arXiv subjects

Dejan Stojkovic

Publications and source records attributed to Dejan Stojkovic.

At least 73 records · Page 4Linked to original sources

arXiv2017

Maximal temperature of the gas in AdS space-time

Assuming only statistical mechanics and general relativity, we calculate the maximal temperature of gas of particles placed in AdS space-time. If two particles with a given center of mass energy come close enough, according to classical gravity they will form a black hole. We focus only on the black holes with Hawking temperature lower than the environment, because they do not disappear. The number density of such black holes grows with the temperature in the system. At a certain finite temperature, the thermodynamical system will be dominated by black holes. This critical temperature is lower than the Planck temperature for the values of the AdS vacuum energy density below the Planck density. This result might be interesting from the AdS/CFT correspondence point of view, since it is different from the Hawking-Page phase transition, and it is not immediately clear what effect dynamically limits the maximal temperature of the thermal state on the CFT side of the correspondence.

gr-qc↗

arXiv2017

Gravity can significantly modify classical and quantum Poincare recurrence theorems

Poincare recurrence theorem states that any finite system will come arbitrary close to its initial state after some very long but finite time. At the statistical level, this by itself does not represent a paradox, but apparently violates the second law of thermodynamics, which may lead to some confusing conclusions for macroscopic systems. However, this statement does not take gravity into account. If two particles with a given center of mass energy come at the distance shorter than the Schwarzschild diameter apart, according to classical gravity they will form a black hole. In the classical case, a black hole once formed will always grow and effectively quench the Poincare recurrence. We derive the condition under which the classical black hole production rate is higher than the classical Poincare recurrence rate. In the quantum case, if the temperature of the black hole is lower than the temperature of the surrounding gas, such a black hole cannot disappear via Hawking evaporation. We derive the condition which gives us a critical temperature above which the black hole production is faster than quantum Poincare recurrence time. However, in quantum case, the quantum Poincare recurrence theorem can be applied to the black hole states too. The presence of the black hole can make the recurrence time longer or shorter, depending on whether the presence of the black hole increases or decreases the total entropy. We derive the temperature below which the produced black hole increases the entropy of the whole system (gas particles plus a black hole). Finally, if evolution of the system is fast enough, then newly formed black holes will merge and accrete particles until one large black hole dominates the system. We give the temperature above which the presence of black holes increase the entropy of the whole system and prolongs the Poincare recurrence time.

gr-qc↗

arXiv2016

Gravitational wave production by Hawking radiation from rotating primordial black holes

In this paper we analyze in detail a rarely discussed question of gravity wave production from evaporating primordial black holes. These black holes emit gravitons which are, at classical level, registered as gravity waves. We use the latest constraints on their abundance, and calculate the power emitted in gravitons at the time of their evaporation. We then solve the coupled system of equations that gives us the evolution of the frequency and amplitude of gravity waves during the expansion of the universe. The spectrum of gravitational waves that can be detected today depends on multiple factors: fraction of the total energy density which was occupied by primordial black holes, the epoch in which they were formed, and quantities like their mass and angular momentum. We conclude that very small primordial black holes which evaporate before the big-bang nucleosynthesis emit gravitons whose spectral energy fraction today can be as large as $10^{-7.5}$. On the other hand, those which are massive enough so that they still exist now can yield a signal as high as $10^{-6.5}$. However, typical frequencies of the gravity waves from primordial black holes are still too high to be observed with the current and near future gravity wave observations.

astro-ph.CO↗

arXiv2016

Hawking-like radiation and the density matrix for an infalling observer during gravitational collapse

We study time-dependant Hawking-like radiation as seen by an infalling observer during gravitational collapse of a thin shell. We calculate the occupation number of particles whose frequencies are measured in the proper time of an infalling observer in Eddington-Finkelstein coordinates. We solve the equations for the whole process from the beginning of the collapse till the moment when the collapsing shell reaches zero radius. The radiation distribution is not thermal in the whole frequency regime, but it is approximately thermal for the wavelengths of the order of the Schwarzschild radius of the collapsing shell. After the Schwarzschild radius is crossed, the temperature increases without limits as the singularity is approached. We also calculate the density matrix associated with this radiation. It turns out that the off-diagonal correlation terms to the diagonal Hawking's leading order terms are very important. While the trace of the diagonal (Hawking's) density matrix squared decreases during the evolution, the trace of the total density matrix squared remains unity at all times and all frequencies.

