Regular Series


Vol. 32 (2001), No. 11, pp. 3555 – 3879


Limitations on Quantum Information from Black Hole Physics

abstract

After reviewing the relation of entropy to information, I derive the entropy bound as applied to bounded weakly gravitating systems, and review the bound’s applications to cosmology as well as its extensions to higher dimensions. I then discuss why black holes behave as 1-D objects when emitting entropy, which suggests that a black hole swallows information at a rate restricted by the one-channel information capacity. I discuss fundamental limitations on the information borne by signal pulses in curved spacetime, from which I verify the mentioned bound on the rate of information disposal by a black hole.


Scalar Vacuum Structure in General Relativity and Alternative Theories Conformal Continuations

abstract

We discuss the global properties of static, spherically symmetric configurations of a self-gravitating real scalar field \(\varphi \) in general relativity (GR), scalar-tensor and high-order (curvature-nonlinear) theories of gravity in various dimensions. In GR, for scalar fields with an arbitrary potential \(V(\varphi )\), not necessarily positive-definite, it is shown that the list of all possible types of space-time causal structure in the models under consideration is the same as the one for \(\varphi = {\rm const}\). In particular, there are no regular black holes with any asymptotics. These features are extended to scalar-tensor and curvature-nonlinear gravity, connected with GR by conformal mappings, unless there is a conformal continuation, i.e. , a case when a singularity in a solution of GR maps to a regular surface in an alternative theory, and the solution is continued through such a surface. Such an effect is exemplified by exact solutions in GR with a massless conformal scalar field, considered as a special scalar-tensor theory. Necessary conditions are found for the existence of a conformal continuation; they only hold for special choices of scalar-tensor and high-order theories of gravity.


Schwarzschild Black Holes and Propagation of Electromagnetic and Gravitational Waves

abstract

Disturbing of a spacetime geometry may result in the appearance of an oscillating and damped radiation — the so-called quasinormal modes. Their periods of oscillations and damping coefficients carry unique information about the mass and the angular momentum, that would allow one to identify the source of the gravitational field. In this talk we present recent bounds on the diffused energy, applicable to the Schwarzschild spacetime, that give also rough estimates of the energy of excited quasinormal modes.


Strong-Field Gravity and Orbital Resonance in Black Holes and Neutron Stars — kHz Quasi-Periodic Oscillations (QPO)

abstract

We explain the origin of the puzzling high frequency peaks in the variability power spectra of accreting neutron stars and black holes as a non-linear 1:2 or 1:3 resonance between orbital and radial epicyclic motion. These resonances are present because the gravitational field deviates strongly from a Newtonian \(1/r\) potential. Our theory agrees with the recently reported observations of two QPOs, at 300 Hz and 450 Hz, in the black hole candidate GRO J 1655-40.


MOND — a Pedagogical Review

abstract

An account is given of the development, and the status, of the modified dynamics (MOND) — a proposed alternative to dark matter, which posits a breakdown of Newtonian dynamics in the limit of small accelerations.


The First Compact Objects in the Mond Model

abstract

We trace the evolution of a spherically symmetric density perturbation in the MOdified Newtonian Dynamics (MOND) model. The background cosmological model is a \({\mit \Lambda }\)-dominated, low-\({\mit \Omega }_b\) Friedmann model with no Cold Dark Matter. We include thermal processes and non-equilibrium chemical evolution of the collapsing gas. We find that the first density perturbations which collapse to form luminous objects have mass \(\sim 10^5 M_{\odot }\). The time of the final collapse of these objects depends mainly on the value of the MOND acceleration \(a_0\) and also on the baryon density \({\mit \Omega }_b\). For the “standard” value \(a_0=1.2\times 10^{-8}\) cm/s\(^2\) the collapse starts at redshift \(z \sim 160\) for \({\mit \Omega }_b=0.05\) and \(z \sim 110\) for \({\mit \Omega }_b=0.02\).


Structure Formation in the Quintessential Universe

abstract

I review the main characteristics of structure formation in the quintes- sential Universe. Assuming equation of state \(w=p/\varrho =\,\)const. I provide a brief description of the background cosmology and discuss the linear growth of density perturbations, the strongly nonlinear evolution, the power spectra and r.m.s. fluctuations as well as mass functions focusing on the three values \(w\!=\!-1, -2/3\) and \(-1/3\). Finally I describe the presently available and future constraints on \(w\).


