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

Abstract

Effective gravitational field equations on a four dimensional brane embedded in a five dimensional bulk have been considered. Using the Einstein-Hilbert action along with the Gauss-Bonnet correction term, we have derived static spherically symmetric vacuum solution to the effective field equations, first order in the Gauss-Bonnet coupling parameter. The solution so obtained, has one part corresponding to general relativity with an additional correction term, proportional to the Gauss-Bonnet coupling parameter. The correction term modifies the spacetime structure, in particular, the location of the event horizon. Proceeding further, we have derived effective field equations for f (R) gravity with Gauss-Bonnet correction term and a static spherically symmetric solution has been obtained. In this case the Gauss-Bonnet term modifies both the event and cosmological horizon of the spacetime. There exist another way of obtaining the brane metric -expanding the bulk gravitational field equations in the ratio of bulk to brane curvature scale and assuming a separable bulk metric ansatz. It turns out that static, spherically symmetric solutions obtained from this perturbative method can be matched exactly, with the solutions derived earlier. This will hold for Einstein-Hilbert plus Gauss-Bonnet as well as for f(R) with the Gauss-Bonnet correction. Implications of these results are discussed.

Tensor Perturbations and Thick Branes in Higher-dimensional $f(R)$ Gravity

“…Particularly, an investigation of spherically symmetric branes in the presence of f (R) gravity was made in Refs. [9,50,51]. Moreover, a complete investigation should include the localization of matter fields on the brane.…”

“…where a newly defined coupling constant κ6 = 3 √ 5κ 6 is adopted. In this special case, we can obtain an analytical expression for the scalar potential V(φ): split for a small n. There is a critical value n c = ( √ 65 + 3)/10 ≃ 1.106 , which satisfies the condition (51). The brane is not split for n > n c .…”

Fate of strong cosmic censorship conjecture in presence of higher spacetime dimensions

“…However, all these analysis are in the context of four dimensional spacetime and thus it seems legitimate to understand the validity of strong cosmic censorship conjecture in presence of higher dimensions. For this purpose we will mainly use two possibilities -(a) The black hole itself could live in a higher dimensional spacetime (for a incomplete set of references, see [32][33][34][35][36][37][38][39][40]) or, (b) The black hole is living on the four dimensional spacetime (which we will call brane), while the spacetime itself is higher dimensional [41][42][43][44][45][46][47][48][49]. In the first context the gravitational field equations will remain the same, but the effect of higher dimension will change the metric elements from the four dimensional one.…”

Echoes from the braneworld black holes

“…As in the standard scenario with an extra spatial dimension, the matter fields are localized on a four dimensional brane and only gravity can propagate in the five dimensional bulk spacetime [25][26][27]. Such an approach calls for obtaining the effective gravitational field equations on the four dimensional brane, which was derived using the Gauss-Codazzi formalism in [28][29][30][31][32]. The effective gravitational field equations so obtained, can be solved for a static and spherically symmetric spacetime, yielding a metric which resembles a Reissner-Nordström black hole with a 'tidal charge' instead of the usual electric charge [33].…”