gr-qc↗

arXiv2016

Maximal temperature in a simple thermodynamical system

Temperature in a simple thermodynamical system is not limited from above. It is also widely believed that it does not make sense talking about temperatures higher than the Planck temperature in the absence of the full theory of quantum gravity. Here, we demonstrate that there exist a maximal achievable temperature in a system where particles obey the laws of quantum mechanics and classical gravity before we reach the realm of quantum gravity. Namely, if two particles with a given center of mass energy come at the distance shorter than the Schwarzschild diameter apart, according to classical gravity they will form a black hole. It is possible to calculate that a simple thermodynamical system will be dominated by black holes at a critical temperature which is about three times lower than the Planck temperature. That represents the maximal achievable temperature in a simple thermodynamical system.

gr-qc↗

arXiv2016

Icezones instead of firewalls: extended entanglement beyond the event horizon and unitary evaporation of a black hole

We examine the basic assumptions in the original setup of the firewall paradox. The main claim is that a single mode of the lathe radiation is maximally entangled with the mode inside the horizon and simultaneously with the modes of early Hawking radiation. We argue that this situation never happens during the evolution of a black hole. Quantum mechanics tells us that while the black hole exists, unitary evolution maximally entangles a late mode located just outside the horizon with a combination of early radiation and black hole states, instead of either of them separately. One of the reasons for this is that the black hole radiation is not random and strongly depends on the geometry and charge of the black hole, as detailed numerical calculations of Hawking evaporation clearly show. As a consequence, one can't factor out the state of the black hole. However, this extended entanglement between the black hole and modes of early and late radiation indicates that, as the black hole ages, the local Rindler horizon is modified out to macroscopic distances from the black hole. Fundamentally non-local physics nor firewalls are not necessary to explain this result. We propose an infrared mechanism called {\it icezone} that is mediated by low energy interacting modes and acts near any event horizon to entangle states separated by long distances. These interactions at first provide small corrections to the thermal Hawking radiation. At the end of evaporation however the effect of interactions is as large as the Hawking radiation and information is recovered for an outside observer. We verify this in an explicit construction and calculation of the density matrix of a spin model.

hep-th↗

arXiv2016

Collapsing objects with the same gravitational trajectory can radiate away different amount of energy

We study radiation emitted during the gravitational collapse from two different types of shells. We assume that one shell is made of dark matter and is completely transparent to the test scalar (for simplicity) field which belongs to the standard model, while the other shell is made of the standard model particles and is totally reflecting to the scalar field. These two shells have exactly the same mass, charge and angular momentum (though we set the charge and angular momentum to zero), and therefore follow the same geodesic trajectory. However, we demonstrate that they radiate away different amount of energy during the collapse. This difference can in principle be used by an asymptotic observer to reconstruct the physical properties of the initial collapsing object other than mass, charge and angular momentum. This result has implications for the information paradox and expands the list of the type of information which can be released from a collapsing object.

gr-qc↗

arXiv2016

Pre-Hawking radiation may allow for reconstruction of the mass distribution of the collapsing object

Hawking radiation explicitly depends only on the black hole's total mass, charge and angular momentum. It is therefore generally believed that one cannot reconstruct the information about the initial mass distribution of an object that made the black hole. However, instead of looking at radiation from a static black hole, we can study the whole time-dependent process of the gravitational collapse, and pre-Hawking radiation which is excited because of the time-dependent metric. We compare radiation emitted by a single collapsing shell with that emitted by two concentric shells of the equivalent total mass. We calculate the gravitational trajectory and the momentum energy tensor. We show that the flux of energy emitted during the collapse by a single shell is significantly different from the flux emitted by two concentric shells of the equivalent total mass. When the static black hole is formed, the fluxes become indistinguishable. This implies that an observer studying the flux of particles from a collapsing object could in principle reconstruct information not only about the total mass of the collapsing object, but also about the mass distribution.

gr-qc↗

arXiv2015

Greybody factors for a black hole in massive gravity

An exact solution was recently found in the massive gravity theory having the form of Schwarzschild-dS black holes with some additional background fields. Hawking radiation will occur at the event and cosmological horizons having the blackbody spectrum, which will be modified by the geometry outside the black hole. In this paper, we study the greybody factors of a test scalar, considering its minimal coupling with the background geometry. The case of small black holes with the horizon radius much smaller than the cosmological dS radius is studied numerically. The case of near-extremal black holes with the horizon radius comparable to the cosmological dS radius is studied analytically. In addition, we considered the coupling of the test field with the background {Stückelberg} fields, which in turn leads to reductions in particle emission and some non-trivial features (resonances) in the greybody factors.

