arXiv:1112.2522v2 [gr-qc] 19 Apr 2012 Circular geodesics and accretion disks in Janis-Newman-Winicour and Gamma metric Anirban N. Chowdhury, ∗ Mandar Patil, † Daniele Malafarina, ‡ and Pankaj S.Joshi § Tata Institute ofFundamental Research, Homi Bhabha Road, Colaba,Mumbai400005,India We study here circular timelike geodesics in the Janis-Newman-Winicour and Gamma metric spacetimes which contain a strong curvature naked singularity and reduce to the Schwarzschild metric for a specific value of one of the parameters. We show that for both the metrics the range of allowed parameters can be divided into three regimes where structure of the circular geodesics is qualitatively different. It follows that the properties of the accretion disks around such naked singularities can be significantly different from those of disks around black holes.This adds to previous studies showing that if naked singularities exist in nature, their observational signature would be significantly different from that of the black hole. PACS numbers: 04.20.Dw,04.20.Jb,04.70 Bw I. INTRODUCTION One of the most important unresolved problems in gen- eralrelativity,and an issue that has far reaching obser- vational implications, is that of the final fate of complete gravitational collapse of a massive body such as a star. The Israel-Carter conjecture asserts that a Kerr black hole, which is described by two parameters, namely mass and angular momentum, would be formed as the endstate of any generic complete gravitational collapse and thus all other information regarding the nature of the mat- ter fields, symmetries, initial conditions will be radiated away in the process of collapse. The above statement re- mains at the stage of conjecture as of now because prov- ing it analytically or numerically is turning out to be a very difficult task. We also do not understand very well how matter would behave at energies beyond nuclear en- ergy scales all the way up to Planck scale as we have no theoretical understanding of evolution of the equation of state ofmatter at such energies. Thus the theoretical studies do not provide a definite answer to the question whether or not black holes are the only possible outcomes of the gravitational collapse. In fact in the last few years new theoretical models and observations seem to suggest that the true nature of the process could be more complicated. Investigations of gravitational collapse of various matter configurations in the context ofthe generaltheory ofrelativity over last couple ofdecades has revealed that the endstates of complete gravitational collapse could either be black holes or naked singularities [1]. Therefore it is natural to ask the question of what hap- pens during a realistic collapse of a massive body and what willbe the endstate of such a collapse. The possi- bilities can be divided into three main categories: ∗ Electronic address:a.chowdhury@iiserpune.ac.in † Electronic address:mandarp@tifr.res.in ‡ Electronic address:daniele.malafarina@polimi.it § Electronic address:psj@tifr.res.in - The body radiates away all higher multipole mo- mentsand all asymmetry,thus forming a Kerr black hole. - Collapse will halt before all matter is squeezed into a spacetime singularity, thus creating a finite sized final object that is different from a black hole. - Matter will fall into the final spacetime singularity preserving its symmetry structure, thus creating a final configuration in the form of vacuum spacetime with a singularity (that can be covered or naked). The analytical solutions describing dynamical collapse of a rotating body away from spherical symmetry are few and not wellunderstood at present. Therefore a possi- ble mechanism to account for the first hypothesis is still missing.For this reason it seems natural to turn atten- tion to the other two options. Ideas following the sec- ond hypothesis have been proposed [2], but the nature of these objects and the physical processes that could lead to the formation ofthe same are not well understood. Furthermore recently some new scenarios have been pro- posed that include the possibility that gravitational col- lapse can asymptotically halt, leading to the formation of static configuration of matter that may or may not con- tain a naked singularity and which could be either finite or infinite in extent [3]. On the other hand, if black holes and naked singular- ities which are hypothetical astrophysical objects occur in nature,a question would be how they would be ob- servationally different. Therefore some researchers have started looking into the observational features that would distinguish these entities. The black holes and naked sin- gularities could have rather different properties and this could also possibly shed a light on the nature of the ex- isting sources, like the supermassive dark objects that dwellat the center of galaxies. Recent studies of gravi- tational lensing (see for example [4]) and accretion disks (see [3, 5, 6] and [7]) have brought out interesting charac- teristic differences for these objects which could possibly distinguish them from each other. Recently it was also suggested by some of us that ultrahigh energy collisions