arXiv subjects

Emil Mottola

Publications and source records attributed to Emil Mottola.

At least 37 records · Page 2Linked to original sources

arXiv2015

Surface Tension and Negative Pressure Interior of a Non-Singular `Black Hole'

The constant density interior Schwarzschild solution for a static, spherically symmetric collapsed star has a divergent pressure when its radius $R\le\frac{9}{8}R_s=\frac{9}{4}GM$. We show that this divergence is integrable, and induces a non-isotropic transverse stress with a finite redshifted surface tension on a spherical surface of radius $R_0=3R\sqrt{1-\frac{8}{9}\frac{R}{R_s}}$. For $r < R_0$ the interior Schwarzschild solution exhibits negative pressure. When $R=R_s$, the surface is localized at the Schwarzschild radius itself, $R_0=R_s$, and the solution has constant negative pressure $p =-\barρ$ everywhere in the interior $r<R_s$, thereby describing a gravitational condensate star, a fully collapsed non-singular state already inherent in and predicted by classical General Relativity. The redshifted surface tension of the condensate star surface is given by $τ_s=Δκ/8πG$, where $Δκ=κ_+-κ_-=2κ_+=1/R_s$ is the difference of equal and opposite surface gravities between the exterior and interior Schwarzschild solutions. The First Law, $dM=dE_v+τ_s dA$ is recognized as a purely mechanical classical relation at zero temperature and zero entropy, describing the volume energy and surface energy change respectively. Since there is no event horizon, the Schwarzschild time t of such a non-singular gravitational condensate star is a global time, fully consistent with unitary time evolution in quantum theory. The $p=-\barρ$ interior acts as a defocusing lens for light passing through the condensate, leading to imaging characteristics distinguishable from a classical black hole. A further observational test of gravitational condensate stars with a physical surface vs. black holes is the discrete surface modes of oscillation which should be detectable by their gravitational wave signatures.

gr-qc↗

arXiv2014

Fermion Pairing and the Scalar Boson of the 2D Conformal Anomaly

We analyze the phenomenon of fermion pairing into an effective boson associated with anomalies and the anomalous commutators of currents bilinear in the fermion fields. In two spacetime dimensions the chiral bosonization of the Schwinger model is determined by the axial current anomaly of massless Dirac fermions. A similar bosonized description applies to the 2D conformal trace anomaly of the fermion stress tensor. For both the chiral and conformal anomalies, correlation functions involving anomalous currents, $j^μ_5$ or $T^{μν}$ of massless fermions exhibit a massless boson $1/k^2$ pole, and the associated spectral functions obey a UV finite sum rule, becoming $δ$-functions in the massless limit. In both cases the corresponding effective action of the anomaly is non-local, but may be expressed in a local form by the introduction of a new bosonic field, which becomes a bona fide propagating quantum field in its own right. In both cases this is expressed in Fock space by the anomalous Schwinger commutators of currents becoming the canonical commutation relations of the corresponding boson. The boson has a Fock space operator realization as a coherent superposition of massless fermion pairs, which saturates the intermediate state sums in quantum correlation functions of fermion currents. The Casimir energy of fermions on a finite spatial interval $[0,L]$ can also be described as a coherent scalar condensation of pairs, and the one-loop correlation function of any number $n$ of fermion stress tensors $\langle TT\dots T\rangle$ may be expressed as a combinatoric sum of $n!/2$ linear tree diagrams of the scalar boson.

