Quantum imprints of a black hole’s shape

Can quantum fields tell us about the curvature of a black hole event horizon?

By Tom Morley,  Peter Taylor, Elizabeth Winstanley

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The event horizon of a black hole completely surrounds a singularity. It seems obvious that the event horizon takes the form of a (possibly distorted) sphere, a surface with positive curvature. If the space-time far from the black hole is flat, this must be the case. Suppose instead that the space-time in which the black hole is situated itself has negative curvature (this is known as anti-de Sitter space-time and arises in string theory). Then the event horizon does not have to have positive curvature; it can have zero or negative curvature.

How do these different horizon shapes affect black hole physics? If we look at our reflection in a flat mirror, it is undistorted, but a mirror with positive or negative curvature distorts our reflection, as might be experienced in a “hall of mirrors” at a fairground (see image below for some similar effects).

Tom Morley is a PhD student at the University of Sheffield.

Peter Taylor is Assistant Professor of Mathematical Sciences at the Centre for Astrophysics and Relativity, Dublin City University.

Elizabeth Winstanley is Professor of Mathematical Physics at the University of Sheffield.

Gravitational waves measure colour of black holes

By Enrico Barausse, Richard Pires Brito, Vitor Cardoso, Irina Dvorkin, and Paolo Pani

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Black holes predicted by Einstein are, well, black. In classical physics, nothing can escape their event horizon, not light, not matter, and neither gravitational waves.

There is a deep reason for this absolute blackness. If the event horizon were not a perfectly absorbing surface, but rather a partially reflective one, spinning black holes would become unstable and would shed most of their rotational energy into gravitational waves. This process is known as superradiant instability [1], and is tightly linked to the presence of an ergoregion, a region of spacetime just outside the event horizon, where modes of negative energy are allowed to exist. Negative energy-modes can form in the ergoregion of normal humdrum black holes, but are eventually doomed to fall in the event horizon.

Enrico Barausse

Richard Pires Brito

Professor Vitor Cardoso

Irina Dvorkin

Paolo Pani

If (what look like) black objects had a surface, such modes would be partially reflected by it, and they would bounce back and forth between the horizon and the boundary of the ergoregion (which they cannot cross, since negative energy modes cannot travel to infinity). Each time they reach the ergoregion boundary, they come out as positive energy-modes, thus inside the ergoregion they would keep growing in amplitude (i.e. their energy would keep decreasing and becoming more negative) eventually producing an instability. Indeed, these ‘bounces’ produce ‘echoes’ in the gravitational wave signal [2] from the remnant black hole forming from binary mergers, and there are claims [3] (albeit controversial [4]) that they may have been seen in the LIGO data.

In this paper we do not look at the black holes that form from binary mergers, but rather at isolated ones. These black holes can have a wide range of masses (from stellar masses for stellar-origin black holes up to millions or billions solar masses for supermassive black holes) and a variety of spins (on which we have some knowledge thanks to electromagnetic observations). Normally, isolated black holes do not emit gravitational waves, but if their event horizon had some reflectivity (that is, if these objects were not totally black), they would turn into black-hole bombs due to superradiance, and they would shed almost all their angular momentum in gravitational waves. These gravitational wave signals would be too weak to be detected singularly, but because there are in general many more black holes in isolation than in binaries, they can produce a very large stochastic background. Indeed, this background would be orders of magnitude larger than the current upper bounds from LIGO/Virgo. Similar results also apply to supermassive black holes, in the yet-unexplored LISA band.

So in conclusion, the existing stochastic background constraints from LIGO and Virgo show that black holes are very black, although some shades of grey may still be allowed. Indeed, while 100% reflection from the horizon is ruled out, smaller reflection coefficients may still be possible depending on the spin of the object [5].

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References:
[1] W. H. Press and S. A. Teukolsky, “Floating Orbits, Superradiant Scattering and the Black-hole Bomb“. Nature. 238 (5361): 211-212 (1972);
Brito, Cardoso, Pani; “Superradiance“, Springer (2015)
[2] Cardoso, Franzin, Pani, “Is the gravitational-wave ringdown a probe of the event horizon?“, Phys. Rev. Lett. 116, 171101 (2016)
[3] Abedi & Afshordi, “Echoes from the Abyss: Tentative evidence for Planck-scale structure at black hole horizons“, Phys. Rev. D 96, 082004 (2017)
[4] Ashton+ https://arxiv.org/abs/1612.05625; Abedi, Dykaar, Afshordi, https://arxiv.org/abs/1701.03485 and https://arxiv.org/abs/1803.08565;
Westerweck+, “Low significance of evidence for black hole echoes in gravitational wave data“, Phys. Rev. D 97, 124037 (2018)
[5] Maggio, Pani, Ferrari “Exotic Compact Objects and How to Quench their Ergoregion Instability“, Phys. Rev. D 96, 104047 (2017); Maggio, Cardoso, Dolan, Pani, http://arxiv.org/abs/arXiv:1807.08840

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Read the full article in Classical and Quantum Gravity:
The stochastic gravitational-wave background in the absence of horizons
Enrico Barausse et al 2018 Class. Quantum Grav. 35 20LT01

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Black and White Hole Twins Connected by Quantum Gravity

By Javier Olmedo, Sahil Saini and Parampreet Singh

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Black holes are perhaps the most exotic objects in our Universe with very intriguing properties. The event horizon does not allow light and matter to escape, and hides the central singularity. As in the case of the big bang singularity, the central singularity is a strong curvature singularity where all in-falling objects are annihilated irrespective of their strength. Since singularities point out pathologies of general relativity, a more fundamental description obtained from quantum gravity must resolve the problem of singularities. Singularity resolution is also important for resolving many of the paradoxes and conundrums that plague the classical theory such as the cosmic censorship conjecture, black hole evaporation, black hole information loss paradox, etc.

Dr. Javier Olmedo is a postdoctoral researcher at Pennsylvania State University

Sahil Saini is a graduate student at Louisiana State University

Dr. Parampreet Singh is an associate professor at Louisiana Stare University

Black holes have mirror versions too. Known as white holes, these are solutions of general relativity with the same spacetime metric.  If the black holes do not allow even the light to escape once it enters the horizon, thus nothing can enter the white hole horizon. Light and matter can only escape from the white hole. It has sometimes been speculated that black hole and white hole solutions can be connected, providing gateways between different universes or travelling within the same universe, but details have been sparse. The reason is due to the presence of the central singularity which does not allow a bridge between the black and white holes.