Anne Marie Nzioki

Collapsing spherical stars in f(R) gravity

We perform a careful investigation of the problem of physically realistic gravitational collapse of massive stars in f(R)-gravity. We show that the extra matching conditions that arise in the modified gravity imposes strong constraints on the stellar structure and thermodynamic properties. In our opinion these constraints are unphysical. We prove that no homogeneous stars with non-constant Ricci scalar can be matched smoothly with a static exterior for any nonlinear function f(R). Therefore, these extra constraints make classes of physically realistic collapse scenarios in general relativity, non-admissible in these theories. We also find an exact solution for an inhomogeneous collapsing star in the Starobinski model that obeys all the energy and matching conditions. However, we argue that such solutions are fine-tuned and unstable to matter perturbations. Possible consequences on black hole physics and the cosmic censorship conjecture are also discussed.

New framework for studying spherically symmetric static solutions in f (R) gravity

We develop a new covariant formalism to treat spherically symmetric spacetimes in metric f(R) theories of gravity. Using this formalism we derive the general equations for a static and spherically symmetric metric in a general f(R) gravity. These equations are used to determine the conditions for which the Schwarzschild metric is the only vacuum solution with vanishing Ricci scalar. We also show that our general framework provides a clear way of showing that the Schwarzschild solution is not a unique static spherically symmetric solution, providing some insight into how the current form of Birkhoffs theorem breaks down for these theories.

On the absence of the usual weak-field limit, and the impossibility of embedding some known solutions for isolated masses in cosmologies with f(R) dark energy

This version deposited at arxiv 02-10-12 arXiv:1210.0730v1. Subsequently published in Physical Review D as Phys. Rev. D 87, 063517 (2013) http://link.aps.org/doi/10.1103/PhysRevD.87.063517. Copyright American Physical Society (APS).

Jebsen-Birkhoff theorem and its stability inf(R)gravity

We prove a Jebsen-Birkhoff like theorem for f(R) theories of gravity in order to to find the necessary conditions required for the existence of the Schwarzschild solution in these theories and demonstrate that the rigidity of such solutions of f(R) gravity is valid even in the perturbed scenario.

Buchdahl-Bondi limit in modified gravity: Packing extra effective mass in relativistic compact stars

We generalise the Buchdahl-Bondi limit for the case of static, spherically symmetric, relativistic compact stars immersed in Schwarzschild vacuum in f(R)-theory of gravity, subject to very generic regularity, thermodynamic stability and matching conditions. Similar to the case of general relativity, our result is model independent and remains true for any physically realistic equation of state of standard stellar matter. We show that an extra-massive stable star can exist in these theories, with surface redshift larger than 2, which is forbidden in general relativity. This result gives a novel and interesting observational test for validity or otherwise of general relativity and also provides a possible solution to the dark matter problem.

Geometrical approach to strong gravitational lensing in f(R) gravity

We present a framework for the study of lensing in spherically symmetric spacetimes within the context of f(R) gravity. Equations for the propagation of null geodesics, together with an expression for the bending angle, are derived for any f(R) theory and then applied to an exact spherically symmetric solution of R{sup n} gravity. We find that for this case more bending is expected for R{sup n} gravity theories in comparison to general relativity and is dependent on the value of n and the value of the distance of closest approach of the incident null geodesic.

Strong gravitational lensing in f(R) gravity

We present a new framework for the study of lensing in spherically symmetric spacetimes within the context of f(R) gravity.

Shear-free perturbations of Friedmann-Lemaître-Robertson-Walker universes

A surprising exact result for the Einstein Field Equations is that if pressure-free matter is moving in a shear-free way, then it must be either expansion-free or rotation-free. It has been suggested this result is also true for any barotropic perfect fluid, but a proof has remained elusive. We consider the case of barotropic perfect fluid solutions linearized about a Robertson-Walker geometry, and prove that the result remains true except for the case of a specific highly non-linear equation of state. We argue that this equation of state is non-physical, and hence the result is true in the linearized case for all physically realistic barotropic perfect fluids. This result, which is not true in Newtonian cosmology, demonstrates that the linearized solutions, believed to result in standard local Newtonian theory, do not always give the usual behaviour of Newtonian solutions.

Covariant perturbations of Schwarzschild black holes in f(R) gravity

We consider general perturbations of a Schwarzschild black holes in the context of f(R) gravity. A reduced set of frame independent master variables are determined, which obey two closed wave equations — one for the transverse, trace-free, tensor perturbations and the other for the additional scalar degree of freedom which characterize fourth-order theories of gravity. We show that for the tensor modes, the underlying dynamics in f(R) gravity is governed by a modified Regge–Wheeler tensor which obeys the same Regge–Wheeler equation as in General Relativity (GR). We find that the possible sources of scalar quasinormal modes (QNMs) that follow from scalar perturbations for the lower multipoles result from primordial black holes, while higher mass, stellar black holes are associated with extremely high multipoles, which can only be produced in the first stage of black hole formation. Since scalar quasinormal modes are short ranged, this scenario makes their detection beyond the range of current experiments.