arXiv subjects

Brett McInnes

Publications and source records attributed to Brett McInnes.

At least 19 recordsLinked to original sources

arXiv2026

Reconciling Inflation with Anisotropies at Small Scales

There have been persistent suggestions, based on several diverse data sets, that some aspects of our Universe were or are not isotropic. It is not easy to develop a coherent theoretical account of such a ``statistical anisotropy'', for, in standard General Relativity, intuition suggests that it contradicts the predictions of the very successful Inflationary hypothesis. We put this intuition on a firm basis, by proving that if we [a] make use of an Inflationary theory in which Inflation isotropises spatial geometry ---$\,$ this, of course, includes the great majority of such theories ---$\,$ and if [b] we insist on assuming that spacetime has a strictly metric geometry (one in which the geometry is completely determined by a metric tensor), then indeed all aspects of the ``Hubble field'' must be isotropic. Conversely, should a statistical anisotropy be confirmed, then either we must contrive to build anisotropy into Inflation from the outset, or we will have to accept that spacetime geometry is not strictly metric. We argue that the second option, implemented by allowing spacetime \emph{torsion} to be non-zero, would be by far the most natural way to accommodate \emph{some} such observations. Such theories can reconcile a non-isotropic Hubble field at the end of Inflation with a perfectly isotropic spatial geometry, and thus are able to reconcile Inflation with certain kinds of possibly observable anisotropies at relatively small cosmic scales (though by no means with all).

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arXiv2026

How Inflation Might Explain Large-Scale Anisotropy

Several recent observational analyses have suggested the possible existence of anisotropy in our Universe. It is often thought that this would contradict the inflationary picture. We have argued that this is not the case: if we relax the artificial restriction that spacetime torsion must be zero, then such anisotropies arise naturally, indeed almost inevitably, in a theory of torsional Inflation. This is seen most clearly if one uses a ``$1\,+\,3\,$'' analysis of a torsional spacetime, leading naturally to concepts of intrinsic torsion and extrinsic torsion. An anisotropic quantum fluctuation of the inflaton leads to an extrinsic torsion field which is anisotropic and which grows throughout the inflationary era, even though the intrinsic geometry of the spatial sections is isotropised in the conventional manner. This leads to an anisotropic Hubble field at the \emph{end} of Inflation. The anisotropy takes a very specific and characteristic form, which in principle could be observable on relatively short cosmic scales. On the other hand, an unusual feature of torsional geometry leads to a short interval, \emph{early} in the inflationary era, during which there is a torsion-induced energy flux, which leaves an anisotropic signal in superhorizon modes and thus ultimately at very large scales in the present Universe. Thus in principle torsion can explain anisotropies both on relatively short cosmic scales and also at the largest scales.

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arXiv2025

Intrinsic Torsion, Extrinsic Torsion, and the Hubble Parameter

We study the intrinsic and extrinsic torsions (defined by analogy with the intrinsic and extrinsic curvatures) of the spatial sections of torsional spacetimes. We consider two possibilities. First, that the intrinsic torsion might prove to be directly observable. Second, that it is not observable, having been ``inflated away'' in the early Universe. We argue that, even in this second case, the extrinsic torsion may grow during the inflationary era and be non-negligible at reheating and thereafter. Even if the spatial intrinsic curvature and torsion are too small to be detected directly, then, the extrinsic torsion might not be. We point out that, if its presence is not recognised, the extrinsic torsion could lead to anomalies in the theoretical estimate of the Hubble parameter -- $\,$ a result with obvious potential applications. We stress that extrinsic torsion is by far the most natural way to produce such anomalies, simply because it mixes naturally with the Hubble parameter; that is, the second fundamental form of a spacelike section depends on a sum of two terms, one determined by the Hubble parameter, the other by the extrinsic torsion.

