motion different from that presented in [22]. We will analyse in this paper only the vacuum case in which the metric is static and possesses spherical symmetry.…”

“…The General Relativity. Let us firstly rewrite some equations coming from the GR, to be used as the inspiration to the modification made by Mignani et al [22]. The spacetime is considered to have the Riemannian manifold, in which the line element is given by…”

“…Hence, all this is well known and established in the GR. In the next section, we will introduce the fundamental concepts of the theory constructed by Mignani et al [22].…”