Not quite a black hole

Abstract

Astrophysical black hole candidates, although long thought to have a horizon, could be horizonless ultra-compact objects. This intriguing possibility is motivated by the black hole information paradox and a plausible fundamental connection with quantum gravity. Asymptotically free quadratic gravity is considered here as the UV completion of general relativity. A classical theory that captures its main features is used to search for solutions as sourced by matter. We find that sufficiently dense matter produces a novel horizonless configuration, the 2-2-hole, which closely matches the exterior Schwarzschild solution down to about a Planck proper length of the would-be horizon. The 2-2-hole is characterized by an interior with a shrinking volume and a seemingly innocuous timelike curvature singularity. The interior also has a novel scaling behavior with respect to the physical mass of the 2-2-hole. This leads to an extremely deep gravitational potential in which particles get efficiently trapped via collisions. As a generic static solution, the 2-2-hole may then be the nearly black endpoint of gravitational collapse. There is a considerable time delay for external probes of the 2-2-hole interior, and this determines the spacing of echoes in a post-merger gravitational wave signal.Comment: 35 pages, 11 figures, added section IIID: A brick wall and entrop

Tests for the existence of black holes through gravitational wave echoes

“…In these models, our parameter is naturally of the order ∼ O( P /M ) ∈ (10 −39 , 10 −46 ) for masses in the range M ∈ (10, 10 8 )M . The 2 − 2-hole model predicts even more compact objects, with ∼ ( P /M ) 2 ∈ (10 −78 , 10 −92 ) [118]. In all these cases, both quantum-gravity or microscopic corrections at the horizon scale select ClePhOs as well-motivated alternatives to BHs.…”

“…On the other hand, if large quantum effects do occur, they would probably act on short timescales to prevent apparent horizon formation. In some models, Planckscale dynamics naturally leads to abrupt changes close to the would-be horizon, without fine tuning [118]. Likewise, in the presence of (exotic) matter or if GR is classically modified at the horizon scale, Birkhoff's theorem no longer holds, and a star-like object might be a more natural outcome than a BH.…”

“…In summary, with the exception of boson stars, we do not know how or if UCOs and ClePhOs form in realistic collapse or merger scenarios. [37,116] (but see [117]) [23,24] 2 − 2 holes ClePhOs ∼ [118] (but see [118]) (but see [118]) [23,24] Collapsed ClePhOs ∼ polymers [119,120] (but see [119,121]) [121] Quantum bounces / ECO -ClePhOs ∼ black stars [7,8,[122][123][124][125] (but see [123,126]) [125] Quantum stars * Table 1: Catalogue of some proposed horizonless compact objects. A tick means that the topic was addressed.…”

A recipe for echoes from exotic compact objects

“…These puzzles have inspired proposals for horizonless alternatives to black holes including gravastars [15], boson stars [16], wormholes [17], fuzzballs [18] and others [19][20][21]. Many of these exotic compact objects (ECOs) can be ruled out on theoretical grounds.…”

Inflationary perturbations in no-scale theories

“…It has been proposed that such theory could make sense above M 2 as a Lee-Wick theory [29][30][31][32]: the ghost is unstable and does not appear among the asymptotic states, leading to a unitary Smatrix. Also, recently there has been progress on the quantum mechanics of four-derivative theories [33,34] and renewed further interest in four-derivative gravity [35][36][37][38][39][40][41][42][43][44][45][46][47]. References [48,49] claimed, however, that the Lee-Wick option might result in a violation of causality.…”