hep-th↗

arXiv2013

Quantum Vacuum Instability of 'Eternal' de Sitter Space

The Euclidean or Bunch-Davies O(4,1) invariant 'vacuum' state of quantum fields in global de Sitter space is shown to be unstable to small perturbations, even for a massive free field with no self-interactions. There are perturbations of this state with arbitrarily small energy density at early times that is exponentially blueshifted in the contracting phase of 'eternal' de Sitter space, and becomes large enough to disturb the classical geometry through the semiclassical Einstein eqs. at later times. In the closely analogous case of a constant, uniform electric field, a time symmetric state equivalent to the de Sitter invariant one is constructed, which is also not a stable vacuum state under perturbations. The role of a quantum anomaly in the growth of perturbations and symmetry breaking is emphasized in both cases. In de Sitter space, the same results are obtained either directly from the renormalized stress tensor of a massive scalar field, or for massless conformal fields of any spin, more directly from the effective action and stress tensor associated with the conformal trace anomaly. The anomaly stress tensor shows that states invariant under the O(4) subgroup of the de Sitter group are also unstable to perturbations of lower spatial symmetry, implying that both the O(4,1) isometry group and its O(4) subgroup are broken by quantum fluctuations. Consequences of this result for cosmology and the problem of vacuum energy are discussed.

gr-qc↗

arXiv2013

On the Instability of Global de Sitter Space to Particle Creation

We show that global de Sitter space is unstable to particle creation, even for a massive free field theory with no self-interactions. The O(4,1) de Sitter invariant state is a definite phase coherent superposition of particle and anti-particle solutions in both the asymptotic past and future, and therefore is not a true vacuum state. In the closely related case of particle creation by a constant, uniform electric field, a time symmetric state analogous to the de Sitter invariant one is constructed, which is also not a stable vacuum state. We provide the general framework necessary to describe the particle creation process, the mean particle number, and dynamical quantities such as the energy-momentum tensor and current of the created particles in both the de Sitter and electric field backgrounds in real time, establishing the connection to kinetic theory. We compute the energy-momentum tensor for adiabatic vacuum states in de Sitter space initialized at early times in global S^3 sections, and show that particle creation in the contracting phase results in exponentially large energy densities at later times, necessitating an inclusion of their backreaction effects, and leading to large deviation of the spacetime from global de Sitter space before the expanding phase can begin.

gr-qc↗

arXiv2013

Solving the Conformal Constraints for Scalar Operators in Momentum Space and the Evaluation of Feynman's Master Integrals

We investigate the structure of the constraints on three-point correlation functions emerging when conformal invariance is imposed in momentum space and in arbitrary space-time dimensions, presenting a derivation of their solutions for arbitrary scalar operators. We show that the differential equations generated by the requirement of symmetry under special conformal transformations coincide with those satisfied by generalized hypergeometric functions (Appell's functions). Combined with the position space expression of this correlator, whose Fourier transform is given by a family of generalized Feynman (master) integrals, the method allows to derive the expression of such integrals in a completely independent way, bypassing the use of Mellin-Barnes techniques, which have been used in the past. The application of the special conformal constraints generates a new recursion relation for this family of integrals.

hep-th↗

arXiv2012

Conformal Invariance, Dark Energy, and CMB Non-Gaussianity

In addition to simple scale invariance, a universe dominated by dark energy naturally gives rise to correlation functions possessing full conformal invariance. This is due to the mathematical isomorphism between the conformal group of certain 3 dimensional slices of de Sitter space and the de Sitter isometry group SO(4,1). In the standard homogeneous isotropic cosmological model in which primordial density perturbations are generated during a long vacuum energy dominated de Sitter phase, the embedding of flat spatial sections in de Sitter space induces a conformal invariant perturbation spectrum and definite prediction for the shape of the non-Gaussian CMB bispectrum. In the case in which the density fluctuations are generated instead on the de Sitter horizon, conformal invariance of the horizon embedding implies a different but also quite definite prediction for the angular correlations of CMB non-Gaussianity on the sky. Each of these forms for the bispectrum is intrinsic to the symmetries of de Sitter space and in that sense, independent of specific model assumptions. Each is different from the predictions of single field slow roll inflation models which rely on the breaking of de Sitter invariance. We propose a quantum origin for the CMB fluctuations in the scalar gravitational sector from the conformal anomaly that could give rise to these non-Gaussianities without a slow roll inflaton field, and argue that conformal invariance also leads to the expectation for the relation n_S-1=n_T between the spectral indices of the scalar and tensor power spectrum. Confirmation of this prediction or detection of non-Gaussian correlations in the CMB of one of the bispectral shape functions predicted by conformal invariance can be used both to establish the physical origins of primordial density fluctuations and distinguish between different dynamical models of cosmological vacuum dark energy.

