journal article Jun 01, 1966

Topology of Some Spheroidal Metrics

Journal of Mathematical Physics Vol. 7 No. 6 pp. 1137-1143 · AIP Publishing

View at Publisher Save 10.1063/1.1705005

Abstract

The solutions of Einstein's vacuum field equations, Rμν = 0, are found when quasi-oblate and prolate spheroidal coordinates are used. The solutions for the ``Newtonian'' potential can be written as a linear combination of Legendre polynomides of integral order l. For oblate coordinates the solutions for each l have a ring singularity and have a double sheeted topology; one can get from one sheet to the other by going through the ring. When the l = 0 and l = 1 solutions are combined an infinite-sheeted topology results from the nonlinear character of the field equations. In general the geometry is asymptotically flat on only one sheet; on the others it is highly distorted. In some cases the region near the ``ring singularity'' opens out into a multisheeted infinite space. For the prolate coordinates the solutions contain a line singularity of finite length. In general, the prolate coordinate solutions are much less rich in varied topologies than are the oblate solutions.

Topics

No keywords indexed for this article. Browse by subject →

References

11

[1]

[2]

Ann. Physik (1917)

[3]

Proc. Natl. Inst. Sci. India (1960)

[4]

Proc. Natl. Inst. Sci. India, Part A (1961)

[5]

Bull. Res. Council Israel (1959)

[6]

[7]

[8]

Maximal Extension of Schwarzschild Metric

M. D. Kruskal

Physical Review 1960 10.1103/physrev.119.1743

[9]

[10]

[11]

Invariant Formulation of Gravitational Radiation Theory

F. A. E. Pirani

Physical Review 1957 10.1103/physrev.105.1089

Cited By

266

Rotating wormholes in Einstein-Dirac-Maxwell theory

Vladimir Dzhunushaliev, Vladimir Folomeev · 2026

General Relativity and Gravitation

Constraining quadrupole deformations with relativistic effects

Daniya Utepova, Kuantay Boshkayev · 2025

The European Physical Journal C

Gravitational capture cross-section in Zipoy-Voorhees spacetimes

Serzhan Momynov, Kuantay Boshkayev · 2025

General Relativity and Gravitation

Removing naked singularities in static axially symmetric spacetimes by patching with flat spacetimes

Daiki Saito, Daisuke Yoshida · 2025

Physical Review D

Geodesic deviation in the q-metric

Anuar Idrissov, Kuantay Boshkayev · 2025

The European Physical Journal C

Charged Zipoy–Voorhees metric in string theory

Odil Yunusov, Bobur Turimov · 2025

Annals of Physics

Rotating spacetimes with a free scalar field in four and five dimensions

José Barrientos, Christos Charmousis · 2025

The European Physical Journal C

Building the blocks of Schwarzschild

Raphaël Dulac, Pierre Heidmann · 2024

Journal of High Energy Physics

Constraining deviations from spherical symmetry using γ -metric

Hrishikesh Chakrabarty, Yong Tang · 2023

Physical Review D

The q-metric naked singularity: a viable explanation for the nature of the central object in the Milky Way

F D Lora-Clavijo, G D Prada-Méndez · 2023

Classical and Quantum Gravity

Probing naked singularities in the charged and uncharged $$\gamma - metrics$$ with quantum wave packets

Ozay Gurtug, Mustafa Halilsoy · 2023

General Relativity and Gravitation

Extreme-mass-ratio inspirals into rotating boson stars: Nonintegrability, chaos, and transient resonances

Kyriakos Destounis, Federico Angeloni · 2023

Physical Review D

Shadows and thin accretion disk images of the $$\gamma $$-metric

Rajibul Shaikh, Suvankar Paul · 2022

The European Physical Journal C

The charged Zipoy–Voorhees metric with astrophysical applications

Ozay Gurtug, Mustafa Halilsoy · 2022

The European Physical Journal C

Black hole mimicker hiding in the shadow: Optical properties of the γ metric

Askar B. Abdikamalov, Ahmadjon A. Abdujabbarov · 2019

Physical Review D

Harmonic oscillations of neutral particles in the γ metric

Bobir Toshmatov, Daniele Malafarina · 2019

Physical Review D

Motion of test particles in the field of a naked singularity

K. Boshkayev, E. Gasperín · 2016

Physical Review D

Stationary and axisymmetric solutions of higher-dimensional general relativity

Troels Harmark · 2004

Physical Review D

Metrics

266

Citations

11

References

Details

Published: Jun 01, 1966
Vol/Issue: 7(6)
Pages: 1137-1143

Authors

University of Maryland, Department of Physics and Astronomy, College Park, Maryland

Cite This Article

David M. Zipoy (1966). Topology of Some Spheroidal Metrics. Journal of Mathematical Physics, 7(6), 1137-1143. https://doi.org/10.1063/1.1705005

Related

You May Also Like

Completely positive dynamical semigroups of N-level systems

Vittorio Gorini, Andrzej Kossakowski · 1976

3,382 citations

The world as a hologram

Leonard Susskind · 1995

3,004 citations

The Einstein Tensor and Its Generalizations

David Lovelock · 1971

2,484 citations

An Approach to Gravitational Radiation by a Method of Spin Coefficients

Ezra Newman, Roger Penrose · 1962

2,225 citations

Brownian Motion of a Quantum Oscillator

Julian Schwinger · 1961

2,187 citations