arXiv subjects

Ram Brustein

Publications and source records attributed to Ram Brustein.

At least 55 records · Page 3Linked to original sources

arXiv2017

Discovering the interior of black holes

The detection of gravitational waves (GWs) from black hole (BH) mergers provides an inroad toward probing the interior of astrophysical BHs. The general-relativistic description of the BH interior is that of empty spacetime with a (possibly) singular core. Recently, however, the hypothesis that the BH interior does not exist has been gaining traction, as it provides a means for resolving the BH information-loss problem. Here, we propose a simple method for answering the following question: Does the BH interior exist and, if so, does it contain some distribution of matter or is it mostly empty? Our proposal is premised on the idea that, similar to the case of relativistic, ultra-compact stars, any BH-like object whose interior has some matter distribution should support fluid modes in addition to the conventional spacetime modes. In particular, the Coriolis-induced Rossby (r-) modes, whose spectrum is mostly insensitive to the composition of the interior matter, should be a universal feature of such BH-like objects. In fact, the frequency and damping time of these modes are determined by only the object's mass and speed of rotation. The r-modes oscillate at a lower frequency, decay at a slower rate and produce weaker GWs than do modes of the spacetime class. Hence, they imprint a model-insensitive signature of a non-empty interior in the GW spectrum resulting from a BH merger. We find that future GW detectors, such as Advanced LIGO with its design sensitivity, have the potential of detecting such r-modes if the amount of GWs leaking out quantum mechanically from the interior of a BH-like object is sufficiently large.

gr-qc↗

arXiv2017

Quantum hair of black holes out of equilibrium

Classically, the black hole (BH) horizon is completely opaque, hiding any clues about the state and very existence of its interior. Quantum mechanically and in equilibrium, the situation is not much different: Hawking radiation will now be emitted, but it comes out at an extremely slow rate, is thermal to a high degree of accuracy and thus carries a minimal amount of information about the quantum state within the BH. Here, it is shown that the situation is significantly different when a quantum BH is out of equilibrium. We argue that the BH can then emit "supersized" Hawking radiation with a much larger amplitude than that emitted in equilibrium. The result is a new type of quantum hair that can reveal the state and composition of the BH interior to an external observer. Moreover, the frequency and amplitude of the new hair can be explained by the observer without invoking any new physical principles. The new hair decays at a parametrically slow rate in comparison to the Schwarzschild time scale and can be detected through the emission of gravitational waves (and possibly other types of waves); for example, during and after a BH-merger event. The current discussion is motivated by a previous analysis, in the context of a recently proposed polymer model for the BH interior, that implies emissions just like those described here. We expect, however, that the new hair is a model-independent property of quantum BHs.

hep-th↗

arXiv2017

When black holes collide: Probing the interior composition by the spectrum of ringdown modes and emitted gravitational waves

The merger of colliding black holes (BHs) should lead to the production of ringdown or quasinormal modes (QNMs), which may very well be sensitive to the state of the interior. We put this idea to the test with a recent proposal that the interior of a BH consists of a bound state of highly excited, long, closed, interacting strings; figuratively, a collapsed polymer. We show that such BHs do indeed have a distinct signature in their QNM spectrum: A new class of modes whose frequencies are parametrically lower than the lowest-frequency mode of a classical BH and whose damping times are parametrically longer. The reason for the appearance of the new modes is that our model contains another scale, the string length, which is parametrically larger than the Planck length. This distinction between the collapsed-polymer model and general-relativistic BHs could be made with gravitational-wave observations and offers a means for potentially measuring the strength of the coupling in string theory. For example, GW150914 already allows us to probe the strength of the string coupling near the regime which is predicted by the unification of the gravitational and gauge-theory couplings. We also derive bounds on the amplitude of the collapsed-polymer QNMs that can be placed by current and future gravitational-wave observations.

