Approximate Kerr-Like Metric  with Quadrupole

Frutos─Alfaro, Francisco

doi:10.4236/ijaa.2016.63028

Cited by 9 publications

(27 citation statements)

References 28 publications

(50 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The first order terms of ψ ms , χ ms and W ms are taken from [19]. The term Jq of W ms represents the interaction of the spin with the quadrupole, which was not considered in [10]. From this Ansatz, the perturbative terms can be determined by solving the EFE.…”

Section: Generating the Metricmentioning

confidence: 99%

“…The complete expansion of the HT including the second order terms in q was found in [9,10]. To guess an improvement of the HT metric, we have to find a solution of the EFE compatible with HT metric.…”

Section: Constructing a New Hartle-thorne Metricmentioning

confidence: 99%

“…In [9], the second order in q for the post-linear HT was found perturbatively. A transformation that converts the post-linear Kerr-like metric (7) without S 3 and M 4 into an improved HT was obtained in [10]. The same transformation can be used to transform the post-linear Kerr-like metric (7) with S 3 and M 4 at first order into an improved HT in the post-linear form of (11) with S 3 and M 4 at first order, changing q → ma 2 − q.…”

Section: Constructing a New Hartle-thorne Metricmentioning

confidence: 99%

See 2 more Smart Citations

Approximate spacetime for neutron stars

Frutos─Alfaro

2019

Gen Relativ Gravit

Self Cite

View full text Add to dashboard Cite

An approximate realistic metric representing the spacetime of neutron stars is obtained by perturbing the Kerr metric. This metric has five parameters, namely the mass, spin or angular momentum, mass quadrupole, spin octupole and mass hexadecapole. Moreover, a version of the Hartle-Thorne metric containing these parameters is constructed by means of a series transformation between these spacetimes and solving the Einstein field equations. The form of the Pappas metric in Schwarzschild spherical coordinates is found. The three relativistic multipole structures are compared. IntroductionAmong compact objects are neutron stars (NS). These stars are relativistic rotating objects with high density, and strong gravitational and magnetic fields. The study of NS is relevant to understand the extrem conditions of matter in there, the behaviour of particles around them, and the structure of its spacetime [12, 3, 1]. The quest to find a realistic spacetime representation for neutron stars (NS) is an important task in astrophysics. Many attemps to obtain this spacetime have been done from approximate metrics until numerical metrics. The first attemp was made by Hartle-Thorne (HT). The relevance of the HT work was that they matched the interior solution with the exterior one [11]. Quevedo and Mashhoon [18] and Manko and Novikov [14] obtained exact solutions with charge and arbitrary mass multipoles. Later, more exact solutions containing other features, for instance magnetic dipole, were found [15]. With the advent of computer technology, the implementations of computer programs to find numerical solutions become a vogue [20]. However, approximate solutions are still important to extract astrophysical information from NS [17]. Moreover, a fourth order HT metric for the exterior of neutron stars was obtained in [21]. There are several techniques to find solutions of the Einstein field equations (EFE). Among them, the Ernst formalism has played an important role in finding new exact and approximate solutions. This formalism is employed in [18,14,17]. In this contribution, however, we include features like mass quadrupole, spin octupole and mass hexadecapole to the Kerr metric perturbatively. This is achieved easily by means of perturbing the Lewis metric form of the Kerr spacetime [7,8]. The form of the perturbations due to spin octupole and mass hexadecapole has the structure proposed by Ryan [19]. Then, one is certain that these features are introduced in the right manner. This metric has the advantage that it reduces to the Kerr metric which is an exact solution with mass and angular momentum. Moreover, it is simple to implement computationaly.

show abstract

Section: Generating the Metricmentioning

confidence: 99%

Section: Constructing a New Hartle-thorne Metricmentioning

confidence: 99%

Section: Constructing a New Hartle-thorne Metricmentioning

confidence: 99%

See 1 more Smart Citation

Approximate spacetime for neutron stars

Frutos─Alfaro

2019

Gen Relativ Gravit

Self Cite

View full text Add to dashboard Cite

show abstract

“…The metric, we will employ to do the calculations was generated in a perturbative form using the Kerr spacetime as seed metric. This approximate rotating spacetime with quadrupole moment written in standard form is as follows [8,30]: This spacetime has three parameters, namely mass M, spin, J=Ma (a as the Kerr rotation parameter) and q, the mass quadrupole. It contains the Kerr and the Schwarzschild metrics.…”

Section: The Metricmentioning

confidence: 99%

“…According to [8], that included the second order in q, it is Table 2. Order of magnitude of the contributions PN, PPN, and PN Q to the gravitation delay of a radio signal grazing the solar limb and the planets predicted by GR using a PPN metric [11].…”

Section: The Metricmentioning

confidence: 99%

Classical general relativity effects to second order in mass, spin, and quadrupole moment

Arce-Gamboa

Frutos─Alfaro

2019

J. Phys. Commun.

View full text Add to dashboard Cite

In this contribution, we calculate the light deflection, perihelion shift, time delay and gravitational redshift using an approximate metric that contains the Kerr metric and an approximation of the Erez-Rosen spacetime. The results were obtained directly using (Mathematica 2018 Wolfram Research, Inc., Version 11.3, Champaign). The results agree with the ones presented in the literature, but they are extended until second order terms of mass, angular momentum and mass quadrupole. The inclusion of the mass quadrupole is done by means of the metric; no expansion of the gravitational potential as in the parameterized post-Newtonian is required.

show abstract

An approximate Kerr–Newman-like metric endowed with a magnetic dipole and mass quadrupole

Frutos-Alfaro

2024

Commun. Theor. Phys.

View full text Add to dashboard Cite

Approximate all-terrain spacetimes for astrophysical applications are presented. The metrics possess five relativistic multipole moments,namely mass, rotation, mass quadrupole, charge, and magnetic dipole moment. All these spacetimes approximately satisfy the Einstein-Maxwell field equations. The first metric is generated by means of the Hoenselaers-Perjés method from given relativistic multipoles. Thesecond metric is a perturbation of the Kerr-Newman metric, which makes it a relevant approximation for astrophysical calculations. Thelast metric is an extension of the Hartle-Thorne metric that is important for obtaining internal models of compact objects perturbatively.The electromagnetic field is calculated using Cartan forms for locally nonrotating observers. These spacetimes are relevant to infer properties of compact objects from astrophysical observations. Furthermore, the numerical implementations of these metrics are straightforward, making them versatile for simulating the potential astrophysical applications.

show abstract

Approximate Kerr-Like Metric with Quadrupole

Cited by 9 publications

References 28 publications

Approximate spacetime for neutron stars

Approximate spacetime for neutron stars

Classical general relativity effects to second order in mass, spin, and quadrupole moment

An approximate Kerr–Newman-like metric endowed with a magnetic dipole and mass quadrupole

Contact Info

Product

Resources

About