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Effective gravitational field equations on a four dimensional brane embeddedin a five dimensional bulk have been considered. Using the Einstein-Hilbertaction along with the Gauss-Bonnet correction term, we have derived staticspherically symmetric vacuum solution to the effective field equations, firstorder in the Gauss-Bonnet coupling parameter. The solution so obtained, has onepart corresponding to general relativity with an additional correction term,proportional to the Gauss-Bonnet coupling parameter. The correction termmodifies the spacetime structure, in particular, the location of the eventhorizon. Proceeding further, we have derived effective field equations for$f(R)$ gravity with Gauss-Bonnet correction term and a static sphericallysymmetric solution has been obtained. In this case the Gauss-Bonnet termmodifies both the event and cosmological horizon of the spacetime. There existanother way of obtaining the brane metric --- expanding the bulk gravitationalfield equations in the ratio of bulk to brane curvature scale and assuming aseparable bulk metric ansatz. It turns out that static, spherically symmetricsolutions obtained from this perturbative method can be matched exactly, withthe solutions derived earlier. This will hold for Einstein-Hilbert plusGauss-Bonnet as well as for f(R) with the Gauss-Bonnet correction. Implicationsof these results are discussed.

Spherically symmetric brane in a bulk of f(R) and Gauss-Bonnet Gravity