gr-qc↗

arXiv2015

Radiation from a collapsing object is manifestly unitary

The process of gravitational collapse excites the fields propagating in the background geometry and gives rise to thermal radiation. We demonstrate by explicit calculations that the density matrix corresponding to such radiation actually describes a pure state. While Hawking's leading order density matrix contains only the diagonal terms, we calculate the off-diagonal correlation terms. These correlations start very small, but then grow in time. The cumulative effect is that the correlations become comparable to the leading order terms and significantly modify the density matrix. While the trace of the Hawking's density matrix squared diverges from unity during the evolution, the trace of the total density matrix squared remains unity at all times and all frequencies. This implies that the process of radiation from a collapsing object is unitary.

gr-qc↗

arXiv2015

Horizon Wave-Function and the Quantum Cosmic Censorship

We investigate the Cosmic Censorship Conjecture by means of the horizon wave-function (HWF) formalism. We consider a charged massive particle whose quantum mechanical state is represented by a spherically symmetric Gaussian wave-function, and restrict our attention to the superxtremal case (with charge-to-mass ratio $α>1$), which is the prototype of a naked singularity in the classical theory. We find that one can still obtain a normalisable HWF for $α^2<{2}$, and this configuration has a non-vanishing probability of being a black hole, thus extending the classically allowed region for a charged black hole. However, the HWF is not normalisable for $α^2 > 2$, and the uncertainty in the location of the horizon blows up at $α^2=2$, signalling that such an object is no more well-defined. This perhaps implies that a quantum Cosmic Censorhip might be conjectured by stating that no black holes with charge-to-mass ratio greater than a critical value (of the order of $\sqrt{2}$) can exist.

gr-qc↗

arXiv2015

Inner Horizon of the Quantum Reissner-Nordström Black Holes

We study the nature of the inner Cauchy horizon of a Reissner-Nordström black hole in a quantum context by means of the horizon wave-function obtained from modelling the electrically charged source as a Gaussian wave-function. Our main finding it that there is a significant range of black hole mass (around the Planck scale) and specific charge for which the probability of realizing the inner horizon is negligible. This result suggests that any semiclassical instability one expects near the inner horizon may not be occur in quantum black holes.

gr-qc↗

arXiv2014

Emergent Spacetime in Stochastically Evolving Dimensions

Changing the dimensionality of the space-time at the smallest and largest distances has manifold theoretical advantages. If the space is lower dimensional in the high energy regime, then there are no ultraviolet divergencies in field theories, it is possible to quantize gravity, and the theory of matter plus gravity is free of divergencies or renormalizable. If the space is higher dimensional at cosmological scales, then some cosmological problems (including the cosmological constant problem) can be attacked from a completely new perspective. In this paper, we construct an explicit model of "evolving dimensions" in which the dimensions open up as the temperature of the universe drops. We adopt the string theory framework in which the dimensions are fields that live on the string worldsheet, and add temperature dependent mass terms for them. At the Big Bang, all the dimensions are very heavy and are not excited. As the universe cools down, dimensions open up one by one. Thus, the dimensionality of the space we live in depends on the energy or temperature that we are probing. In particular, we provide a kinematic Brandenberger-Vafa argument for how a discrete {\it causal set}, and eventually a continuum $(3+1)$-dim spacetime along with Einstein gravity emerge in the Infrared from the worldsheet action. The $(3+1)$-dim Planck mass and the string scale become directly related, {\it without any} compactification. Amongst other predictions, we argue that LHC might be blind to new physics even if it comes at the TeV scale. In contrast, cosmic ray experiments, especially those that can register the very beginning of the shower, and collisions with high multiplicity and density of particles, might be sensitive to the dimensional cross-over.

hep-th↗

arXiv2014

Extending cascading gravity model to lower dimensions

The cascading gravity model was proposed to eliminate instabilities of the original DGP model by embedding our 4D universe into a 5D brane, which is itself embedded in a 6D bulk. Thus gravity cascades from 6D down to 4D as we decrease the length scales. We show that it is possible to extend this setup to lower dimensions as well, i.e. there is a self-consistent embedding of a 3D brane into a 4D brane, which is itself embedded in a 5D bulk and so on. This extension fits well into the "vanishing dimensions" framework in which dimensions open up as we increase the length scales.