gr-qc↗

arXiv2012

Graviton Vertices and the Mapping of Anomalous Correlators to Momentum Space for a General Conformal Field Theory

We investigate the mapping of conformal correlators and of their anomalies from configuration to momentum space for general dimensions, focusing on the anomalous correlators $TOO$, $TVV$ - involving the energy-momentum tensor $(T)$ with a vector $(V)$ or a scalar operator ($O$) - and the 3-graviton vertex $TTT$. We compute the $TOO$, $TVV$ and $TTT$ one-loop vertex functions in dimensional regularization for free field theories involving conformal scalar, fermion and vector fields. Since there are only one or two independent tensor structures solving all the conformal Ward identities for the $TOO$ or $TVV$ vertex functions respectively, and three independent tensor structures for the $TTT$ vertex, and the coefficients of these tensors are known for free fields, it is possible to identify the corresponding tensors in momentum space from the computation of the correlators for free fields. This works in general $d$ dimensions for $TOO$ and $TVV$ correlators, but only in 4 dimensions for $TTT$, since vector fields are conformal only in $d=4$. In this way the general solution of the Ward identities including anomalous ones for these correlators in (Euclidean) position space, found by Osborn and Petkou is mapped to the ordinary diagrammatic one in momentum space. We give simplified expressions of all these correlators in configuration space which are explicitly Fourier integrable and provide a diagrammatic interpretation of all the contact terms arising when two or more of the points coincide. We discuss how the anomalies arise in each approach [...]

hep-th↗

arXiv2011

New Horizons in Gravity: Dark Energy and Condensate Stars

Black holes are an apparently unavoidable prediction of classical General Relativity, at least if matter obeys the strong energy condition rho + 3p > 0. However quantum vacuum fluctuations generally violate this condition, as does the eq. of state of cosmological dark energy. When quantum effects are considered, black holes lead to a number of thermodynamic paradoxes associated with the Hawking temperature and assumption of black hole entropy, which are briefly reviewed. It is argued that the largest quantum effects arise from the conformal scalar degrees of freedom generated by the trace anomaly of the stress-energy tensor in curved space. At event horizons these can have macroscopically large backreaction effects on the geometry, potentially removing the classical event horizon of black hole and cosmological spacetimes, replacing them with a quantum phase boundary layer, where the effective value of the gravitational vacuum energy density can change. In the effective theory including the quantum effects of the anomaly, the cosmological term becomes a dynamical condensate, whose value depends upon boundary conditions at the horizon. By taking a positive value in the interior of a fully collapsed star, the effective cosmological term removes any singularity, replacing it with a smooth dark energy de Sitter interior. The resulting gravitational vacuum condensate star (or gravastar) configuration resolves all black hole paradoxes, and provides a testable alternative to black holes as the final quantum mechanical end state of complete gravitational collapse. The observed dark energy of our universe likewise may be a macroscopic finite size effect whose value depends not on Planck scale or other microphysics but on the cosmological Hubble horizon scale itself.

gr-qc↗

arXiv2011

Conformal Invariance, Dynamical Dark Energy and the CMB

General Relativity receives quantum corrections relevant at cosmological distance scales from the conformal scalar degrees of freedom required by the trace anomaly of the quantum stress tensor in curved space. In the theory including the trace anomaly terms, the cosmological "constant" becomes dynamical and hence potentially dependent upon both space and time. The fluctuations of these anomaly scalars may also influence the spectrum and statistics of the Cosmic Microwave Background. Under the hypothesis that scale invariance should be promoted to full conformal invariance, an hypothesis supported by the exact equivalence of the conformal group of three dimensions with the de Sitter group SO(4,1), the form of the CMB bispectrum can be fixed, and the trispectrum constrained. The non-Gaussianities predicted by conformal invariance differ from those suggested by simple models of inflation.

