Geometric horizons in the Kastor-Traschen multi-black-hole solutions

McNutt, David; Coley, A. A.

doi:10.1103/physrevd.98.064043

Cited by 14 publications

(13 citation statements)

References 74 publications

(147 reference statements)

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“…its behavior at null spatial infinity, for locating its horizon(s) which can therefore be observed by experimental devices of finite sizes, taming its teleological nature pointed out in [43,44]. Therefore, we have explicitly shown that the horizon constitutes a local property of the manifold (in agreement with the core principles of any relativistic field theory), and that a curvature invariant can be constructed for its detection once the geometrical symmetries of the spacetime are known regardless the gravitational theory behind it: this is consistent with the geometric horizon conjecture [40,[45][46][47][48][49][50][51][52][53]. On the other hand, our results are important also from the practical point of view in light of the so-called excision technique in numerical relativity: the black hole horizon constitutes a causal boundary separating the evolutions of phenomena occurring outside it from what it may happen inside; thus, the spacetime region delimited by the horizon must be removed (or excised) when performing numerical simulations of the evolution of a black hole.…”

Section: Curvature Syzygyssupporting

confidence: 82%

A critical assessment of black hole solutions with a linear term in their redshift function

2021

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Different theories of gravity can admit the same black hole solution, but the parameters usually have different physical interpretations. In this work we study in depth the linear term $$\beta r$$ β r in the redshift function of black holes, which arises in conformal gravity, de Rham–Gabadadze–Tolley (dRGT) massive gravity, f(R) gravity (as approximate solution) and general relativity. Geometrically we quantify the parameter $$\beta $$ β in terms of the curvature invariants. Astrophysically we found that $$\beta $$ β can be expressed in terms of the cosmological constant, the photon orbit radius and the innermost stable circular orbit (ISCO) radius. The metric degeneracy can be broken once black hole thermodynamics is taken into account. Notably, we show that under Hawking evaporation, different physical theories with the same black hole solution (at the level of the metric) can lead to black hole remnants with different values of their physical masses with direct consequences on their viability as dark matter candidates. In particular, the mass of the graviton in massive gravity can be expressed in terms of the cosmological constant and of the formation epoch of the remnant. Furthermore the upper bound of remnant mass can be estimated to be around $$0.5 \times 10^{27}$$ 0.5 × 10 27 kg.

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Section: Curvature Syzygyssupporting

confidence: 82%

A critical assessment of black hole solutions with a linear term in their redshift function

2021

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“…To address this, a new set of curvature invariants has been introduced that are adapted to the interpretation of QS Szekeres PBH solutions. In addition to showing that the apparent horizon is detected by the vanishing of a Cartan invariant, implying that it is a geometric horizon [9,10,11], we have also introduced invariants to characterize the expansion or contraction of spacetime itself, the spatial rate of change and extrema of the areal radius, the spatial rate of change and extrema of the mass function, the relative movement of matter shells, the existence of shell-crossings and regular spatial extrema in a QS Szekeres solution. We note that this new set of invariants can describe the evolution of any QS Szekeres dust models and has a physical interpretation.…”

Section: Discussionmentioning

confidence: 99%

“…To show that R = 2M is a geometric horizon, we note that the extended Cartan invariant ρ, defined in equation ( 14), will vanish on the surface R = 2M [9,10]. This surface is a dynamical geometric horizon since the extended invariant, µ, which also appears in the covariant derivative of the curvature tensor, is negative within the surface R = 2M [11]. The spin-coeficients ρ and µ correspond to the expansion of the ingoing and outgoing null directions; i.e., ρ = θ ( ) and µ = θ (n) .…”

Section: Detection Of the Horizonmentioning

confidence: 99%

“…In the case of a geometric horizon the preferred null directions a and n a in (9) are not geodesic but lie in the timelike plane spanned by the null normals to the hypersurface R = 2M [10]. In general, geometric horizons are not necessarily apparent horizons or any other horizon based on trapped surfaces [11].…”

Section: Detection Of the Horizonmentioning

confidence: 99%

“…However, due to the foliation dependence of the apparent horizon, it is observer dependent, and this can lead to ambiguities if care is not taken to relate the differing observers' reference frames [7]. For this reason it is important to determine an alternative surface that is defined invariantly, such as the geometric horizon which is a hypersurface defined by the vanishing of particular curvature invariants [9,10,11].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

An invariant characterization of the quasi-spherical Szekeres dust models

2019

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The quasi-spherical Szekeres dust solutions are a generalization of the spherically symmetric Lemaitre-Tolman-Bondi dust models where the spherical shells of constant mass are non-concentric. The quasi-spherical Szekeres dust solutions can be considered as cosmological models and are potentially models for the formation of primordial black holes in the early universe. Any collapsing quasi-spherical Szekeres dust solution where an apparent horizon covers all shell-crossings that will occur can be considered as a model for the formation of a black hole. In this paper we will show that the apparent horizon can be detected by a Cartan invariant. We will show that particular Cartan invariants characterize properties of these solutions which have a physical interpretation such as: the expansion or contraction of spacetime itself, the relative movement of matter shells, shell-crossings and the appearance of necks and bellies.

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Charges and fluxes on (perturbed) non-expanding horizons

Ashtekar

Khera

Kolanowski

et al. 2022

J. High Energ. Phys.

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In a companion paper [1] we showed that the symmetry group $$ \mathfrak{G} $$ G of non-expanding horizons (NEHs) is a 1-dimensional extension of the Bondi-Metzner-Sachs group $$ \mathfrak{B} $$ B at $$ \mathcal{I} $$ I +. For each infinitesimal generator of $$ \mathfrak{G} $$ G , we now define a charge and a flux on NEHs as well as perturbed NEHs. The procedure uses the covariant phase space framework in presence of internal null boundaries $$ \mathcal{N} $$ N along the lines of [2–6]. However, $$ \mathcal{N} $$ N is required to be an NEH or a perturbed NEH. Consequently, charges and fluxes associated with generators of $$ \mathfrak{G} $$ G are free of physically unsatisfactory features that can arise if $$ \mathcal{N} $$ N is allowed to be a general null boundary. In particular, all fluxes vanish if $$ \mathcal{N} $$ N is an NEH, just as one would hope; and fluxes associated with symmetries representing ‘time-translations’ are positive definite on perturbed NEHs. These results hold for zero as well as non-zero cosmological constant. In the asymptotically flat case, as noted in [1], $$ \mathcal{I} $$ I ±are NEHs in the conformally completed space-time but with an extra structure that reduces $$ \mathfrak{G} $$ G to $$ \mathfrak{B} $$ B . The flux expressions at $$ \mathcal{N} $$ N reflect this synergy between NEHs and $$ \mathcal{I} $$ I +. In a forthcoming paper, this close relation between NEHs and $$ \mathcal{I} $$ I + will be used to develop gravitational wave tomography, enabling one to deduce horizon dynamics directly from the waveforms at $$ \mathcal{I} $$ I +.

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Geometric horizons in the Kastor-Traschen multi-black-hole solutions

Cited by 14 publications

References 74 publications

A critical assessment of black hole solutions with a linear term in their redshift function

A critical assessment of black hole solutions with a linear term in their redshift function

An invariant characterization of the quasi-spherical Szekeres dust models

Charges and fluxes on (perturbed) non-expanding horizons

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