Harmonic oscillations of neutral particles in the 
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>γ</mml:mi></mml:math>
 metric

Toshmatov, Bobir; Malafarina, Daniele; Dadhich, Naresh

doi:10.1103/physrevd.100.044001

Cited by 43 publications

(31 citation statements)

References 42 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The total gravitational mass of the source is M = mγ and from the computation of the quadrupole moment Q = γ m 3 (1 − γ 2 )/3 one can see that values of γ < 1 (γ > 1) correspond to prolate (oblate) deformations. The properties of the ZV space-time were studied in [12][13][14][15][16][17][18][19][20], while interior solutions for the ZV metric were obtained in [42,43]. A stationary generalization of the ZV metric was obtained by Halilsoy in [37].…”

Section: Stationary Zipoy-voorhees Metricmentioning

confidence: 99%

“…For example in recent times some attention has been given to the Zipoy-Voorhees (ZV) metric which is a static generalization of the Schwarzschild solution to include higher multipole moments and describes the field outside prolate or oblate spheroids [10,11]. The properties of the motion of test particles in the ZV space-time and the possibility of testing the geometry from astrophysical observations has been discussed in several articles [12][13][14][15][16][17][18][19][20]. However, astrophysical compact objects typically rotate and therefore it would be more interesting to study the properties of stationary solutions.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

On the properties of a deformed extension of the NUT space-time

et al. 2020

Self Cite

View full text Add to dashboard Cite

We consider a class of space-times given by a stationary extension of the Zipoy–Voorhees metric that was found by Halilsoy. We show that the solutions do not describe rotating sources but must be interpreted, similarly to the NUT case, as deformed sources endowed with a gravitomagnetic charge. We show that the Halilsoy family is directly linked to the NUT space-time, which can be obtained in the limit of vanishing deformations. We investigate the motion of test particles and photons in this class of space-times, in particular the innermost stable circular orbits and photon capture radius. Finally we show that this class of solutions possesses a sub-manifold where closed time-like curves are allowed.

show abstract

Section: Stationary Zipoy-voorhees Metricmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On the properties of a deformed extension of the NUT space-time

et al. 2020

Self Cite

View full text Add to dashboard Cite

show abstract

“…and hence, accounting for the reality of m 1 and m 2 , one might think that the allowed negative values of q lie in the interval (− 1 4 , 0), thus being even more restrictive than in the case of the ZV solution. However, it is easy to see that for all q < − 1 4 the parameters m 1 and m 2 in (10) become complex conjugate quantities, m 2 =m 1 , and these preserve the reality of the axis expression (8), so that the reality of the metric functions f and γ in (7) is also preserved.…”

Section: The Extended 2-parameter Static Vacuum Solutionmentioning

confidence: 99%

Simplest static and stationary vacuum quadrupolar metrics

2019

View full text Add to dashboard Cite

In the present paper we argue that a special case of the Bach-Weyl metric describing a static configuration of two Schwarzschild black holes gives rise, after extending its parameter space to complex values, to a very simple 2-parameter model for the gravitational field of a static deformed mass. We compare this model, which has no restrictions on the quadrupole parameter, with the well-known Zipoy-Voorhees δ-metric and show in particular that the mass quadrupole moment in the latter solution cannot take arbitrary negative values. We subsequently add an arbitrary angular momentum to our static model and study some properties of the resulting 3-parameter stationary solitonic spacetime, which permits us to introduce the notion of the Fodor-Hoenselaers-Perjés relativistic multipole moments.

show abstract

“…Metric (1) is known by various names in GR and has been the subject of numerous investigations, see Refs. [9][10][11][12][13][14] and the references cited therein. The singularities of the δ-metric occur for r ≤ 2 m; the outer singularity at r = 2 m is either a timelike or a null hypersurface, the latter occurs for oblate deformations up to q ≈ 0.6 [5].…”

Section: Introductionmentioning

confidence: 99%

Quasinormal modes of generalized black holes: δ-Kerr spacetime

Allahyari¹,

Firouzjahi²,

Mashhoon³

2020

Class. Quantum Grav.

View full text Add to dashboard Cite

The nonlinear superposition of the δ-metric and the Kerr metric results in δ-Kerr metric that represents a deformed Kerr black hole with δ = 1 + q, where q > 0 is proportional to the nonrelativistic quadrupole moment of the collapsed configuration.We study this spacetime and determine q + such that for q, 0 < q < q + , the outer spacetime singularity remains a null hypersurface. In this case, δ-Kerr spacetime represents a generalized black hole, namely, an asymptotically flat, stationary and axisymmetric vacuum solution of general relativity for which the outer singularity is a closed null hypersurface. For an approximate variant of δ-Kerr spacetime characterized by mass M , quadrupole parameter q and angular momentum parameter a, where the latter two parameters are treated to first and second orders of approximation, respectively, we analytically determine the quasinormal mode (QNM) frequencies in the ray approach using the light-ring method as well as in the complementary wave approach for massless scalar field perturbations in the a = 0 limit.The QNM frequencies of this generalized black hole turn out to be nearly the same as those of the rotating Hartle-Thorne spacetime. * Electronic address: alireza.al@ipm.ir † Electronic address: firouz@ipm.ir ‡ Electronic address: mashhoonb@missouri.edu

show abstract

Harmonic oscillations of neutral particles in the γ metric

Cited by 43 publications

References 42 publications

On the properties of a deformed extension of the NUT space-time

On the properties of a deformed extension of the NUT space-time

Simplest static and stationary vacuum quadrupolar metrics

Quasinormal modes of generalized black holes: δ-Kerr spacetime

Contact Info

Product

Resources

About