Search

In this work, we investigate tidal forces in the Lemaitre-Tolman-Bondi (LTB) metric, focusing on both hidden and locally visible singularities. We discuss the strength of these singularities in terms of deformationally strong singularities. Specifically, we analyze tidal forces in LTB spacetime, calculating radial and angular tidal forces and Jacobi fields for the radially co-moving shell. To provide a comparative study, we consider both homogeneous and inhomogeneous cases. The matter field distribution at one-time slice can differ significantly from another, highlighting the potential for time-dependent tidal deformation as a distinct observational signature. We focus on a specific feature: the time-varying maximum of stretching in the radial tidal force, which we term the "critical tidal boundary." In the inhomogeneous case, close to singularity time ($t

In this paper, we investigate the caustic point developed by outgoing null hypersurfaces and the behavior of null curves. We analyze three cases: Future, past, and zero caustic point terminology for outgoing null hypersurfaces in the marginally bound Lemaitre-Tolman-Bondi (LTB) metric for homogenous and inhomogeneous cases defined in the present work. We show the criteria to form local and globally visible singularity in terms of the tangent on the apparent horizon curve., Comment: 10 pages, 3 figures

In this article, we investigate the gravitational field of a charged, non-vacuum, non-rotating, spherically symmetric body of mass $M$ assuming a static solution to the Einstein-Maxwell field equations. We demonstrate that the characteristics of perihelion precession of orbits in Schwarzschild and Null singularity spacetimes are similar, whereas, in the case of charged naked singularity (CNS) spacetime, the characteristics are the opposite of those in Schwarzschild and Null singularity spacetime. Here we discuss some novel features of the timelike and lightlike geodesics in this spacetime. We also discuss the comparative study of tidal force in the null singularity spacetime and charged naked singularity spacetime., Comment: 9 pages, 6 figures

In the case of unhindered gravitational collapse of matter cloud governed by the Lemaitre-Tolman-Bondi (LTB) spacetime, the end-state singularity is either locally visible, globally visible or completely hidden. We have a past-null singularity in the first two cases while a future-spacelike singularity in the last case. Here, we show an example of a gravitational collapse model whose end-state is a future-null-singularity (it has a causal property that is unlike the cases involving LTB spacetime). We depict such a distinct causal structure of the singularity by conformal diagrams., Comment: 7 pages, 4 figures

Software engineering activities such as package migration, fixing errors reports from static analysis or testing, and adding type annotations or other specifications to a codebase, involve pervasively editing the entire repository of code. We formulate these activities as repository-level coding tasks. Recent tools like GitHub Copilot, which are powered by Large Language Models (LLMs), have succeeded in offering high-quality solutions to localized coding problems. Repository-level coding tasks are more involved and cannot be solved directly using LLMs, since code within a repository is inter-dependent and the entire repository may be too large to fit into the prompt. We frame repository-level coding as a planning problem and present a task-agnostic framework, called CodePlan to solve it. CodePlan synthesizes a multi-step chain of edits (plan), where each step results in a call to an LLM on a code location with context derived from the entire repository, previous code changes and task-specific instructions. CodePlan is based on a novel combination of an incremental dependency analysis, a change may-impact analysis and an adaptive planning algorithm. We evaluate the effectiveness of CodePlan on two repository-level tasks: package migration (C#) and temporal code edits (Python). Each task is evaluated on multiple code repositories, each of which requires inter-dependent changes to many files (between 2-97 files). Coding tasks of this level of complexity have not been automated using LLMs before. Our results show that CodePlan has better match with the ground truth compared to baselines. CodePlan is able to get 5/6 repositories to pass the validity checks (e.g., to build without errors and make correct code edits) whereas the baselines (without planning but with the same type of contextual information as CodePlan) cannot get any of the repositories to pass them.

