Spinning test body orbiting around a Schwarzschild black hole: Comparing spin supplementary conditions for circular equatorial orbits

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985815%3A_____%2F21%3A00549683" target="_blank" >RIV/67985815:_____/21:00549683 - isvavai.cz</a>

Result on the web

<a href="https://doi.org/10.1103/PhysRevD.104.024042" target="_blank" >https://doi.org/10.1103/PhysRevD.104.024042</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1103/PhysRevD.104.024042" target="_blank" >10.1103/PhysRevD.104.024042</a>

Result language

angličtina

Original language name

Spinning test body orbiting around a Schwarzschild black hole: Comparing spin supplementary conditions for circular equatorial orbits

Original language description

The Mathisson-Papapetrou-Dixon (MPD) equations describe the motion of an extended test body in general relativity. This system of equations, though, is underdetermined and has to be accompanied by constraining supplementary conditions, even in its simplest version, which is the pole-dipole approximation corresponding to a spinning test body. In particular, imposing a spin supplementary condition (SSC) fixes the center of mass of the spinning body, i.e., the centroid of the body.In the present study, we examine whether characteristic features of the centroid of a spinning test body, moving in a circular equatorial orbit around a massive black hole, are preserved under the transition to another centroid of the same physical body, governed by a different SSC. For this purpose, we establish an analytical algorithm for deriving the orbital frequency of a spinning body, moving in the background of an arbitrary, stationary, axisymmetric spacetime with reflection symmetry, for the Tulczyjew-Dixon, the Mathisson-Pirani, and the Ohashi-Kyrian-Semerak SSCs. Then, we focus on the Schwarzschild black hole background, and a power series expansion method is developed in order to investigate the discrepancies in the orbital frequencies expanded in power series of the spin among the different SSCs. Lastly, by employing the fact that the position of the centroid and the measure of the spin alters under the centroid's transition, we impose proper corrections to the power expansion of the orbital frequencies, which allows to improve the convergence between the SSCs. Our concluding argument is that when we shift from one circular equatorial orbit to another in the Schwarzschild background, under the change of a SSC, the convergence between the SSCs holds only up to certain powers in the spin expansion, and it cannot be achieved for the whole power series.

Czech name

—

Czech description

—

Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

—

OECD FORD branch

10308 - Astronomy (including astrophysics,space science)

Project

—

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2021

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Physical Review D

ISSN

2470-0010

e-ISSN

2470-0029

Volume of the periodical

104

Issue of the periodical within the volume

2

Country of publishing house

US - UNITED STATES

Number of pages

15

Pages from-to

024042

UT code for WoS article

000674578400005

EID of the result in the Scopus database

2-s2.0-85110292218