Geodesic motion in the Tomimatsu-Sato space-times

Astronomy and Astrophysics – Astronomy

Scientific paper

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Black Holes (Astronomy), Geodesic Lines, Gravitational Collapse, Space-Time Functions, Angular Momentum, Cosmology, Relativity, Stellar Motions

Scientific paper

Axial and equatorial geodesics in Tomimatsu-Sato (1973) spacetime are investigated in the case where the specific angular momentum of a black hole exceeds its gravitational mass, giving rise to a naked singularity. Solutions to Einstein's vacuum field equations in this spacetime are obtained, and geodesic motion is analyzed for different values of a parameter, delta, related to the quadrupole moment of the black hole. In the case of equatorial motion, it is found that for all values of delta except unity (the Kerr metric), no photons can escape to infinity, even though no event horizon exists. In the case of axial motion, it is found for all values of delta that particles with suitable energy may reach certain potential barriers and bounce back to infinity. The possibility of causality violation is discussed along with some observational properties of a spinning naked singularity.

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