Invariant characterization of the Kerr spacetime: Locating the horizon and measuring the mass and spin of rotating black holes using curvature invariants

Abdelqader, Majd; Lake, Kayll

doi:10.1103/physrevd.91.084017

Cited by 42 publications

(59 citation statements)

References 24 publications

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“…The research looking for connections between the zeros of certain curvature invariants and the location of the horizon has begun because numerical relativity simulations can extract the mass and angular momentum of a black hole only by locating its horizon and by computing its area through the excision method. Finding the location of the black hole horizon provides information about which region must be excised [88].…”

Section: Discussionmentioning

confidence: 99%

Curvature invariants and lower dimensional black hole horizons

2019

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It is known that the event horizon of a black hole can often be identified from the zeroes of some curvature invariants. The situation in lower dimensions has not been thoroughly clarified. In this work we investigate both (2+1)-and (1+1)-dimensional black hole horizons of static, stationary and dynamical black holes, identified with the zeroes of scalar polynomial and Cartan curvature invariants, with the purpose of discriminating the different roles played by the Weyl and Riemann curvature tensors. The situations and applicability of the methods are found to be quite different from that in 4-dimensional spacetime. The suitable Cartan invariants employed for detecting the horizon can be interpreted as a local extremum of the tidal force suggesting that the horizon of a black hole is a genuine special hypersurface within the full manifold, contrary to the usual claim that there is nothing special at the horizon, which is said to be a consequence of the equivalence principle.

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Section: Discussionmentioning

confidence: 99%

Curvature invariants and lower dimensional black hole horizons

2019

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“…Given a metric representing a spacetime, the usual search for an event horizon proceeds as follows: one assumes that the event horizon H is a smooth level set of a single function F satisfying g µν ∂ µ F ∂ ν F = 0 which clearly requires well-chosen coordinates in spacetime. Instead of this coordinate-dependent method, there have been some recent developments initiated by the work of Abdelqader and Lake [2] who gave an invariant characterization of the Kerr black hole, significantly extending the earlier method of Karlhede et al [3] which works for the case of the Schwarzschild black hole. In [2] the following set of curvature scalars was suggested as a basis to detect the location of the event horizon and the ergosurface as well as to define some other properties, such as the mass and the spin of the black hole…”

Section: Introductionmentioning

confidence: 99%

“…For the Kerr black hole, none of the above invariants are enough to locate the event horizon. Hence in [2], the following nonlinear combination was found…”

Section: Introductionmentioning

confidence: 99%

Event horizon detecting invariants

Tavlayan

Tekin

2020

Phys. Rev. D

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Some judiciously chosen local curvature scalars can be used to invariantly characterize event horizons of black holes in D > 3 dimensions, but they fail for the three dimensional Bañados-Teitelboim-Zanelli (BTZ) black hole since all curvature invariants are constant. Here we provide an invariant characterization of the event horizon of the BTZ black hole using the curvature invariants of codimension one hypersurfaces instead of the full spacetime. Our method is also applicable to black holes in generic dimensions but is most efficient in three, four, and five dimensions. We give four dimensional Kerr, five dimensional Myers-Perry and three dimensional warped-anti-de Sitter, and the three dimensional asymptotically flat black holes as examples.PACS numbers:

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“…Last but not least, our analysis about the location of the event horizon can play a role in numerical relativity simulations about gravitational waves in which the excision method is adopted, and information about the location of the event horizon (i.e. about the region to excise) are necessary [32].…”

Section: Discussionmentioning

confidence: 99%

“…Moreover, a procedure for locating the McVittie horizon in terms of the zeros of an appropriate curvature invariant has been proposed along the research which has been trying to develop local techniques for detecting a black hole horizon [31]. Those algorithms do not rely on the non-local propagation of light rays and constitute the ground for the geometric horizon conjecture [32][33][34][35][36][37][38]. In this paper we are interested in understanding how the horizon actually looks like when specific and different matter contents of the universe are considered.…”

Section: The Mcvittie Horizon: Setup Of the Problemmentioning

confidence: 99%

The horizon of the McVittie black hole: on the role of the cosmic fluid modeling

2020

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In this paper, we investigate the existence and time evolution of the cosmological and event horizons in a McVittie universe whose expansion is driven by the Redlich-Kwong, (Modified) Berthelot, Dieterici, and Peng-Robinson fluids, respectively. The equations of state of these fluids are rich enough to account for both exotic and regular, as well as ideal and non-ideal matter contents of the universe. We show that the cosmological horizon is expanding, while the event horizon is shrinking along the cosmic time evolution. The former achieves larger size for regular types of matter, contrary to the latter. The strength of interactions within the cosmic fluid are shown to play a more important role in affecting the evolution of the event horizon, rather than of the cosmological horizon in the case of a singularity-free universe. While the cosmological horizon always exists during the time evolution, the event horizon can exist only when a certain relationship between the Hawking-Hayward quasi-local mass and the Hubble function is fulfilled. In this manner, we can study the role played by the large-scale physics (cosmic evolution) on the local scale physics (evolution of a black hole).

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Invariant characterization of the Kerr spacetime: Locating the horizon and measuring the mass and spin of rotating black holes using curvature invariants

Cited by 42 publications

References 24 publications

Curvature invariants and lower dimensional black hole horizons

Curvature invariants and lower dimensional black hole horizons

Event horizon detecting invariants

The horizon of the McVittie black hole: on the role of the cosmic fluid modeling

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