arXiv subjects
Publications and source records attributed to Rituparno Goswami.
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.
The problem of matching different regions of spacetime in order to construct inhomogeneous cosmological models is investigated in the context of Lagrangian theories of gravity constructed from general analytic functions f(R), and from non-analytic theories with f(R)=R^n. In all of the cases studied, we find that it is impossible to satisfy the required junction conditions without the large-scale behaviour reducing to that expected from Einstein's equations with a cosmological constant. For theories with analytic f(R) this suggests that the usual treatment of weak-field systems as perturbations about Minkowski space may not be compatible with late-time acceleration driven by anything other than a constant term of the form f(0), which acts like a cosmological constant. In the absence of Minkowski space as a suitable background for weak-field systems, one must then choose and justify some other solution to perform perturbative analyses around. For theories with f(R)=R^n we find that no known spherically symmetric vacuum solutions can be matched to an expanding FLRW background. This includes the absence of any Einstein-Straus-like embeddings of the Schwarzschild exterior solution in FLRW spacetimes.
The relation between the expanding universe and local vacuum solutions, such as that for the Solar System, is crucially mediated by Birkhoff's theorem. Here we consider how that relation works, and give generalizations of Birkhoff's theorem when there are geometric and matter and perturbations. The issue of to what degree dark matter might influence the solar system emerges as a significant question.
This paper examines the various arguments that have been put forward suggesting either that time does not exist, or that it exists but its flow is not real. I argue that (i) time both exists and flows; (ii) an Evolving Block Universe (`EBU') model of spacetime adequately captures this feature, emphasizing the key differences between the past, present, and future; (iii) the associated surfaces of constant time are uniquely geometrically and physically determined in any realistic spacetime model based in General Relativity Theory; (iv) such a model is needed in order to capture the essential aspects of what is happening in circumstances where initial data does not uniquely determine the evolution of spacetime structure because quantum uncertainty plays a key role in that development. Assuming that the functioning of the mind is based in the physical brain, evidence from the way that the mind apprehends the flow of time prefers this evolving time model over those where there is no flow of time.
We construct a compact phase space for flat FLRW spacetimes with standard matter described by a perfect fluid with a barotropic equation of state for general f(R) theories of gravity, subject to certain conditions on the function f. We then use this framework to study the behaviour of the phase space of Universes with a non-negative Ricci scalar in R + αR^n gravity. We find a number of interesting cosmological evolutions which include the possibility of an initial unstable power-law inflationary point, followed by a curvature fluid dominated phase mimicking standard radiation, then passing through a standard matter (CDM) era and ultimately evolving asymptotically towards a de-Sitter-like late-time accelerated phase.
We analyze here the final fate of complete gravitational collapse of a massless scalar field within general relativity. A class of dynamical solutions with initial data close to the Friedmann-Lemaitre-Robertson-Walker (FLRW) collapse model is explicitly given and the Einstein equations are integrated numerically in a neighborhood of the center. We show that the initial data space is evenly divided between the dynamical evolutions that terminate in a black hole final state and those that produce a locally naked singularity. We comment on the genericity aspects of the collapse end-states and the connection to cosmic censorship conjecture is pointed out.
We show in a fully covariant way that, there exist a class of $f(R)$ models for which a shear-free, almost FLRW universe can expand and rotate at the same time .
Birkhoff's theorem for spherically symmetric vacuum spacetimes is a key theorem in studying local systems in general relativity theory. However realistic local systems are only approximately spherically symmetric and only approximately vacuum. In a previous paper, we showed the theorem remains approximately true in an approximately spherically symmetric vacuum space time. In this paper we prove the converse case: the theorem remains approximately true in a spherically symmetric, approximately vacuum space time.
Recently it was shown that if the matter congruence of a general relativistic perfect fluid flow in an almost FLRW universe is shear-free, then it must be either expansion or rotation-free. Here we generalize this result for a general f(R) theory of gravity and show there exist scenarios where this result can be avoided. This suggests that there are situations where linearized forth-order gravity shares properties with Newtonian theory not valid in General Relativity.
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.
The phenomena of collapse and dispersal for a massless scalar field has drawn considerable interest in recent years, mainly from a numerical perspective. We give here a sufficient condition for the dispersal to take place for a scalar field that initially begins with a collapse. It is shown that the change of the gradient of the scalar field from a timelike to a spacelike vector must be necessarily accompanied by the dispersal of the scalar field. This result holds independently of any symmetries of the spacetime. We demonstrate the result explicitly by means of an example, which is the scalar field solution given by Roberts. The implications of the result are discussed.
We extend Birkhoff's theorem for almost LRS-II vacuum spacetimes to show that the rigidity of spherical vacuum solutions of Einstein's field equations continues even in the perturbed scenario.
Several different explicit reconstructions of f(R) gravity are obtained from the background FRW expansion history. It is shown that the only theory whose Lagrangian is a simple function of the Ricci scalar R, that admits an exact LCDM expansion history is standard General Relativity with a positive cosmological constant and the only way to obtain this behaviour of the scale factor for more general functions of R is to add additional degrees of freedom to the matter sector.
We present a new approach of the reconstruction method based on the use of the cosmic parameters instead of a time law for the scale factor. This allows the derivation and analysis of a set of new non-trivial cosmological solutions for $f(R)$-gravity. A number of simple examples are given.
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 incite on how the current form of Birkhoff's theorem breaks down for these theories.
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^n gravity. We find that for this case more bending is expected for R^n gravity theories in comparison to GR and is dependent on the value of n and the value of distance of closest approach of the incident null geodesic.
We study here the evolution of a massless scalar field in a spacetime, developing from a regular initial spacelike surface. The Einstein equations and regularity and boundary conditions governing the same are specified. Both homogeneous and inhomogeneous collapse models are considered and we analyze when the occurrence of singularity will be simultaneous or otherwise. In the inhomogeneous collapse case, we characterize a wide family of black hole solutions arising in scalar field collapse. We also discuss the possibility of existence of classes of non-singular models where collapse could almost freeze if suitable conditions are satisfied.
Working within the theory of modified Gauss-Bonnet gravity, we show that FLRW--like power--law solutions only exist for a very special class of f(G)theories. Furthermore, we point out that any transition from decelerated to accelerated expansion must pass through G=0, and no function f(G) that is differentiable at this point can admit both a decelerating power--law solution and any accelerating solution. This strongly constrains the cosmological viability of f(G)-gravity, since it may not be possible to obtain an expansion history of the universe which is compatible with observations. We explain why the same issue does not occur in f(R)-gravity and discuss possible caveats for the case of f(G)-gravity.