Characteristic formulation for metric f(R) gravity

Abstract

In recent years, the Characteristic formulation of numerical relativity has found increasing use in the extraction of gravitational radiation from numerically generated spacetimes. In this paper, we formulate the Characteristic initial value problem for f (R) gravity. We consider, in particular, the vacuum field equations of Metric f (R) gravity in the Jordan frame, without utilising the dynamical equivalence with scalar-tensor theories. We present the full hierarchy of non-linear hypersurface and evolution equations necessary for numerical implementation in both tensorial and eth forms. Furthermore, we specialise the resulting equations to situations where the spacetime is almost Minkowski and almost Schwarszchild using standard linearization techniques. We obtain analytic solutions for the dominant ℓ = 2 mode and show that they satisfy the concomitant constraints. These results are ideally suited as testbed solutions for numerical codes. Finally, we point out that the Characteristic formulation can be used as a complementary analytic tool to the 1 + 1 + 2 semi-tetrad formulation. * Electronic address: bishop.mongwane@uct.ac.za Within the numerical relativity community, there are now a number of Characteristic codes being used, with differing levels of sophistication. For instance, some codes employ second order finite difference schemes [38], others use higher order schemes [68] while others have adopted Spectral methods [41]. Another point of distinction among different codes is the coordinate system used to cover the sphere labelling the null directions of the light cones. Common choices range from stereographic coordinate system [15] to multi-patch coordinate systems [38,67]. There has also been efforts to introduce Adaptive Mesh Refinement schemes to Characteristic evolution codes [64,78]. Overall, these codes have made it possible to demonstrate the versatility of Characteristic methods in numerical relativity and have found extensive applications in, for example, binary black hole mergers [4,15,42,65], stellar core collapse [61,66,73], Einstein-Klein-Gordon systems [6,39,62], Observational Cosmology [9, 79, 80] etc. These systems represent potential astrophysical laboratories for testing general relativity in the non-linear regime.Over the years, the theory of general relativity has been subjected to a wide range of experimental tests and has no doubt emerged as one of the most successful theories in Physics. However, there has been considerable interest in the literature to study gravity theories whose Lagrangians contain higher order curvature invariants such as 29,71,74]. The motivation for these alternative theories of gravity stems from a variety of grounds, most notably from within the dark sector in Cosmology [28]. Moreover, the inflationary paradigm arises naturally in alternative theories of gravity without postulating additional inflaton fields [29,74,75]. These higher order corrections also arise in the effective action of quantum gravity. For example, in the low energy limit of string theory o...

Wormhole solutions in f(R) gravity

“…From f (R) gravity viewpoint, Capozziello and Laurentis 55 have given an alternate approach to dark matter problem. A few notable works under f (R) gravity are as follows: Tripathy and Mishra 56 presented a vacuum solution with reconstructed Ricci scalar, Mongwane 57 formulated the characteristic initial value problem for f (R) gravity, Liu et al 58 have constrained the f (R) gravity in cosmology, solar system as well as binary pulsar systems, and Lazkoz et al 59 reformulated f (R) Lagrangian terms as an explicit functions of the redshift. It is worth to mention here that, Bronnikov and Starobinsky 60 proved that wormholes can not be formed in dark energy models governed by scalar tensor theory even in the presence of electric or magnetic fields.…”

Gravitational baryogenesis models comparison in f(R) Gravity

“…Tripathy and Mishra [23] have obtained anisotropic solutions in f (R) gravity without invoking any matter field. Mongwane [24] has formulated the characteristic initial value problem for f (R) gravity. Liu et al [25] have constrained the f (R) gravity in cosmology, solar system and pulsar systems.…”

Black Hole Dynamics in Power-law based Metric $f(R)$ Gravity

“…There are many ways to modifying the theory of gravity such as f (R) gravity [41][42][43][44][45][46][47][48], f (T ) gravity [49,50], f (R, T ) gravity [51][52][53] etc., where T is the trace of energy-momentum tensor. Among them simplest one is f(R) gravity obeying metric formalism [54,55].…”