174 research outputs found
Field equations for Lovelock gravity: An alternative route
We present an alternative derivation of the gravitational field equations for
Lovelock gravity starting from the Newton's law, which is closer in spirit to
the thermodynamic description of gravity. As a warm up exercise, we have
explicitly demonstrated that projecting the Riemann curvature tensor
appropriately and taking a cue from Poisson's equation, the Einstein's
equations immediately follow. The above derivation naturally generalizes to
Lovelock gravity theories where an appropriate curvature tensor satisfying the
symmetries as well as the Bianchi derivative properties of the Riemann tensor
has to be used. Interestingly, in the above derivation, the thermodynamic route
to gravitational field equations, suited for null hypersurfaces, emerge quiet
naturally.Comment: Invited Article; 11 pages, no figure
Effective field equation on m-brane embedded in n-dimensional bulk of Einstein and f(R) gravity
We have derived effective gravitational field equations on a lower
dimensional hypersurface (known as a brane), placed in a higher dimensional
bulk spacetime for both Einstein and gravity theories. We have
started our analysis on -dimensional bulk from which the effective field
equations on a -dimensional brane has been obtained by imposing
symmetry. Subsequently, we have arrived at the effective equations in
-dimensions starting from the effective equations for
dimensional brane. This analysis has been carried forward and is used to obtain
the effective field equations in -dimensional brane, embedded in a
-dimensional bulk. Having obtained the effective field equations in Einstein
gravity, we have subsequently generalized the effective field equation in
-dimensional brane which is embedded the -dimensional bulk spacetime
endowed with gravity. We have also presented applications of
our results in the context of Einstein and gravity. In both
the cases we have discussed vacuum static spherically symmetric solutions as
well as solutions in cosmological context. Implications are also discussed.Comment: v2, Revised, Accepted in EPJC, 35 pages, no figure
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