How Would Be Kerr-Like Phantom Wormhole? (Cosmology / Astronomy)

Miranda and colleagues in their paper, studied a Kerr-like wormhole with phantom matter as source. It has three parameters: mass, angular momentum and scalar field charge. This wormhole has a naked ring singularity (very similar to kerr black hole), otherwise it is regular everywhere (except on ring) (please refer note below if you don’t know about ring singularity). It has also a gauge parameter which determine the radius of the throat and a naked ring singularity, exactly the same one as the Kerr solution.

Ergosphere and ring singularity of wormhole © uncover reality

The mean feature of this wormhole is that throat is found outside of the ring singularity, the mouth of the throat lie on a sphere of the same radius as the ring singularity around the wormhole, this avoids any observer to see or to reach the singularity, it behaves like an anti-horizon.

They analyzed the geodesics of the wormhole and showed that the null polar geodesics/light-rays, that means, geodesics going through the polar line are regular, an observer can go through the throat if the observer trajectory remains on the polar geodesics and contains an energy bigger than 1/2f, for any values of the free parameters. On this trajectory the tidal forces are very small, therefore this wormhole is traversable. For any other angle the mouth of the wormhole lie on the sphere, but close to the equator, the effect of the wormhole is to repel the test particles. On the equator, the repulsion is infinity and nothing can reach the singularity, even the light is repealed by the wormhole.

“We analyse the geodesics of the wormhole and find that an observer can go through the geodesics without troubles, but the equator presents an infinity potential barrier which avoids to reach the throat.”

— told Miranda, first author of the study

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Thus, the sphere of the same radius as the ring singularity has an effect contrary to the horizon of a black hole, namely, an observer can reach the sphere, goes thought the throat, but this sphere avoids the traveller to observe or to reach the singularity. Of course, the traveller can come back to its original world without much troubles.

“From an analysis of the Riemann tensor we obtain that the tidal forces permits the wormhole to be traversable for an observer like a human being.”

— told Miranda, first author of the study

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Note: Ring singularity: A ring singularity is the gravitational singularity of a rotating kerr black hole/ wormhole shaped like a ring (as shown in fig below).

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Reference: Miranda, G., Matos, T. & García, N.M. Kerr-like phantom wormhole. Gen Relativ Gravit 46, 1613 (2014). https://link.springer.com/article/10.1007/s10714-013-1613-y https://doi.org/10.1007/s10714-013-1613-y

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Copyright of this article totally belongs to our author S. Aman. One is allowed to reuse it only by giving proper credit either to him or to us

Shadow of A Black Hole Part 1: Kerr BH (Planetary Science)

In 1973, James Bardeen initiated his research on gravitational lensing by spinning black holes. Bardeen gave a thorough analysis of null geodesics (light-ray propagation) around a Kerr black hole.

The Kerr solution had been discovered in 1962 by the New Zealand physicist Roy Kerr and since then focused the attention of many researchers in General Relativity, because it represents the most general state of equilibrium of an astrophysical black hole.

The Kerr spacetime’s metric depends on two parameters : the black hole mass “M” and its normalized angular momentum “a”. An important difference with usual stars, which are in differential rotation, is that Kerr black holes are rotating with perfect rigidity : all the points on their event horizon move with the same angular velocity. There is however a critical angular momentum, given by a = M (in units where G=c=1) above which the event horizon would “break up”: this limit corresponds to the horizon having a spin velocity equal to the speed of light. For such a black hole, called “extreme”, the gravitational field at the event horizon would cancel, because the inward pull of gravity would be compensated by huge repulsive centrifugal forces.

In the last twenty years increasing evidence has been found for the existence of a supermassive black hole at the center of our galaxy. It is expected that a distant observer should “see” this black hole as a dark disk in the sky which is known as the “shadow”. It is sometimes said that the shadow is an image of the event horizon.

James Bardeen was the first to correctly calculate the shape of the shadow of a Kerr black hole. He computed how the black hole’s rotation would affect the shape of the shadow that the event horizon casts on light from a background star field. For a black hole spinning close to the maximum angular momentum, the result is a D-shaped shadow.

Apparent shape of an extreme Kerr black hole as seen by a distant observer in the equatorial plane, if the black hole is in front of a source of illumination with an angular size larger than that of the black hole. The shadow bulges out on the side of the hole moving away from the observer (at right) and squeezes inward and flattens on the side moving toward the observer (at left). © Bardeen

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Reference: Bardeen, J. M. 1973, Timelike and null geodesics in the Kerr metric, in Black Holes”, Gordon and Breach, Science Publishers, Inc; New York; 23, 6(5), pp. 215–239, 1973. https://inis.iaea.org/search/search.aspx?orig_q=RN:6166516

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Copyright of this article totally belongs to our author S. Aman. One is allowed to reuse it only by giving proper credit either to him or to us