gr-qc↗

arXiv2010

New Horizons in Gravity: The Trace Anomaly, Dark Energy and Condensate Stars

General Relativity receives quantum corrections relevant at macroscopic distance scales and near event horizons. These arise from the conformal scalar degrees of freedom in the extended effective field theory of gravity generated by the trace anomaly of massless quantum fields in curved space. The origin of these conformal scalar degrees of freedom as massless poles in two-particle intermediate states of anomalous amplitudes in flat space is exposed. At event horizons the conformal anomaly scalar degrees of freedom can have macroscopically large effects on the geometry, potentially removing the classical event horizon of black hole and cosmological spacetimes, replacing them with a quantum boundary layer where the effective value of the gravitational vacuum energy density can change. In the effective theory, the cosmological term becomes a dynamical condensate, whose value depends upon boundary conditions near the horizon. In the conformal phase where the anomaly induced fluctutations dominate, and the condensate dissolves, the effective cosmological "constant" is a running coupling which has an infrared stable fixed point at zero. By taking a positive value in the interior of a fully collapsed star, the effective cosmological term removes any singularity, replacing it with a smooth dark energy interior. The resulting gravitational condensate star configuration resolves all black hole paradoxes, and provides a testable alternative to black holes as the final state of complete gravitational collapse. The observed dark energy of our universe likewise may be a macroscopic finite size effect whose value depends not on microphysics but on the cosmological horizon scale.

gr-qc↗

arXiv2010

The Trace Anomaly and Dynamical Vacuum Energy in Cosmology

The trace anomaly of conformal matter implies the existence of massless scalar poles in physical amplitudes involving the stress-energy tensor. These poles may be described by a local effective action with massless scalar fields, which couple to classical sources, contribute to gravitational scattering processes, and can have long range gravitational effects at macroscopic scales. In an effective field theory approach, the effective action of the anomaly is an infrared relevant term that should be added to the Einstein-Hilbert action of classical General Relativity to take account of macroscopic quantum effects. The additional scalar degrees of freedom contained in this effective action may be understood as responsible for both the Casimir effect in flat spacetime and large quantum backreaction effects at the horizon scale of cosmological spacetimes. These effects of the trace anomaly imply that the cosmological vacuum energy is dynamical, and its value depends on macroscopic boundary conditions at the cosmological horizon scale, rather than sensitivity to the extreme ultraviolet Planck scale.

gr-qc↗

arXiv2010

Systematics of High Temperature Perturbation Theory: The Two-Loop Electron Self-Energy in QED

In order to investigate the systematics of the loop expansion in high temperature gauge theories beyond the leading order hard thermal loop (HTL) approximation, we calculate the two-loop electron proper self-energy in high temperature QED. The two-loop bubble diagram contains a linear infrared divergence. Even if regulated with a non-zero photon mass M of order of the Debye mass, this infrared sensitivity implies that the two-loop self-energy contributes terms to the fermion dispersion relation that are comparable to or even larger than the next-to-leading-order (NLO) contributions at one-loop. Additional evidence for the necessity of a systematic restructuring of the loop expansion comes from the explicit gauge parameter dependence of the fermion damping rate at both one and two-loops. The leading terms in the high temperature expansion of the two-loop self-energy for all topologies arise from an explicit hard-soft factorization pattern, in which one of the loop integrals is hard, nested inside a second loop integral which is soft. There are no hard-hard contributions to the two-loop Sigma at leading order at high T. Provided the same factorization pattern holds for arbitrary ell loops, the NLO high temperature contributions to the electron self-energy come from ell-1 hard loops factorized with one soft loop integral. This hard-soft pattern is both a necessary condition for the resummation over ell to coincide with the one-loop self-energy calculated with HTL dressed propagators and vertices, and to yield the complete NLO correction to the self-energy at scales ~eT, which is both infrared finite and gauge invariant. We employ spectral representations and the Gaudin method for evaluating finite temperature Matsubara sums, which facilitates the analysis of multi-loop diagrams at high T.