Quintessence in Advanced Gravity Wave Experiments

abstract

Recent observations of distant type Ia supernovae light-curves suggest that the expansion of the Universe has recently begun to accelerate. A popular explanation of present accelerating expansion of the Universe is to assume that some part \({\mit \Omega }_Q\) of the matter-energy density is in the form of dark component called “the quintessence” with the equation of state \(p_Q = w \rho _Q\) with \(w \geq -1.\) Determining the cosmic equation of state is, therefore, one of the greatest challenges of modern cosmology. Future generation of interferometric gravitational wave detectors is hoped to detect the final stages of binary inspirals. The sources probed by such experiments are of extragalactic origin and the observed chirp mass can be translated into the redshift of the source. Moreover, the luminosity distance is a direct observable in such experiments. This creates the possibility to establish a new kind of cosmological tests, supplementary to more standard ones. In this paper we review the standard methods of probing the dark energy, introduce the basic concepts underlying the utility of advanced LIGO type interferometric experiments in making cosmological inferences and we extend some recent results in this respect to the case of \(z\) varying equation of state.


Standard Cosmology in the DGP Brane Model

abstract

Large extra dimensions provide interesting extensions of our parameter space for gravitational theories. There exist now brane models which can perfectly reproduce standard four-dimensional Friedmann cosmology. These models are not motivated by observations, but they can provide interesting new insights and approaches to the dimensionality problem in string theory. I describe the embedding of standard Friedmann cosmology in the DGP model, and in particular the realization of our current (dust + \({\mit \Lambda }\))-dominated Universe.


White Dwarfs as a Source of Constraints on Exotic Physics

abstract

In this paper we briefly review main ideas underlying the constraints on exotic physics coming from Astrophysics already used by the others. Next we present a new bound coming from the White Dwarf cooling. Such stringent bound is possible due to accurate measurements offered by astroseismology. Specifically we consider the G117-B15A pulsating white dwarf (ZZ Ceti star) for which the speed of the period increase has been accurately measured for its fundamental oscillation mode. It has been claimed that this mode detected in G117-B15A is perhaps the most stable oscillation ever recorded in the optical band. Then we review our result concerning the bounds on compactification scale in the theory with large extra dimensions according to Arkani-Hamed, Dimopoulos and Dvali. Because an additional channel of energy loss (Kaluza–Klein gravitons) would speed up the cooling rate, one is able to use the aforementioned stability to derive a bound on compactification scale. We find the lower bound on compactification scale to be \(M_s \gt 14.3 \; {\rm TeV}/c^2\) which is more stringent than solar or red-giant bounds, as well as the bound coming from LEP. In final section we point out that pulsating hot “pre-White Dwarf” PG 1159-035 (GW Virginis) whose oscillation period increases at the rate of the order of magnitude larger than predicted could be a promising object for further investigations.


TeV Strings and Ultrahigh-Energy Cosmic Rays

abstract

The origin and nature of ultrahigh-energy cosmic ray events, above the Greisen–Zatsepin–Kuzmin (GZK) cutoff energy, constitute a long-standing, unsolved mystery. Neutrinos are proposed candidates but their standard interactions with matter are too weak. In the context of a TeV-scale string theory, motivated by possible extra space dimensions, the neutrino–nucleon scattering is examined. Resonant string contributions increase substantially the standard model neutrino-nucleon cross section. Although they seem insufficient to explain the trans-GZK cosmic ray events, their effects might be detected in next experiments.


Neutrino Masses in GUTs and the Baryon Asymmetry

abstract

We study the implications of large neutrino mixings for grand unified theories based on the seesaw mechanism. In SU(5) GUTs large mixings can be accommodated by means of U\((1)_F\) flavour symmetries. In these models the heavy Majorana neutrinos are essentially decoupled from low energy neutrino physics. On the contrary in SO(10) GUTs large neutrino mixings severely constrain the mass spectrum of the heavy Majorana neutrinos. This leads to predictions for a variety of observables in neutrino physics as well as for the baryon asymmetry.


