The geometry of photon surfaces

Given, in an arbitrary spacetime (M, g), a 2-dimensional timelike submanifold Σ and an observer field n on Σ, we assign gravitational, centrifugal, Coriolis and Euler forces to every particle worldline λ in Σ with respect to n. We prove that centrifugal and Coriolis forces vanish, for all λ in Σ with respect to any n, if and only if Σ is a photon 2-surface, i.e., generated by two families of lightlike geodesics. We further demonstrate that a photon 2-surface can be characterized in terms of gyroscope transport and we give several mathematical criteria for the existence of photon 2-surfaces. Finally, examples of photon 2-surfaces in conformally flat spacetimes, in Schwarzschild and Reissner-Nordström spacetimes, and in Gödel spacetime are worked out.

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“…For timelike hypersurfaces, i.e., for the case dim(M ) = 3, the same result can be deduced from Claudel, Virbhadra and Ellis [10], Theorem 2.2.…”

Section: The Existence Of Photon Surfacessupporting

confidence: 68%

“…This definition slightly modifies the notion of "photon surfaces" as it was extensively discussed by Claudel, Virbhadra and Ellis [10]. The modification is in the fact that Claudel, Virbhadra and Ellis consider only hypersurfaces, i.e., submanifolds of codimension one.…”

Section: The Existence Of Photon Surfacesmentioning

confidence: 99%

Inertial forces and photon surfaces in arbitrary spacetimes

Foertsch

Haße

Perlick

2003

Class. Quantum Grav.

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“…For a > 0 the black hole rotates counterclockwise, while for a < 0 the black hole and the photons rotate in converse direction. A starting point of the strong field limit expansion is the photon sphere, which has been defined by Virbhadra and Ellis [16] and has subsequently been investigated by Claudel, Virbhadra and Ellis [56]. Combining the null geodesics equations and Eqs.…”

Section: B Deflection Angle In the Equatorial Planementioning

confidence: 99%

Kerr-Sen dilaton-axion black hole lensing in the strong deflection limit

2007

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In the present work we study numerically quasi-equatorial lensing by the charged, stationary, axially-symmetric Kerr-Sen dilaton-axion black hole in the strong deflection limit. In this approximation we compute the magnification and the positions of the relativistic images. The most outstanding effect is that the Kerr-Sen black hole caustics drift away from the optical axis and shift in clockwise direction with respect to the Kerr caustics. The intersections of the critical curves on the equatorial plane as a function of the black hole angular momentum are found, and it is shown that they decrease with the increase of the parameter Q 2 /M . All of the lensing quantities are compared to particular cases as Schwarzschild, Kerr and Gibbons-Maeda black holes. I. INTRODUCTIONOne of the consequences of Einstein's General Theory of Relativity is that light rays are deflected by gravity. Although this discovery was made in the last century, the possibility that there could be such a deflection had been suspected much earlier, by Newton and Laplace, for the first time. The phenomena resulting from the deflection of electromagnetic radiation in a gravitational field are referred to as gravitational lensing (GL) and an object causing a detectable deflection is known as a gravitational lens. Nowadays, gravitational lensing is a rapidly developing area of research, and it has found applications ranging from the search of extrasolar planets and compact dark matter to the estimation of the values of the cosmological parameters [10]. In most of these cases it is possible to assume that the gravitational field is weak, hence the angle of deflection of the light in the field of a spherically symmetric body with mass M can be approximated by: that the present lens model could be able to distinguish observationally a black hole from naked singularity.The study of the gravitational lensing when light passes very close to a massive body, such as a black hole (a process also known as gravitational lensing in the strong deflection

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“…where ′ denotes derivative with respect to r. For a generalization of the concept of photon sphere to arbitrary spacetime see [33]. It can be argued that any spherically symmetric and static spacetime that has a horizon and is asymptotically flat for r → ∞ must contain a photon sphere [34] and hence any black hole will always give rise to relativistic deflection and relativistic images.…”

Section: Spacetimes Under Considerationmentioning

confidence: 99%

Time delay between relativistic images as a probe of cosmic censorship

et al. 2013

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We study the time delay between successive relativistic images in gravitational lensing as a possible discriminator between various collapse end states and hence as a probe of cosmic censorship. Specifically we consider both black hole and naked singularity spacetimes admitting photon spheres where an infinite number of relativistic Einstein Rings can be formed at almost the same radius and naked singularity spacetimes without a photon sphere where multiple relativistic Einstein Rings can form almost up to the center of the lens. The metrics we have considered to sample these scenarios are the Schwarzschild black hole, Janis-Newman-Winicour (naked singularity with photon sphere), Joshi-Malafarina-Narayan, and Tolman-VI (naked singularities without photon sphere) which are a fair sample of the theoretical possibilities.We show that the differential time delay between the relativistic images for naked singularities without a photon sphere progressively decreases for the models we study as opposed to that for black holes and naked singularities with a photon sphere, where it is known to be roughly constant. This characteristic difference in the time delay between successive images for these two cases can be potentially exploited for a source with known intrinsic variability to discriminate between these scenarios even when the images are not spatially resolved.

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The geometry of photon surfaces

Cited by 507 publications

References 11 publications

Inertial forces and photon surfaces in arbitrary spacetimes

Inertial forces and photon surfaces in arbitrary spacetimes

Kerr-Sen dilaton-axion black hole lensing in the strong deflection limit

Time delay between relativistic images as a probe of cosmic censorship

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