For spacetime (2), the
Einstein field equations (1) read
Assume [bar.M] admits the following imperfect fluid
Einstein field equations:
Einstein used tensors to develop his equation describing the gravitational field, known as the
Einstein field equation.
Solutions of the
Einstein field equations are certain types of spacetime.
If spherical symmetry is maintained and if, in addition, the matter distribution contained charge, then the
Einstein field equations must be supplemented by Maxwell's equations which incorporate the effects of the electromagnetic field.
In the Einstein's field equations the Gravitational constant G has been introduced via the Newtonian approximation of the
Einstein field equation. Later on the constant G is related to the long-range scalar field and hence, it varies as the universe expands [3].
Observer participancy: In his 1998 work, Physics From Fisher Information: A Unification, Roy Frieden has derived most known physics, including statistical mechanics, thermodynamics, quantum mechanics, and the
Einstein field equations, from a new theory that makes the observer part of the measured phenomenon.
Jacobson [17] obtained the
Einstein field equations using fundamental relation known as Clausius relation dQ = TdS (S, T, and dQ represent the entropy, Unruh temperature, and energy flux observed by accelerated observer just inside the horizon, resp.) together with the proportionality of entropy and horizon area in the context of Rindler space-time.
The outer region is described by the Vaidya solution and the space-time metric in the interior is obtained by solving the
Einstein field equations. Further, proper boundary conditions are imposed in order to guarantee a smooth matching of the solutions in the surface of the junction.
Key words: Ricci curvature tensors,
Einstein Field Equations, Black hole, Vacuum Solutions
Utilizing (1)-(3), we obtain the
Einstein field equations