gr-qc↗

arXiv2016

Black holes as collapsed polymers

We propose that a large Schwarzschild black hole (BH) is a bound state of highly excited, long, closed strings at the Hagedorn temperature. The size of the bound state is smaller than the string random-walk scale and determined dynamically by the string attractive interactions. It is further proposed that the effective free-energy density of the bound state should be expressed as a function of its entropy density. For a macroscopic BH, the free-energy density contains only linear and quadratic terms, in analogy with that of a collapsed polymer when expressed as a function of the polymer concentration. Using the effective free energy, we derive scaling relations for the entropy, energy and size of the bound state and show that these agree with the scaling relations of the BH; in particular, with the area law for the BH entropy. The area law originates from the inverse scaling of the effective temperature with the bound-state radius. We also find that the energy density of the bound state is equal to its pressure.

hep-th↗

arXiv2016

Hypercharge Axion and the Diphoton $750$ GeV Resonance

The CMS and ATLAS reports on a possible excess of diphoton events at $750$ GeV are the cause of great excitement and hope. We show that a pseudoscalar axion coupled to the topological density of hypercharge, suggested in the past by Brustein and Oaknin as a candidate for inducing baryogenesis, can explain the signal in the diphoton channel. The hypercharge axion (HCA) can also decay to $Zγ$ and $ZZ$. The expected number of events in these channels is too small to have been detected, but such decays should be observed in the future. The HCA can be produced via vector boson fusion (VBF) or via associated production (AP). The latter should be manifested by a characteristic decay to 3 photons which should be observed soon. We adapt the previous analysis of possible detection of the HCA at the LHC by Brustein and Oaknin and by Elfgren to the case that the mass of the HCA is 750 GeV and find the expected cross section and decay width in terms of the HCA coupling. We find that the expected cross-section fits well the observed number of excess events and that there is tension between the measured cross-section and the reported partial decay width. The tension is caused because for both VBF and AP the production cross-section and the decay width depend linearly on each other. We therefore expect that if the new resonance is indeed the HCA, either its width should be significantly smaller than the reported width or the production cross-section should be significantly higher than the reported one.

hep-ph↗

arXiv2015

Teleporting entanglement during black hole evaporation

The unitary evaporation of a black hole (BH) in an initially pure state must lead to the eventual purification of the emitted radiation. It follows that the late radiation has to be entangled with the early radiation and, as a consequence, the entanglement among the Hawking pair partners has to decrease continuously from maximal to vanishing during the BH's life span. Starting from the basic premise that both the horizon radius and the center of mass of a finite-mass BH are fluctuating quantum mechanically, we show how this process is realized. First, it is shown that the horizon fluctuations induce a small amount of variance in the total linear momentum of each created pair. This is in contrast to the case of an infinitely massive BH, for which the total momentum of the produced pair vanishes exactly on account of momentum conservation. This variance leads to a random recoil of the BH during each emission and, as a result, the center of mass of the BH undergoes a quantum random walk. Consequently, the uncertainty in its momentum grows as the square root of the number of emissions. We then show that this uncertainty controls the amount of deviation from maximal entanglement of the produced pairs and that this deviation is determined by the ratio of the cumulative number of emitted particles to the initial BH entropy. Thus, the interplay between the horizon and center-of-mass fluctuations provides a mechanism for teleporting entanglement from the pair partners to the BH and the emitted radiation.

hep-th↗

arXiv2015

Density matrix of black hole radiation

Hawking's model of black hole evaporation is not unitary and leads to a mixed density matrix for the emitted radiation, while the Page model describes a unitary evaporation process in which the density matrix evolves from an almost thermal state to a pure state. We compare a recently proposed model of semiclassical black hole evaporation to the two established models. In particular, we study the density matrix of the outgoing radiation and determine how the magnitude of the off-diagonal corrections differs for the three frameworks. For Hawking's model, we find power-law corrections to the two-point functions that induce exponentially suppressed corrections to the off-diagonal elements of the full density matrix. This verifies that the Hawking result is correct to all orders in perturbation theory and also allows one to express the full density matrix in terms of the single-particle density matrix. We then consider the semiclassical theory for which the corrections, being non-perturbative from an effective field-theory perspective, are much less suppressed and grow monotonically in time. In this case, the Rényi entropy for the outgoing radiation is shown to grow linearly at early times; but this growth slows down and the entropy eventually starts to decrease at the Page time. In addition to comparing models, we emphasize the distinction between the state of the radiation emitted from a black hole, which is highly quantum, and that of the radiation emitted from a typical classical black body at the same temperature.

