Abstract
There are many modification of Einstein theory have been established which explain the behavior of universe realistically or hypo-theoretically. Out of those, an f(R) theory of gravity based on non-conformal invariance of gravitational waves has been developed. We attempted to find the solution of this theory for spherically symmetric spacetime in vacuum and compared its result to Einstein theory. We have concluded that solution is consistent with Newtonian limit at large distance from source. Solution predicts two horizon in the spacetime, none of them coincides with Schwarzschild counterpart. However, as this f(R) theory converges to Einstein theory, these horizons coincide.
Highlights
(General Relativity), its spherically symmetric solution is inevitable
Here κ is coupling constant between energy and matter and Tij is energy momentum tensor which provides a further generalization of f (R) theories to f (R, T ) theories [19] with T as trance of energy momentum tensor
An f (R) theory of gravity motivated by Gravitational waves provides space-time ds2 =
Summary
The trace of (1.4) relates R with T diffentially not algebraically as in case of Einstein field equation, where R = κT. An f (R) theory of gravity motivated by Gravitational waves provides space-time ds2 =. If all of b’s are zero in equation (2.9), we get spherically symmetric solution of Einstein field equation i.e. Schwarzschild solution. These terms appear due to the correction in the Hilbert Lagrangian, R and the contribution of each successive term becomes smaller and smaller as we go to higher powers of r in equation (2.8).
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