The fate of observers in circular motion

Lehébel, Antoine; Cardoso, Vitor

doi:10.48550/arxiv.2202.08850

Cited by 2 publications

(2 citation statements)

References 16 publications

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“…Obviously, for a black hole, its spin must be a/M ∈ (0, 1). From (19), the effective potential V can be obtained, and e 1,2 are given by…”

Section: A Effective Potentialmentioning

confidence: 99%

Topology of equatorial timelike circular orbits around stationary black holes

Wei¹,

Liu²

2022

Preprint

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Topological approach has been successfully used to study the properties of the light ring and the null circular orbit, in a generic black hole background. However, for the equatorial timelike circular orbit, quite different from the light ring case, its radius is closely dependent of the energy and angular momentum of a test particle. This fact restricts the extension of the topological treatment to the timelike circular orbits. In this paper, we confirm that if we take the angular momentum as the control parameter, the energy of the test particle does not influence the asymptotic behavior of the constructed vector with its zero points denoting the equatorial timelike circular orbits. As a result, a well-behaved topology to characterize the equatorial timelike circular orbits can be constructed.Our study shows that the total topological charge of the timelike circular orbits vanishes for a generic black hole background, which is dependent of the energy of the particle. Significantly it reveals that the timelike circular orbits always come in pairs. Meanwhile, the stable and unstable timelike circular orbits have a positive or negative winding number. Of particular interest is that the innermost stable circular orbit corresponds to the bifurcation point of the zero point of the constructed vector. Moreover, we also examine the case when the particle energy acts as the control parameter. It is shown that there will be topological phase transition when the value of the particle energy is one. We further apply the treatment to the Kerr black hole. All the results given in a generic black hole background are exactly reproduced. These strongly indicate that our topological approach can be well generalized to the equatorial timelike circular orbits.

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“…Obviously, for a black hole, its spin must be a/M ∈ (0, 1). From (19), the effective potential V can be obtained, and e 1,2 are given by…”

Section: A Effective Potentialmentioning

confidence: 99%

Topology of equatorial timelike circular orbits around stationary black holes

Wei¹,

Liu²

2022

Preprint

View full text Add to dashboard Cite

show abstract

“…In Refs. [22,23], it was found that an unstable (stable) LR delimits a region of unstable (stable) TCOs radially above (below) it. Moreover, the corresponding corollary was discussed for both horizonless ultracompact objects and black holes.…”

Section: Introductionmentioning

confidence: 99%

Topological study of equatorial timelike circular orbit for spherically symmetric (hairy) black holes

Ye¹,

Wei²

2023

Preprint

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Topological approach has been shown a promising study toward to the light ring in a generic black hole background. We in this paper generalize it to the study of timelike circular orbits in static, spherically symmetric, and asymptotic flat black holes. By making use of the equation of motion of the massive particles, we construct a vector with its zero points exactly relating with the timelike circular orbits. Since each zero point of the vector can be endowed with a winding number, the topology of the timelike circular orbits is established. Stable and unstable timelike circular orbits respectively have winding number +1 and -1. In particular, different from that of the light ring, the timelike circular orbits possess vanishing topological number and appear in pairs for given angular momentum. Moreover, we apply the study to the Schwarzschild, scalarized Einstein-Maxwell, and dyonic black holes, which have distinct topological configurations. It is shown that although the existence of scalar hair and quasi-topological term leads to richer topological configurations of the timelike circular orbits, whereas they have no influence on the topological number. These results indicate that the topological approach indeed provides us a novel way to understand the timelike circular orbits. More information is expected to be disclosed when other different topological configurations are present.

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The fate of observers in circular motion

Cited by 2 publications

References 16 publications

Topology of equatorial timelike circular orbits around stationary black holes

Topology of equatorial timelike circular orbits around stationary black holes

Topological study of equatorial timelike circular orbit for spherically symmetric (hairy) black holes

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