Various astrophysical and cosmological observations today serve as an indirect evidence of the existence of dark matter in the universe. In the present work, we propose a class of spacetimes that show some important characteristics relevant to the spacetime of a dark matter halo. These spacetimes are static and spherically symmetric solutions of the Einstein field equations. The proposed spacetimes satisfy the flat velocity profile of a galactic object far away from the center, they give good agreement to the astrometric data of the S2 star, and these also cast a central shadow. Using the Penrose diagram, we show that the causal nature of the central singularity here is null. This single spacetime model for galactic dark matter may therefore be used to explain some of the properties of galactic dynamics at different length scales., Comment: 16 pages, 8 figures

The general theory of relativity predicts the relativistic effect in the orbital motions of S-stars which are orbiting around our Milky-way galactic center. The post-Newtonian or higher-order approximated Schwarzschild black hole models have been used by GRAVITY and UCLA galactic center groups to carefully investigate the S2 star's periastron precession. In this paper, we investigate the scalar field effect on the orbital dynamics of S2 star. Hence, we consider a spacetime, namely Janis-Newman-Winicour (JNW) spacetime which is seeded by a minimally coupled, mass-less scalar field. The novel feature of this spacetime is that one can retain the Schwarzschild spacetime from JNW spacetime considering zero scalar charge. We constrain the scalar charge of JNW spacetime by best fitting the astrometric data of S2 star using the Monte-Carlo-Markov-Chain (MCMC) technique assuming the charge to be positive. Our best-fitted result implies that similar to the Schwarzschild black hole spacetime, the JNW naked singularity spacetime with an appropriate scalar charge also offers a satisfactory fitting to the observed data for S2 star. Therefore, the JNW naked singularity could be a contender for explaining the nature of Sgr A* through the orbital motions of the S2 star., Comment: 6 pages, 3 figures, 2 tables

In this paper, we investigate the light trajectories and shadow properties in the rotating version of null naked singularity (NNS) spacetime which is derived using the Newman- Janis algorithm without complexification method. We discuss some of the geometrical properties and causal structure of Rotating Naked Singularity (RNS) spacetime. The gravitational lensing in a rotating naked singularity is analyzed, and the results are compared to those of a Kerr black hole. In the case of a Kerr black hole, the photon sphere exists for both prograde and retrograde photon orbits, whereas for RNS, the photon sphere exists only for retrograde photon orbits. As a result, the naked singularity projects an arc-shaped shadow that differs from the contour-shaped shadow cast by a Kerr black hole., Comment: 12 pages, 4 figures

In the present paper, we study the thermal properties of the geometrically thin accretion disks surrounding the null naked singularity (NNS) and the first type of Joshi-Malafarina-Narayan (JMN1) spacetimes and compare the results with the accretion disk around equally massive Schwarzschild black hole. First, we examine the properties of the circular orbits in these spacetimes. The emitted flux, radiation spectra, disk efficiency, and temperature distribution on the disk surface are then investigated. The efficiency of the conversion of the accreting matter into radiation is found to be substantially higher for naked singularities than that for black holes. We also verify that the flux radiated from the disk surface is greater for null and JMN1 naked singularities than black holes. Hence, the accretion disks around naked singularities are much more luminous than the black holes of the same mass and accretion rate. In the luminosity spectra of the NNS, we find that the significant contribution of the low-frequency is coming from the nearby regions of the NNS. Furthermore, the spectral luminosity distribution for the "non-zero torque" at the inner boundary is also analysed by the inclusion of the non-zero torque value at the inner edge of the disk. The slopes of the luminosity distribution with respect to frequency for naked singularity spacetimes differ significantly from those of black holes. These unique features of the naked singularities serve as an effective tool to distinguish them from the equally massive black holes., Comment: 16 pages, 20 figures

In this paper, we investigate the properties of the Lense-Thirring precession frequency and periastron precession of the relativistic bound orbits in slowly rotating naked singularity spacetimes. We show that the precession frequencies of a stationary test gyroscope are quite unique in slowly rotating naked singularity spacetimes, and therefore, one can easily distinguish them from the slowly rotating Kerr black hole spacetime. On the other hand, we also show that in slowly rotating Joshi-Malafarina-Narayan (JMN1) naked singularity spacetime, negative precession of the timelike bound orbits is allowed which is not possible in Kerr and slowly rotating null naked singularity spacetimes., Comment: 14 pages, 20 figures