hep-th↗

arXiv2015

Quantum state of the black hole interior

If a black hole (BH) is initially in an approximately pure state and it evaporates by a unitary process, then the emitted radiation will be in a highly quantum state. As the purifier of this radiation, the state of the BH interior must also be in some highly quantum state. So that, within the interior region, the mean-field approximation cannot be valid and the state of the BH cannot be described by some semiclassical metric. On this basis, we model the state of the BH interior as a collection of a large number of excitations that are packed into closely spaced but single-occupancy energy levels; a sort-of "Fermi sea" of all light-enough particles. This highly quantum state is surrounded by a semiclassical region that lies close to the horizon and has a non-vanishing energy density. It is shown that such a state looks like a BH from the outside and decays via gravitational pair production in the near-horizon region at a rate that agrees with the Hawking rate. We also consider the fate of a classical object that has passed through to the BH interior and show that, once it has crossed over the near-horizon threshold, the object meets its demise extremely fast. This result cannot be attributed to a "firewall", as the trauma to the in-falling object only begins after it has passed through the near-horizon region and enters a region where semiclassical spacetime ends but the energy density is still parametrically smaller than Planckian.

hep-th↗

arXiv2015

Constraints on the quantum state of pairs produced by semiclassical black holes

The pair-production process for a black hole (BH) is discussed within the framework of a recently proposed semiclassical model of BH evaporation. Our emphasis is on how the requirements of unitary evolution and strong subadditivity act to constrain the state of the produced pairs and their entanglement with the already emitted BH radiation. We find that the state of the produced pairs is indeed strongly constrained but that the semiclassical model is consistent with all requirements. We are led to the following picture: Initially, the pairs are produced in a state of nearly maximal entanglement amongst the partners, with a parametrically small entanglement between each positive-energy partner and the outgoing radiation, similar to Hawking's model. But, as the BH evaporation progresses past the Page time, each positive-energy partner has a stronger entanglement with the outgoing radiation and, consequently, is less strongly entangled with its negative-energy partner. We present some evidence that this pattern of entanglement does not require non-local interactions, only EPR-like non-local correlations.

hep-th↗

arXiv2015

Falling through the black hole horizon

We consider the fate of a small classical object, a "stick", as it falls through the horizon of a large black hole (BH). Classically, the equivalence principle dictates that the stick is affected by small tidal forces, and Hawking's quantum-mechanical model of BH evaporation makes essentially the same prediction. If, on the other hand, the BH horizon is surrounded by a "firewall", the stick will be consumed as it falls through. We have recently extended Hawking's model by taking into account the quantum fluctuations of the geometry and the classical back-reaction of the emitted particles. Here, we calculate the strain exerted on the falling stick for our model. The strain depends on the near-horizon state of the Hawking pairs. We find that, after the Page time when the state of the pairs deviates significantly from maximal entanglement (as required by unitarity), the induced strain in our semiclassical model is still parametrically small. This is because the number of the disentangled pairs is parametrically smaller than the BH entropy. A firewall does, however, appear if the number of disentangled pairs near the horizon is of order of the BH entropy, as implicitly assumed in previous discussions in the literature.

hep-th↗

arXiv2014

How Black Holes Burn

We present a calculation of the rate of information release from a Schwarzschild BH. We have recently extended Hawking's theory of black hole (BH) evaporation to account for quantum fluctuations of the background geometry, as well as for back-reaction and time-dependence effects. Our main result has been a two-point function matrix for the radiation that consists of Hawking's thermal matrix plus off-diagonal corrections that are initially small and become more important as the evaporation proceeds. Here, we show that, if the phases and amplitudes of the radiation matrix are recorded over the lifetime of the BH, then the radiation purifies in a continuous way. We conjecture that our results establish the maximal rate at which information can be released from a semiclassical BH, to be contrasted with the minimal rate that was predicted by Page on the basis of generic unitarity arguments. When the phases of the radiation matrix are not tracked, we show that it purifies only parametrically close to the end of the BH evaporation and does so extremely fast. Our main technical tool in the quantitative treatment of this purification is the purity of the radiation matrix and, its inverse, the participation ratio. These can be related to the Renyi entropy of the density matrix of the emitted radiation.

