Light rings of stationary spacetimes

Classical and Quantum Gravity, 2021

The Kerr black holes possess a photon region with prograde and retrograde orbits radii, respectively, M ⩽ r p − ⩽ 3 M and 3 M ⩽ r p + ⩽ 4 M , and thereby always cast a closed photon ring or a shadow silhouette for a ⩽ M. For a > M, it is a no-horizon spacetime (naked singularity) wherein prograde orbits spiral into the central singularity, and retrograde orbits produce an arc-like shadow with a dark spot at the center. We compare Kerr black holes’ photon ring structure with those produced by three rotating regular spacetimes, viz Bardeen, Hayward, and nonsingular. These are non-Kerr black hole metrics with an additional deviation parameter of g related to the nonlinear electrodynamics charge. It turns out that for a given a, there exists a critical value of g, g E such that Δ = 0 has no zeros for g > g E, one double zero at r = r E for g = g E, respectively, corresponding to a no-horizon regular spacetime and extremal black hole with degenerate horizon. We demonstrate that, un...

Physics Letters A, 1992

We present a peculiar feature of our soliton solution to the higher-dimensional Einstein equations. The solution describes a black hole surrounded by null rings.

Physical Review D

Modelling of gravitational waves from binary black hole inspiral has played an important role in the recent observations of such signals. The late-stage ringdown phase of the gravitational waveform is often associated with the null particle orbit ("light ring") of the black hole spacetime. With simple models we show that this link between the light ring and spacetime ringing is based more on the history of specific models than on an actual constraining relationship. We also show, in particular, that a better understanding of the dissociation of the two may be relevant to the astrophysically interesting case of rotating (Kerr) black holes.

Physical Review D, 2007

We consider black ring with a cosmological constant in the five dimensional N=4 de Sitter supergravity theory. Our solution preserves half of the de Sitter supersymmetries and has one rotation symmetry. Unlike the flat case, there is no angular momentum and the stability against gravitational self-attraction is balanced by the cosmological repulsion due to the cosmological constant. Our solution describes a singular black ring since although it has horizons of topology S^1 x S^2, the horizons are singular. Despite the singularity, our solution displays some interesting regular physical properties: it carries a dipole charge and this charge contributes to the first law of thermodynamics; it has an entropy and mass which conform to the entropic N-bound proposal and the maximal mass conjecture We conjecture that the Gregory-Laflamme instability leads to a resolution of the singularity and results in a regular black ring.

2013

This Dissertation covers three aspects of General Relativity: inequivalent Einstein metrics on Lie Group Manifolds, proving the Hoop Conjecture for Black Rings, and investigating ergoregions in magnetised black hole spacetimes. A number of analytical and numerical techniques are employed to that end.

We focus on main differences between stationary frames in the Kerr geometry and the Kerr-de Sitter geometry. This comparison leads to new solutions on the symmetry axis and in the equatorial plane. This solution can clearly be described and physically interpreted. The most interesting is the case of freely falling stationary observers on the symmetry axis. We found a solution which can show that rotating supermassive black holes (not necessary fast rotating) could differ in a certain way from the same bodies for which the present value of the cosmological constant is not included. We show that an interesting family of "freely falling stationary observers" can be found. We found stationary observers in the equatorial plane, which can become (at a particular radius) counter rotating if they previously co rotated and vice versa. We also describe and compare stationary observers in the equatorial plane between themselves, showing how depends their angular velocity ω at the rad...

2006

We consider black ring with a cosmological constant in the five dimensional N = 4 de Sitter supergravity theory. Our solution preserves half of the de Sitter supersymmetries and has one rotation symmetry. Unlike the flat case, there is no angular momentum and the stability against gravitational self-attraction is balanced by the cosmological repulsion due to the cosmological constant. Our solution describes a singular black ring since although it has horizons of topology S 1 × S 2, the horizons are singular. Despite the singularity, our solution displays some interesting regular physical properties: it carries a dipole charge and this charge contributes to the first law of thermodynamics; it has an entropy and mass which conform to the entropic N-bound proposal and the maximal mass conjecture. We conjecture that the Gregory-Laflamme instability leads to a resolution of the singularity and results in a regular A remarkable black hole solution, the black ring, admitting a horizon of n...

Physical Review D, 2007

We consider in more detail the covariant counterterm proposed by Mann and Marolf in asymptotically flat spacetimes. With an eye to specific practical computations using this counterterm, we present explicit expressions in general d dimensions that can be used in the so-called 'cylindrical cut-off' to compute the action and the associated conserved quantities for an asymptotically flat spacetime. As applications, we show how to compute the action and the conserved quantities for the NUT-charged spacetime and for the Kerr black hole in four dimensions.

Classical and Quantum Gravity, 2002

We construct non-trivial vacuum space-times with a global I + . The construction proceeds by proving extension results for initial data sets across compact boundaries, adapting the gluing arguments of Corvino and Schoen. Another application of the extension results is existence of initial data which are exactly Schwarzschild both near infinity and near each of the connected component of the apparent horizon. * Supported in part by a grant of the Polish Research Foundation KBN. † Supported in part by the ACI program of the French Ministry of Research. 1 Here we mean the metric induced by the Schwarzschild metric on the usual t = 0 hypersurface in Schwarzschild space-time; we will make such an abuse of terminology throughout.

Journal of High Energy Physics, 2007

We develop solution-generating techniques for stationary metrics with one angular momentum and axial symmetry, in the presence of a cosmological constant and in arbitrary spacetime dimension. In parallel we study the related lower dimensional Einstein-Maxwell-dilaton static spacetimes with a Liouville potential. For vanishing cosmological constant, we show that the field equations in more than four dimensions decouple into a four dimensional Papapetrou system and a Weyl system. We also show that given any four dimensional "seed" solution, one can construct an infinity of higher dimensional solutions parametrised by the Weyl potentials, associated to the extra dimensions. When the cosmological constant is non-zero, we discuss the symmetries of the field equations, and then extend the well known works of Papapetrou and Ernst (concerning the complex Ernst equation) in four-dimensional general relativity, to arbitrary dimensions. In particular, we demonstrate that the Papapetrou hypothesis generically reduces a stationary system to a static one even in the presence of a cosmological constant. We also give a particular class of solutions which are deformations of the (planar) adS soliton and the (planar) adS black hole. We give example solutions of these techniques and determine the four-dimensional seed solutions of the 5 dimensional black ring and the Myers-Perry black hole.