It is now theoretically well established that not only a black hole can cast shadow, but other compact objects such as naked singularities, gravastar or boson stars can also cast shadows. An intriguing fact that has emerged is that the event horizon and the photon sphere are not necessary for a shadow to form. Now, when two different types of equally massive compact objects cast shadows of same size, then it would be very difficult to distinguish them from each other. However, the nature of the nulllike and timelike geodesics around the two compact objects would be different, since their spacetime geometries are different. Therefore, the intensity distribution of light emitted by the accreting matter around the compact objects would also be different. In this paper, we emphasize this phenomenon in detail. Here, we show that a naked singularity spacetime, namely, the first type of Joshi-Malafarina-Narayan (JMN1) spacetime can be distinguishable from the Schwarzschild blackhole spacetime by the intensity distribution of light, though they have same mass and shadow size. We also use the image processing techniques here to show this difference, where we use the theoretical intensity data. The differences that we get by using the image processing technique may be treated as a theoretical template of intensity differences, which may be useful to analyse the observational data of the image of a compact object., Comment: 11 pages, 7 figures

It is now known that the shadow is not only the property of a black hole, it can also be cast by other compact objects like naked singularities. However, there exist some novel features of the shadow of the naked singularities which are elaborately discussed in some recent articles. In the earlier literature, it is also shown that a naked singularity may admit negative precession of bound timelike orbits which cannot be seen in Schwarzschild and Kerr black hole spacetimes. This distinguishable behavior of timelike bound orbit in the presence of the naked singularity along with the novel features of the shadow may be useful to distinguish between a black hole and a naked singularity observationally. However, in this paper, it is shown that deformed Kerr spacetime can allow negative precession of bound timelike orbits when the central singularity of that spacetime is naked. We also show that negative precession and shadow both can exist simultaneously in deformed Kerr naked singularity spacetime. Therefore, any observational evidence of negative precession of bound orbits, along with the central shadow may indicate the presence of a deformed Kerr naked singularity., Comment: 13 pages, 20 figures

Astrometric observations of S-stars provide a unique opportunity to probe the nature of Sagittarius-A* (Sgr-A*). In view of this, it has become important to understand the nature and behavior of timelike bound trajectories of particles around a massive central object. It is known now that whereas the Schwarzschild black hole does not allow the negative precession for the S-stars, the naked singularity spacetimes can admit the positive as well as negative precession for the bound timelike orbits. In this context, we study the perihelion precession of a test particle in the Kerr spacetime geometry. Considering some approximations, we investigate whether the timelike bound orbits of a test particle in Kerr spacetime can have negative precession. In this paper, we only consider low eccentric timelike equatorial orbits. With these considerations, we find that in Kerr spacetimes, negative precession of timelike bound orbits is not allowed., Comment: 12 pages, 18 figures

It is generally believed that the shadows of either a black hole or naked singularity arise due to photon spheres developing in these spacetimes. Here we propose a new spherically symmetric naked singularity spacetime solution of Einstein equations which has no photon sphere, and we show that the singularity casts a shadow in the absence of the photon sphere. We discuss some novel features of this shadow and the lightlike geodesics in this spacetime. We compare the shadow of the naked singularity here with shadows cast by Schwarzschild black hole and the first type of Joshi-Malafarina-Narayan (JMN1) naked singularity, where for the last two spacetimes the shadow is formed due to the presence of a photon sphere. It is seen, in particular, that the size of shadow of the singularity is considerably smaller than that of a black hole. Our analysis shows that the shadow of this naked singularity is distinguishable from the shadow of a Schwarzschild black hole and the JMN1 naked singularity. These results are useful and important in the context of recent observations of shadow of the M87 galactic center., Comment: 9 pages, 12 figures