hep-th↗

arXiv2014

Canonical structure of higher derivative theories

The canonical structure of theories whose Lagrangian contains higher powers of time derivatives is often obscured by the nonlinear relationship between the velocities and momenta. We use the Dirac formalism and define a generalized Legendre transform to overcome some of the difficulties associated with inverting the relation between velocities and momenta. We are then able to define a standard single valued symplectic structure on phase space and a compatible single valued Hamiltonian. We demonstrate the application of our formalism in several examples.

hep-th↗

arXiv2014

Horizons of semiclassical black holes are cold

We calculate, using our recently proposed semiclassical framework, the quantum state of the Hawking pairs that are produced during the evaporation of a black hole (BH). Our framework adheres to the standard rules of quantum mechanics and incorporates the quantum fluctuations of the collapsing shell spacetime in Hawking's original calculation, while accounting for back-reaction effects. We argue that the negative-energy Hawking modes need to be regularly integrated out; and so these are effectively subsumed by the BH and, as a result, the number of coherent negative-energy modes $N_{coh}$ at any given time is parametrically smaller than the total number of the Hawking particles $N_{total}$ emitted during the lifetime of the BH. We find that $N_{coh}$ is determined by the width of the BH wavefunction and scales as the square root of the BH entropy. We also find that the coherent negative-energy modes are strongly entangled with their positive-energy partners. Previously, we have found that $N_{coh}$ is also the number of coherent outgoing particles and that information can be continually transferred to the outgoing radiation at a rate set by $N_{coh}$. Our current results show that, while the BH is semiclassical, information can be released without jeopardizing the nearly maximal inside-out entanglement and imply that the state of matter near the horizon is approximately the vacuum. The BH firewall proposal, on the other hand, is that the state of matter near the horizon deviates substantially from the vacuum, starting at the Page time. We find that, under the usual assumptions for justifying the formation of a firewall, one does indeed form at the Page time. However, the possible loophole lies in the implicit assumption that the number of strongly entangled pairs can be of the same order of $N_{total}$.

hep-th↗

arXiv2014

Firewalls, smoke and mirrors

The radiation emitted by a black hole (BH) during its evaporation has to have some degree of quantum coherence to accommodate a unitary time evolution. We parametrize the degree of coherence by the number of coherently emitted particles $N_{coh}$ and show that it is severely constrained by the equivalence principle. We discuss, in this context, the fate of a shell of matter that falls into a Schwarzschild BH. Two points of view are considered, that of a stationary external observer and that of the shell itself. From the perspective of the shell, the near-horizon region has an energy density proportional to $N_{coh}^2$ in Schwarzschild units. So, if $N_{coh}$ is parameterically larger than the square root of the BH entropy $S_{BH}^ {1/2}$, a firewall or more generally a "wall of smoke" forms and the equivalence principle is violated while the BH is still semiclassical. To have a degree of coherence that is parametrically smaller than $S_{BH}^{1/2}$, one has to introduce a new sub-Planckian gravitational length scale, which likely also violates the equivalence principle. And so our previously proposed model which has $N_{coh}=S_{BH}^{1/2}$ is singled out. From the external-observer perspective, we find that the time it takes for the information about the state of the shell to get re-emitted from the BH is inversely proportional to $N_{coh}$. When the rate of information release becomes order unity, the semiclassical approximation starts to break down and the BH becomes a perfect reflecting information mirror.