Softly Broken Lepton Numbers: an Approach to Maximal Neutrino Mixing

abstract

We discuss models where the U(1) symmetries of lepton numbers are responsible for maximal neutrino mixing. We pay particular attention to an extension of the Standard Model (SM) with three right-handed neutrino singlets in which we require that the three lepton numbers \(L_e\), \(L_\mu \), and \(L_\tau \) be separately conserved in the Yukawa couplings, but assume that they are softly broken by the Majorana mass matrix \(M_{\rm R}\) of the neutrino singlets. In this framework, where lepton-number breaking occurs at a scale much higher than the electroweak scale, deviations from family lepton number conservation are calculable, i.e., finite, and lepton mixing stems exclusively from \(M_{\rm R}\). We show that in this framework either maximal atmospheric neutrino mixing or maximal solar neutrino mixing or both can be imposed by invoking symmetries. In this way those maximal mixings are stable against radiative corrections. The model which achieves maximal (or nearly maximal) solar neutrino mixing assumes that there are two different scales in \(M_{\rm R}\) and that the lepton number \(\bar L = L_e - L_\mu - L_\tau \) is conserved in between them. We work out the difference between this model and the conventional scenario where (approximate) \(\bar L\) invariance is imposed directly on the mass matrix of the light neutrinos.


Nonunitary Neutrino Mixing Matrix and \(CP\) Violating Neutrino Oscillations

abstract

In the standard approach to the neutrino oscillations a unitary relation among weak and mass eigenstates of light neutrinos is imposed. However, in many extensions of the SM left-handed, active neutrinos mix with additional heavy neutrino states. Consequences of this additional mixing, driven by experimental constraints, on the neutrino oscillations are considered.


The \(\gamma ^* p\) Total Cross Section at Low \({x}\)

abstract

The scaling in \(\sigma _{\gamma ^*p\,}(W^2, Q^2)\) cross sections (for \(Q^2/W^2 \ll 1\)) in terms of the scaling variable \(\eta = \left (Q^2 + m^2_0\right )/{\mit \Lambda }^2 \left (W^2\right )\) is interpreted in the Generalized Vector Dominance/Color-Dipole Picture (GVD/CDP). The quantity \({\mit \Lambda }^2 \left (W^2\right )\) is identified as the average gluon transverse momentum absorbed by the \(q \bar q\) state, \(\left \lt \vec l_\bot ^{~2}\right \gt \!=\! ({1}/{6}) {\mit \Lambda }^2 \left (W^2\right )\). At any \(Q^2\), for \(W^2\!\to \!\infty \), the cross sections for virtual and real photons become universal, \(\sigma _{\gamma ^*p}\left (W^2\!,Q^2\right )\!/ \sigma _{\gamma p}\left (W^2\right )\to 1\). The gluon density corresponding to the color-dipole cross section in the appropriate limit is found to be consistent with the results from QCD fits.


Supersymmetric Lepton Flavour Violation at \(e^+e^-\) Linear Colliders

abstract

The neutrino experiment results suggest that neutrinos have finite masses and violate lepton flavour. In supersymmetric extensions of the Standard Model, the Yukawa and/or mass terms of the heavy neutrinos can generate radiatively the lepton flavour violating slepton masses. These new sources of lepton flavour violation may enhance the rates of charged lepton flavour violating processes, like \(\mu \to e\gamma \). At future colliders they can also generate distinct final states, e.g. \(\tau \mu + {\rm jets} + {E\hskip -6pt/}_T\). In this paper the supersymmetric lepton flavour violating processes and their signals at future \(e^+e^-\) colliders are discussed.


Triviality and Vacuum Stability Bounds on the Higgs Boson Mass Beyond the Standard Model

abstract

The triviality and vacuum stability bounds on the Higgs-boson mass were revisited in presence of weakly-coupled new interactions parameterized in a model-independent way by effective operators of dimension 6. It was shown that for the scale of new physics in the region \(\Lambda \simeq 0.5 \div 50\) TeV the Standard Model triviality upper bound remains unmodified whereas it is natural to expect that the lower bound derived from the requirement of vacuum stability is increased by \(40\div 60\) GeV depending on the scale \(\Lambda \) and strength of coefficients of effective operators. It turns out that if the Higgs-boson mass is close to its lower LEP limit then the scale of new physics that follows from the vacuum stability requirement would be decreased dramatically even for modest values of coefficients of effective operators implying new physics already at the scale of a few Tev.


