Geodesics in the field of a rotating deformed gravitational source

Boshkayev, Kuantay; Quevedo, Hernando; Abutalip, M.; Kalymova, Zh. A.; Suleymanova, Sh. S.

doi:10.1142/s0217751x16410062

Cited by 8 publications

(7 citation statements)

References 17 publications

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“…As emphasized by Urbanec et al (2010b), , Kluźniak & Rosińska (2013), Török et al (2014), Rosińska et al (2014) and Boshkayev et al (2015), Newtonian effects following from the influence of the quadrupole moment act on the orbital frequencies in a way opposite to that which is related to relativis- tic effects following from the increase of the angular momentum. The behaviour of the relations shown in the left panel of Figure 3 is determined by this interplay.…”

Section: Results For the Rp Modelmentioning

confidence: 96%

Constraining Models of Twin-Peak Quasi-Periodic Oscillations With Realistic Neutron Star Equations of State

Török

Goluchová

Urbanec

et al. 2016

ApJ

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Twin-peak quasi-periodic oscillations (QPOs) are observed in the X-ray power-density spectra of several accreting low-mass neutron star (NS) binaries. In our previous work we have considered several QPO models. We have identified and explored mass-angular-momentum relations implied by individual QPO models for the atoll source 4U 1636-53. In this paper we extend our study and confront QPO models with various NS equations of state (EoS). We start with simplified calculations assuming Kerr background geometry and then present results of detailed calculations considering the influence of NS quadrupole moment (related to rotationally induced NS oblateness) assuming Hartle-Thorne spacetimes. We show that the application of concrete EoS together with a particular QPO model yields a specific mass-angular-momentum relation. However, we demonstrate that the degeneracy in mass and angular momentum can be removed when the NS spin frequency inferred from the X-ray burst observations is considered. We inspect a large set of EoS and discuss their compatibility with the considered QPO models. We conclude that when the NS spin frequency in 4U 1636-53 is close to 580Hz we can exclude 51 from 90 of the considered combinations of EoS and QPO models. We also discuss additional restrictions that may exclude even more combinations. Namely, there are 13 EOS compatible with the observed twin peak QPOs and the relativistic precession model. However, when considering the low frequency QPOs and Lense-Thirring precession, only 5 EOS are compatible with the model.

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Section: Results For the Rp Modelmentioning

confidence: 96%

Constraining Models of Twin-Peak Quasi-Periodic Oscillations With Realistic Neutron Star Equations of State

Török

Goluchová

Urbanec

et al. 2016

ApJ

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“…We shall adopt for this case the Hartle's slow-rotation approximation. The angular momentum per unit mass of a Keplerian orbit with a radius equal to the NS radius is, within this approximation, given by (Boshkayev et al 2016)…”

Section: Time Evolution Of the Accreting Nsmentioning

confidence: 99%

“…where u ≡ GM NS /(c 2 R NS ). This formula can be also obtained by taking the second order slow rotation limit of the angular momentum of the last stable circular orbit around a Kerr BH (Rees et al 1974;Boshkayev et al 2012Boshkayev et al , 2016. Therefore, by solving (numerically) simultaneously equations ( 8) and ( 14), with the aid of Eqs.…”

Section: Time Evolution Of the Accreting Nsmentioning

confidence: 99%

On the Induced Gravitational Collapse Scenario of Gamma-Ray Bursts Associated With Supernovae

Becerra

Bianco

Fryer

et al. 2016

ApJ

215

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Following the induced gravitational collapse (IGC) paradigm of gamma-ray bursts (GRBs) associated with type Ib/c supernovae, we present numerical simulations of the explosion of a carbon-oxygen (CO) core in a binary system with a neutron-star (NS) companion. The supernova ejecta trigger a hypercritical accretion process onto the NS thanks to a copious neutrino emission and the trapping of photons within the accretion flow. We show that temperatures 1-10 MeV develop near the NS surface, hence electron-positron annihilation into neutrinos becomes the main cooling channel leading to accretion rates 10 −9 -10 −1 M s −1 and neutrino luminosities 10 43 -10 52 erg s −1 (the shorter the orbital period the higher the accretion rate). We estimate the maximum orbital period, P max , as a function of the NS initial mass, up to which the NS companion can reach by hypercritical accretion the critical mass for gravitational collapse leading to black-hole (BH) formation. We then estimate the effects of the accreting and orbiting NS companion onto a novel geometry of the supernova ejecta density profile. We present the results of a 1.4 × 10 7 particle simulation which show that the NS induces accentuated asymmetries in the ejecta density around the orbital plane. We elaborate on the observables associated with the above features of the IGC process. We apply this framework to specific GRBs: we find that X-ray flashes (XRFs) and binary-driven hypernovae (BdHNe) are produced in binaries with P > P max and P < P max , respectively. We analyze in detail the case of XRF 060218.

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“…Due to the recent results [33][34][35][36], it will be interesting to find the connection between the Erez-Rosen and Zipoy-Voorhees (q-metric) solutions. This will be the issue of future studies.…”

Section: Discussionmentioning

confidence: 99%

To the Inverse Problem of Celestial Mechanics

Boshkayev¹,

Malybayev²,

Quevedo³

et al. 2021

SPM

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The link between exterior solutions to the Einstein gravitational field equations such as the exact Erez-Rosen metric and approximate Hartle-Thorne metric is established here for the static case in the limit of linear mass quadrupole moment (Q) and second order terms in total mass (M). To this end, the Geroch-Hansen multipole moments are calculated for the Erez-Rosen and Hartle-Thorne solutions in order to find the relationship among the parameters of both metrics. The coordinate transformations are sought in a general form with two unknown functions in the corresponding limit of ~Q and ~M^2. By employing the perturbation theory, the approximate Erez-Rosen metric is written in the same coordinates as the Hartle-Thorne metric. By equating the radial and azimuthal components of the metric tensor of both solutions the sought functions are found in a straightforward way. It is shown that the approximation ~Q and ~M^2, which is used throughout the article, is physical and suitable for solving most problems of celestial mechanics in post-Newtonian physics. This approximation does not require the use of the Zipoy-Voorhees transformation, which is a necessary strict mathematical requirement in the ~Q approximation, i.e. when no other approximations are made. This implies that the explicit form of the coordinate transformations depends entirely on the approximation that is adopted in each particular case. The results obtained here are in agreement with the previous results in the literature and can be applied to different astrophysical goals. The paper pursues not only pure scientific, but also academic purposes and can be used as an auxiliary and additional material to the special courses of general theory of relativity, celestial mechanics and relativistic astrophysics.

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Geodesics in the field of a rotating deformed gravitational source

Cited by 8 publications

References 17 publications

Constraining Models of Twin-Peak Quasi-Periodic Oscillations With Realistic Neutron Star Equations of State

Constraining Models of Twin-Peak Quasi-Periodic Oscillations With Realistic Neutron Star Equations of State

On the Induced Gravitational Collapse Scenario of Gamma-Ray Bursts Associated With Supernovae

To the Inverse Problem of Celestial Mechanics

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