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arXiv2024

Superradiance in the Bulk Protects Quantum State Evolution of Rapidly Rotating Matter on the Boundary

It has been argued that the rate at which the interior of an AdS black hole evolves is dual to the rate of evolution of the (quantum state of the) strongly coupled matter on the boundary which, according to holography, is dual to the black hole. However, we have shown elsewhere that it seems to be possible, by adjusting the specific angular momentum of an AdS$_5$-Kerr black hole, to reduce this rate to (effectively) zero. We argue that this is unphysical, and that it is prevented by the intervention of a superradiant instability, which causes the black hole to shed angular momentum when the angular velocity exceeds a certain critical value. The precise way in which this works has recently been explained by the ``grey galaxy'' model of the end state, in which the angular momentum is transferred to a ``galactic disc.'' Thus, the black hole itself cannot sustain a specific angular momentum beyond a critical value: there is an effective upper bound. The holographic interpretation is that, beyond a certain limiting specific angular momentum, strongly coupled matter (corresponding to the black hole) will spontaneously shed angular momentum to some other, confined, form of matter (corresponding to the disc). This idea is supported by recent numerical work on ultra-vortical plasmas. Such an upper bound on specific angular momentum would prevent arbitrarily small rates of quantum state evolution on the boundary. We give a tentative discussion of the relevant observational data in the case of the vortical Quark-Gluon Plasma, and suggest a way in which such an upper bound might appear in future observations.

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arXiv2024

Evidence that the Rate of Evolution of a Black Hole Interior Has a Holographic Dual

A ``large'' AdS black hole can attain equilibrium with its own Hawking radiation, and in that condition it is thought to be dual to a strongly coupled field theory, also at equilibrium. But the interior of the black hole is by no means static: the geometry of spatial sections lying inside the event horizon evolves at some rate. This prompts the obvious question: can this rate possibly have a holographic dual? We present circumstantial evidence that such a dual does exist. We do this by making concrete proposals for two objects: first, a rough measure (already suggested in the literature) of the rate at which the unitary evolution of the state vector describing equilibrated strongly coupled matter evolves; and, second, a rough measure of the rate at which the interior (just under the horizon) evolves (in the case of the AdS$_5$-Kerr black hole). We then study how these two very different objects change as two physical parameters describing the exterior of the bulk black hole (the specific angular momentum and the temperature) are varied. We find that they change in remarkably similar ways, as holographic duals should.

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arXiv2023

Slow Complexification

The fact that AdS black hole interior geometries are time-dependent presents two challenges: first, to holographic duality (the boundary matter tends to equilibrate, often very quickly), and, second, to the idea that wormholes can be traversable (the wormhole geometry is dynamic, and the wormhole is apt to collapse too quickly for traversal to be possible). As is well known, the first puzzle can be addressed by considering the quantum circuit complexity of the strongly coupled boundary matter, which can continue to grow long after equilibrium is established. We show that data from a phenomenological model of the Quark-Gluon Plasma indicate the existence of an upper bound on the rate of increase of the (specific) complexity, in agreement with a simple holographic model. We then point out that, in this model, this upper bound becomes stricter if angular momentum is added to the bulk black hole while fixing the temperature (at any value, so the black hole is \emph{not} near-extremal). We show that the dual phenomenon, a dramatic slowing of the black hole interior dynamics at high specific angular momentum, also occurs. We conjecture that sufficiently slow complexification of the field theories dual to rotating black holes is associated with traversability of the bulk wormhole, when quantum effects are taken into account.

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arXiv2023

Why is Black Hole Entropy Affected by Rotation?

It is well known that an asymptotically flat four-dimensional Kerr black hole has a smaller (specific) entropy than a Schwarzschild black hole of the same mass. We show here that the same is true if the temperature, rather than the mass, is held fixed; and we also show that an asymptotically AdS$_5$-Kerr black hole has a smaller specific entropy than an AdS$_5$-Schwarzschild black hole of the same temperature, except in a negligibly small class of special examples. The AdS$_5$-Kerr case is particularly interesting, because here the gauge-gravity duality applies; if we further accept that there is a useful analogy between the strongly coupled field theories dual to AdS black holes and the best-understood example of a strongly coupled fluid (the Quark-Gluon Plasma), then we can apply QGP theory to predict the behaviour of black hole entropy in this case. The prediction agrees with our study of AdS$_5$-Kerr entropy. The hope is that such results might lead ultimately to an identification of black hole microstates.

