Geodesics in the Γ Spacetime

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.

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“…The complete structure of geodesic motion in the γ-metric was studied by Herrera et al [13]. The γ-metric is axially symmetric and static.…”

Section: Circular Geodesics In the Gamma Metricmentioning

confidence: 99%

Circular geodesics and accretion disks in the Janis-Newman-Winicour and gamma metric spacetimes

et al. 2012

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“…It is worth mentioning that the sensitivity of the trajectories of test particles in the γ spacetime [7], to small changes of γ, for orbits close to 2M, has been brought out [8]. Also, the influence of the quadrupole moment on the motion of test particles within the context of Erez-Rosen metric [9] has been investigated by many authors (see [10], [11] and references therein) Motivated by the above mentioned facts, we want to present in this work another approach to the problem of describing deviations from spherical symmetry.…”

Section: Introductionmentioning

confidence: 98%

Geodesics in a Quash-Spherical Spacetime: A Case of Gravitational Repulsion

Herrera

2005

Found Phys Lett

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Geodesics are studied in one of the Weyl metrics, referred to as the M-Q solution. First, arguments are provided, supporting our belief that this space-time is the more suitable (among the known solutions of the Weyl family) for discussing the properties of strong quasi-spherical gravitational fields. Then, the behaviour of geodesics is compared with the spherically symmetric situation, bringing out the sensitivity of the trajectories to deviations from spherical symmetry. Particular attention deserves the change of sign in proper radial acceleration of test particles moving radially along symmetry axis, close to the r = 2M surface, and related to the quadrupole moment of the source.2

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“…In some non-spherical static spacetimes, properties of the photon spheres are shared by the photon surfaces of non-spherical shape [33], examples of spacetime admitting non-spherical photon surfaces are presented by asymptotically non-flat metrics (vacuum C-metric, Melvin's solution of Einstein-Maxwell theory and its generalizations tical images which recently became subject of the observational study. Here we will investigate a popular family of oblate deformations of the Schwarzschild metric known as Zipoy-Voorhees (ZV) solutions or gamma-metrics [45][46][47][48][49][50][51], which are the static axially symmetric but not spherically symmetric solutions belonging to the Weyl class. This spacetime is non-separable for geodesic motion, so its description in terms of characteristic trapping surfaces and regions is especially relevant.…”

Section: Introductionmentioning

confidence: 99%

Photon trapping in static axially symmetric spacetime

Gal’tsov

Kobialko

2019

Phys. Rev. D

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Recently, several new characteristics have been introduced to describe null geodesic structure of strong gravitational field, such as photon regions, transversely trapping surfaces and some generalizations. They give an alternative and concise way to describe lensing and shadow features of compact objects with strong gravitational field without recurring to complete integration of the geodesic equations. Here we test this construction in the case of the Weyl metrics when geodesic equations are non-separable, and thus can not be integrated analytically, while the above characteristic surfaces and regions can be described in a closed form. We develop further our formalism for a class of static axially symmetric spacetimes introducing more detailed specification of transversely trapping surfaces in terms of their principal curvatures. Surprisingly, we find in the static case without spherical symmetry certain features, such as photon regions, previously known in the Kerr space. These photon regions can be regarded as photon spheres, "thickened" due to oblateness of the metric.including the dilaton field [34]).Meanwhile, in the stationary spacetimes photon surfaces generically do not exist, being, in some sense, disintegrated by rotation. The Taub-NUT metric, though belongs to this class, is an exception, whose existence is explained by local SO(3) symmetry which is preserved. In the Kerr metric the circular photon orbits exist in the equatorial plane [35]. Non-equatorial orbits with constant Boyer-Lindquist radii no longer belong to any plane, but lie on the surface of a sphere instead ("spherical photon orbits" [36]). But such surfaces are not photon spheres, which by definition should be densely filled. In the Kerr case every spherical orbit corresponds to certain value of the impact parameter defined as ratio of the angular momentum to the energy. Altogether spherical orbits now will a three-dimensional photon region (PR) [37][38][39], which can be regarded as "thickened" photon sphere. Note that the closed photon orbits may exist in more general spacetimes in which case the name of fundamental or/and spheroidal photon orbits was suggested [40][41][42].More general trapping surfaces, proposed in [43] and further studied in [44], were called transversely trapping surfaces (TTS). In Schwarzschild case TTS are the spheres with the radii r ≤ 3M . These are defined as surfaces such that initially tangent photons either remain in them or move inward; these do exist in Kerr and more general stationary axially symmetric metrics.The totality of TTSs form a three-dimensional region (TTR), which apparently will be invisible if one looks at the Schwarzschild black hole illuminated from behind. Further generalizations suggested in [44] include partial TTS (PTTS) which are non-closed surfaces (contrary to the definition in [43]) of the shape of a spherical cap. Finally, it is reasonable to introduce anti-TTS and PTTS (abbreviated as ATTS and APPTS, the corresponding regions -TTR and PTTR respoctively) replacing inward to outwa...

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Geodesics in the Γ Spacetime

Abstract: Geodesics are studied in the spacetime described by the γ metric. Their behaviour is compared with the spherically symmetric situation, bringing out the sensitivity of the trajectories to deviations from spherical symmetry.

Cited by 53 publications

References 16 publications

Circular geodesics and accretion disks in the Janis-Newman-Winicour and gamma metric spacetimes

Circular geodesics and accretion disks in the Janis-Newman-Winicour and gamma metric spacetimes

Geodesics in a Quash-Spherical Spacetime: A Case of Gravitational Repulsion

Photon trapping in static axially symmetric spacetime

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