hep-th↗

arXiv2013

Phases of information release during black hole evaporation

In a recent article, we have shown how quantum fluctuations of the background geometry modify Hawking's density matrix for black hole (BH) radiation. Hawking's diagonal matrix picks up small off-diagonal elements whose influence becomes larger with the number of emitted particles. We have calculated the "time-of-first-bit", when the first bit of information comes out of the BH, and the "transparency time", when the rate of information release becomes order unity. We have found that the transparency time is equal to the "Page time", when the BH has lost half of its initial entropy to the radiation, in agreement with Page's results. Here, we improve our previous calculation by keeping track of the time of emission of the Hawking particles and their back-reaction on the BH. Our analysis reveals a new time scale, the radiation "coherence time", which is equal to the geometric mean of the evaporation time and the light crossing time. We find, as for our previous treatment, that the time-of-first-bit is equal to the coherence time, which is much shorter than the Page time. But the transparency time is now much later than the Page time, just one coherence time before the end of evaporation. Close to the end, when the BH is parametrically of Planckian dimensions but still large, the coherence time becomes parametrically equal to the evaporation time, thus allowing the radiation to purify. We also determine the time dependence of the entanglement entropy of the early and late-emitted radiation. This entropy is small during most of the lifetime of the BH, but our qualitative analysis suggests that it becomes parametrically maximal near the end of evaporation.

hep-th↗

arXiv2013

Universal stress-tensor correlation functions of strongly coupled conformal fluids

We have shown in two accompanying papers that, for Einstein gravity, the graviton multi-point functions are universal in a particular kinematic region and depend only on the (generalized) Mandelstam variable s. The effects of the leading corrections to Einstein gravity were shown to be similarly universal, inducing a specific difference in the angular dependence. Here we show, relying on the gauge-gravity duality, that the stress-tensor correlation functions of conformal fluids whose gravitational dual is either Einstein gravity or its leading correction are also universal. We discuss the possible significance of these results to multi-particle correlations in heavy-ion collisions. We show that, to test our ideas, the stress-energy correlation functions have to measured rather than the standard multiplicity correlation functions. We then discuss schematically how stress-energy correlations in heavy-ion collisions can be used to test our findings. We argue that, if these correlations can be measured precisely enough, they will provide a unique way to probe the existence of a gravitational dual to the quark-gluon plasma and to determine its universality class.

hep-th↗

arXiv2013

Restoring predictability in semiclassical gravitational collapse

Hawking showed that the radiation emitted from a classical collapsing shell is thermal. Here, we show that a semiclassical collapsing shell emits radiation that is only approximately thermal, with small but significant deviations. The most important difference is the presence of small off-diagonal elements in the radiation density matrix with a magnitude of order $1/\sqrt{S_{BH}}$, $S_{BH}$ being the Bekenstein-Hawking entropy of the incipient black hole. The off-diagonal elements store the correlations between the collapsing shell and the emitted radiation and allow information to continuously leak from the collapsed body. The rate of escape of information is initially very small, increasing to order one by the Page time, when the black hole has lost half its original entropy. We show that, until the Page time, the radiation is almost exactly thermal and that, from this time on, it begins to purify at an increasing rate.

hep-th↗

arXiv2013

Semiclassical black holes expose forbidden charges and censor divergent densities

Classically, the black hole (BH) horizon is a rigid surface of infinite redshift; whereas the uncertainty principle dictates that the semiclassical (would-be) horizon cannot be fixed in space nor can it exhibit any divergences. We propose that this distinction underlies the BH information-loss paradox, the apparent absence of BH hair, the so-called trans-Planckian problem and the recent "firewall" controversy. We argue that the correct prescription is to first integrate out the fluctuations of the background geometry and only then evaluate matter observables. The basic idea is illustrated using a system of two strongly coupled harmonic oscillators, with the heavier oscillator representing the background. We then apply our proposal to matter fields near a BH horizon, initially treating the matter fields as classical and the background as semiclassical. In this case, the average value of the associated current does not vanish; so that it is possible, in principle, to measure the global charge of the BH. Then the matter is, in addition to the background, treated quantum mechanically. We show that the average energy density of matter as seen by an asymptotic observer is finite and proportional to the BH entropy, rather than divergent. We discuss the implications of our results for the various controversial issues concerning BH physics.

hep-th↗