Fermion Mass Effects at Linear Colliders

abstract

A few physical examples are discussed which illustrate a role of fermion masses in the Standard Model predictions for reactions which will be measured at future linear colliders. Taking into account nonzero fermion masses is important not only in the context of the Higgs boson, or the top quark pair production and decay. The mass effects may also become numerically sizable for reactions involving light fermion flavours only. It is interesting that the mass effects do not always disappear in the presence of cuts. In some situations, the cuts may even enlarge the mass effect or make it inverse, i.e. stronger for lighter fermion flavours than for heavier ones.


Anomalous \(Wtb\) Vertex in Top Quark Production in \(e^{+}e^{-}\) Colliders

abstract

The potential of high energy \(e^{+}e^{-}\) collisions to detect an anomalous \(Wtb\) coupling is discussed. The anomalous \(Wtb\) coupling is implemented in the calculation of cross sections of four fermion reactions containing a single on-mass-shell top quark and numerical results for \({e^+ e^- \rightarrow t \bar {b} \mu ^- \bar {\nu }_{\mu }}\) are presented.


Tau Polarisation and Its Correlations as a Signal for Higgs Bosons — Universal Spin Interface for TAUOLA Package

abstract

We show how the \(\tau ^{+}\tau ^{-}\) spin correlations can be used to improve the recognition of the parent boson spin, and hence to identify scalar boson \(H^{0}\to \tau ^{+}\tau ^{-}\) events from the vector boson \(Z/\gamma ^{*}\to \tau ^{+}\tau ^{-}\) background in high energy accelerator experiments.


Neutrino Masses Measurement in Future Tritium Beta Decay Experiment

abstract

The end of the electron energy distribution \(\frac {dN}{dE}\) in \(\beta \) decays of nuclei depends on neutrino masses and mixing angles. Various approximate parametrization of the \(\frac {dN}{dE}\), proposed in literature, and the definition of effective neutrino masses \(m_{\beta }\) are investigated. Bounds or future measured values of \(m_{\beta }\) together with the oscillation parameters are a source of information about the mass of the lightest neutrino.


Why and How to Use a Differential Equation Method to Calculate Multi-Loop Integrals

abstract

A short pedagogical introduction to a differential method used to calculate multi-loop scalar integrals is presented. As an example it is shown how to obtain, using the method, large mass expansion of the two-loop sunrise master integrals.


Radiative Return at NLO and the Measurement of the Hadronic Cross-Section

abstract

The measurement of the hadronic cross-section in \(e^+ e^-\) annihilation at high luminosity factories using the radiative return method is motivated and discussed. A Monte Carlo generator which simulates the radiative process \(e^+ e^- \rightarrow \gamma +\) hadrons at the next-to-leading order accuracy is presented. The analysis is then extended to the description of events with hard photons radiated at very small angle.


Leptogenesis, Neutrinoless Double Beta Decay and Terrestrial \(CP\) Violation

abstract

Leptogenesis in left–right symmetric theories is studied. The usual see-saw mechanism is modified by the presence of a left-handed Higgs triplet. A simple connection between the properties of the light left-handed and heavy right-handed neutrinos is found. Predictions of this scenario for neutrinoless double beta decay and terrestrial \(CP\) violation in long-baseline experiments are given. These observables can in principle distinguish different realizations of the model.


Formal Languages and Model Theoretic Perspectives in Physics

abstract

We show that recent big growth of applications of Category Theory to Physics might be associated with unavoidable appearance of model theoretical structures coming from formal languages used to describe mathematical models of so called physical reality. Even in the simplest case of Elementary Protocolar Theory we are (to fulfil the conditions of consistency and simplicity of the language) confined to some model theoretical limitations. We discuss some examples. We also formulate conjectures and perspectives for future investigations.


Quantum-Like Approach to Financial Risk: Quantum Anthropic Principle

abstract

We continue the analysis of quantum-like description of market phenomena and economics. We show that it is possible to define a risk inclination operator acting in some Hilbert space that has a lot of common with quantum description of the harmonic oscillator. The approach has roots in the recently developed quantum game theory and quantum computing. A quantum anthropic principle is formulated.


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