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arXiv2023

The Special Role of Toroidal Black Holes in Holography

In the standard holographic ``dictionary'', the deep infrared of the strongly coupled boundary field theory is studied by examining the bulk region near to the event horizon of a simple AdS-Reissner-Nordström black hole, near to extremality. Recently Horowitz et al. have argued that this is not correct, \emph{except} in the case of small toroidal black holes, which are therefore revealed to be particularly interesting and important. On the other hand, the Weak Gravity Conjecture postulates that black holes (including toroidal black holes) which are extremely near to extremality spontaneously emit black holes of the same kind. We show that, in the toroidal case, these ``emitted'' black holes are always small in the sense of Horowitz et al. As an application, we discuss the Grinberg-Maldacena analysis of the way one-point functions, evaluated outside an AdS-Reissner-Nordström black hole, depend on the proper time of fall from the event horizon to the Cauchy horizon. We find that, for emitted toroidal black holes, this dependence effectively drops out.

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arXiv2022

Planar Black Holes as a Route to Understanding the Weak Gravity Conjecture

One version of the Weak Gravity Conjecture requires that it should be possible for an extremal black hole to emit a smaller black hole: that is, the original black hole bifurcates. For asymptotically flat and asymptotically AdS Reissner-Nordström black holes with spherical event horizons, such a bifurcation reduces the total classical entropy of the system, and so it is apparently forbidden by the second law of thermodynamics. It may well be possible to remedy this by taking other (for example, quantum-gravitational) effects into account, but it is difficult to understand this in a quantitative way. In the case of asymptotically AdS Reissner-Nordström black holes with \emph{planar} event horizons, however, one can show that bifurcations are definitely compatible with the second law. (Naked singularities, generated by the bifurcation, may play an important role here.) Furthermore, in this case one can exhibit a detailed mechanism explaining precisely why planar black holes must indeed be unstable (through emission of branes) when they are sufficiently close to extremality. Thus planar black holes can improve our understanding of the WGC.

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arXiv2022

Characterising the Most Rapidly Rotating AdS$_5$-Kerr Black Holes

Classical Censorship permits AdS$_5$-Kerr black holes with arbitrarily large angular momenta per unit mass, which does not seem reasonable from a holographic point of view. However, it has been shown that, when these black holes are embedded in string theory, their angular momentum per unit mass is in fact bounded by $2\sqrt{2}L$, where $L$ is the asymptotic curvature scale. One might suppose that the most rapidly rotating AdS$_5$-Kerr black holes, with angular momentum per unit mass close to this bound, might be unstable, for example, to a superradiant instability. We show that this is not always true: there is a small domain in the AdS$_5$-Kerr parameter space corresponding to black holes which are stable against superradiance and yet nearly saturate the stringy bound.

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arXiv2022

Extremal Instability for Topological Black Holes

The initial idea underlying the Weak Gravity Conjecture is that extremal black holes must always be "unstable", in the sense that they should slowly decay by emitting either particles or smaller black holes. Here we show that, when this idea is applied to the \emph{planar} asymptotically AdS black holes which play a central role in applications of holography, the result, via gauge-gravity duality, is a prediction that there should exist a lower bound on the possible densities of cold strongly coupled matter. Recent observations of neutron stars suggest that, in many cases, even the extreme densities in their cores may not be sufficient to generate quark matter, showing that there is indeed a (very high) lower bound on the possible density of cold quark matter.

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arXiv2021

Extremal Bifurcations of Rotating AdS$_4$ Black Holes

The Weak Gravity Conjecture arises from the assertion that all extremal black holes, even those which are "classical" in the sense of being very massive, must decay by quantum-mechanical emission of particles or smaller black holes. This is interesting, because some observed astrophysical black holes are on the brink of being extremal -- $\,$ though this is due to rapid rotation rather than a large electric or magnetic charge. The possibility that rotating near-extremal black holes might, in addition to radiating spinning particles, also bifurcate by emitting smaller black holes, has attracted much attention of late. There is, however, a basic question to be answered here: can such a bifurcation be compatible with the second law of thermodynamics? This is by no means clear. Here we show that, if there is indeed such a mechanism for bifurcations of AdS$_4$-Kerr-Newman black holes, then this process can in fact satisfy the second law.