gr-qc↗

arXiv2014

Multibrane DGP model: Our universe as a stack of $(2+1)$-dim branes

We consider scenario in which our $(3+1)$-dim universe is actually a dense stack of multiple parallel $(2+1)$-dim branes. For this purpose, we generalize the DGP model to a multi-brane case. We solve for the propagation of the scalar field and gravity in this setup. At short distances (high momenta) along the branes interactions follow the $(2+1)$-dim laws, while at large distances (low momenta) interactions follow the usual $(3+1)$-dim laws. This feature is inherited from the original DGP model. In the direction perpendicular to the brane, we show that interactions become $(3+1)$-dim at low momenta which are unable to resolve the interbrane separation. Thus, this is one of the explicit constructs of the "vanishing dimensions" scenario where high energy physics appears to be lower dimensional rather than higher dimensional.

hep-th↗

arXiv2014

String Resonances at Hadron Colliders

[Abridged] We consider extensions of the standard model based on open strings ending on D-branes. Assuming that the fundamental string mass scale M_s is in the TeV range and that the theory is weakly coupled, we discuss possible signals of string physics at the upcoming HL-LHC run (3000 fb^{-1}) with \sqrt{s} = 14 TeV, and at potential future pp colliders, HE-LHC and VLHC, operating at \sqrt{s} = 33 and 100 TeV, respectively. In such D-brane constructions, the dominant contributions to full-fledged string amplitudes for all the common QCD parton subprocesses leading to dijets and γ+ jet are completely independent of the details of compactification, and can be evaluated in a parameter-free manner. We make use of these amplitudes evaluated near the first (n=1) and second (n=2) resonant poles to determine the discovery potential for Regge excitations of the quark, the gluon, and the color singlet living on the QCD stack. We show that for string scales as large as 7.1 TeV (6.1 TeV), lowest massive Regge excitations are open to discovery at 5σin dijet (γ+ jet) HL-LHC data. We also show that for n=1, the dijet discovery potential at HE-LHC and VLHC exceedingly improves: up to 15 TeV and 41 TeV, respectively. To compute the signal-to-noise ratio for n=2 resonances, we first carry out a complete calculation of all relevant decay widths of the second massive level string states. We demonstrate that for string scales M_s <~ 10.5 TeV (M_s <~ 28 TeV), detection of n=2 Regge recurrences at HE-LHC (VLHC) would become the smoking gun for D-brane string compactifications. Our calculations have been performed using a semi-analytic parton model approach which is cross checked against an original software package. The string event generator interfaces with HERWIG and Pythia through BlackMax. The source code is publically available in the hepforge repository.

hep-ph↗

arXiv2014

Vanishing dimensions: Review

We review a growing theoretical motivation and evidence that the number of dimensions actually reduces at high energies. This reduction can happen near the Planck scale, or much before, the dimensions that are reduced can be effective, spectral, topological or the usual dimensions, but many things points toward the fact that the high energy theories appear to propagate in a lower dimensional space, rather than a higher dimensional one. We will concentrate on a particular scenario of "vanishing" or "evolving dimensions" where the dimensions open up as we increase the length scale that we are probing, but will also mention related models that point to the same direction, i.e. the causal dynamical triangulation, asymptotic safety, as well as evidence coming from a non-commutative quantum theories, the Wheeler-DeWitt equation and phenomenon of "asymptotic silence". It is intriguing that experimental evidence for the high energy dimensional reduction may already exists - a statistically significant planar alignment of events with energies higher than TeV has been observed in high altitude cosmic ray experiments. A convincing evidence for dimensional reduction may be found in future in collider experiments and gravity waves observatories.

gr-qc↗

arXiv2014

Symmetron Inflation

We define a new inflationary scenario in which inflation starts naturally after the Big Bang when the energy density drops below some critical value. As a model, we use recently proposed symmetron field whose effective potential depends on the energy density of the environment. At high densities, right after the Big Bang, the potential for the symmetron is trivial, and the field sits in equilibrium at the bottom of the potential. When the density drops below some critical value, the potential changes its shape into a symmetry breaking potential, and the field starts rolling down. This scenario does not require any special initial conditions for inflation to start. We also construct a concrete model with two fields, i.e. with symmetron as an inflaton and an additional scalar field which describes the matter content in the early universe. For the simplest coupling, the amplitude and shape of the power spectrum are the same as in the single field slow-roll inflation.

astro-ph.CO↗