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arXiv2021

The Weak Gravity Conjecture Requires the Existence of Exotic AdS Black Holes

The Weak Gravity Conjecture arises from the requirement that it be possible for all (classically stable) extremal black holes to decay. The ``black hole version'' of the conjecture requires that it should be possible for this to occur through the emission of smaller black holes. We consider this version in the case of extremal AdS$_4$-Kerr-Newman black holes which are stable against a superradiant instability. One finds that the emitted black hole must be rather exotic, having an ``angular horizon'' analogous to the more familiar (radial) horizon.

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arXiv2020

About Magnetic AdS Black Holes

There has recently been a strong revival of interest in quasi-extremal magnetically charged black holes. In the asymptotically flat case, it is possible to choose the magnetic charge of such an object in such a manner that the black hole is surrounded by a corona in which electroweak symmetry is restored on macroscopic scales, a result of very considerable interest. We argue that holographic duality indicates that the asymptotically AdS analogues of these black holes have several interesting properties: the dual theory is only physical if the black hole is required to rotate; in the rotating case, the magnetic field at the poles does not attain its maximum on the event horizon, but rather somewhat outside it; the magnetic field at the equator is not a monotonically decreasing function of the magnetic charge; the electric fields induced by the rotation, while smaller than their magnetic counterparts, are by no means negligible; the maximal electric field often occurs neither at the poles nor at the equator; and so on. Most importantly, in the magnetically charged case it is possible to avoid the superradiant instability to which neutral AdS-Kerr black holes are subject; but the need to avoid this instability imposes upper bounds on the magnetic and electric fields. In some circumstances, therefore, the corona may not exist in the asymptotically AdS case.

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arXiv2020

Holographic Dual of The Weak Gravity Conjecture

The much-discussed \emph{Weak Gravity Conjecture} is interesting and important in both the asymptotically flat and the asymptotically AdS contexts. In the latter case, it is natural to ask what conditions it (and the closely related Cosmic Censorship principle) imposes, via gauge-gravity duality, on the boundary field theory. We find that these conditions take the form of lower bounds on the number of colours in this theory: that is, the WGC and Censorship might (depending on the actual sizes of the bounds) enforce the familiar holographic injunction that this number should be "large". We explicitly estimate lower bounds on this number in the case of the application of holography to the quark-gluon plasma produced in heavy ion collisions. We find that classical Censorship alone prohibits realistically small values for the number of colours, but that the WGC offers hope of resolving this problem.

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arXiv2020

Fragmentation of AdS$_5$-Kerr Black Holes

Black hole spacetimes asymptotic to five-dimensional anti-de Sitter spacetime are of great interest in connection with the string-gauge duality. In the rotating case, such black holes tend to become unstable, in several different ways, if their specific angular momenta fall in certain ranges. Here we consider the well-known Emparan-Myers fragmentation instability for singly rotating AdS$_5$-Kerr black holes, paying particular attention to the case where the specific angular momentum exceeds the asymptotic AdS$_5$ curvature length scale.

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arXiv2020

Event Horizon Wrinklification

The possible existence of stable black holes with entropies larger than the corresponding Schwarzschild black hole has been discussed extensively. The recently proposed "rough" black holes provide a concrete example of this. The fear is that, in accordance with the Second Law of thermodynamics, the familiar smooth-skinned black holes might spontaneously "wrinklify" into such an object. We show that this fear is to some extent justified, in the sense that AdS black holes with more entropy than the AdS-Schwarzschild black hole of the same mass do exist.

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arXiv2020

Large Numbers in Holography

The AdS/CFT correspondence is useful primarily when the number of colours, $N_{\textsf{c}}$, characterising the boundary field theory, is "large", and when the mass of the bulk black hole that is usually present is "large" relative to the bulk Planck mass. But this prompts two questions: first, can these large numbers be estimated, even very approximately, in a given application? Second: if these quantities are themselves computed holographically from physical data constraining the field theory, is this computation self-consistent, in the sense that it actually produces large numbers, an outcome which is far from obvious? Here we consider these questions in the case of the application of holographic techniques to the study of the quark-gluon plasma. We find that holography in this case is able to generate estimates of the dimensionless numbers in question, and, very remarkably, they are indeed large, despite the fact that the dimensionless input data are of order unity.

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