hep-ph↗

arXiv2009

Cosmological Horizon Modes and Linear Response in de Sitter Spacetime

Linearized fluctuations of quantized matter fields and the spacetime geometry around de Sitter space are considered in the case that the matter fields are conformally invariant. Taking the unperturbed state of the matter to be the de Sitter invariant Bunch-Davies state, the linear variation of the stress tensor about its self-consistent mean value serves as a source for fluctuations in the geometry through the semi-classical Einstein equations. This linear response framework is used to investigate both the importance of quantum backreaction and the validity of the semi-classical approximation in cosmology. The full variation of the stress tensor, delta T^a_b contains two kinds of terms: (1) those that depend explicitly upon the linearized metric variation delta g_{cd} through the [T^a_b, T^{cd}] causal response function; and (2) state dependent variations, independent of delta g_{cd}. For perturbations of the first kind, the criterion for the validity of the semi-classical approximation in de Sitter space is satisfied for fluctuations on all scales well below the Planck scale. The perturbations of the second kind contain additional massless scalar degrees of freedom associated with changes of state of the fields on the cosmological horizon scale. These scalar degrees of freedom arise necessarily from the local auxiliary field form of the effective action associated with the trace anomaly, are potentially large on the horizon scale, and therefore can lead to substantial non-linear quantum backreaction effects in cosmology.

gr-qc↗

arXiv2008

The Trace Anomaly and Massless Scalar Degrees of Freedom in Gravity

The trace anomaly of quantum fields in electromagnetic or gravitational backgrounds implies the existence of massless scalar poles in physical amplitudes involving the stress-energy tensor. Considering first the axial anomaly and using QED as an example, we compute the full one-loop triangle amplitude of the fermionic stress tensor with two current vertices, , and exhibit the scalar pole in this amplitude associated with the trace anomaly, in the limit of zero electron mass m -> 0. To emphasize the infrared aspect of the anomaly, we use a dispersive approach and show that this amplitude and the existence of the massless scalar pole is determined completely by its ultraviolet finite terms, together with the requirements of Poincare invariance of the vacuum, Bose symmetry under interchange of J^a and J^b, and vector current and stress tensor conservation. We derive a sum rule for the appropriate positive spectral function corresponding to the discontinuity of the triangle amplitude, showing that it becomes proportional to delta function of k^2, and therefore contains a massless scalar intermediate state in the conformal limit of zero electron mass. The effective action corresponding to the trace of the triangle amplitude can be expressed in local form by the introduction of two scalar auxiliary fields which satisfy massless wave equations. These massless scalar degrees of freedom couple to classical sources, contribute to gravitational scattering processes, and can have long range gravitational effects.

hep-th↗

arXiv2007

Effects of quantized fields on the spacetime geometries of static spherically symmetric black holes

Analytic approximations for the stress-energy of quantized fields in the Hartle-Hawking state in static black hole spacetimes predict divergences on the event horizon of the black hole for a number of important cases. Such divergences, if real, could substantially alter the spacetime geometry near the event horizon, possibly preventing the black hole from existing. The results of three investigations of these types of effects are presented. The first involves a new analytic approximation for conformally invariant fields in Reissner-Nordstrom spacetimes which is finite on the horizon. The second focuses on the stress-energy of massless scalar fields in Schwarzschild-de Sitter black holes. The third focuses on the stress-energy of massless scalar fields in zero temperature black hole geometries that could be solutions to the semiclassical backreaction equations near the event horizon of the black hole.

gr-qc↗

arXiv2007

Stress Tensor from the Trace Anomaly in Reissner-Nordstrom Spacetimes

The effective action associated with the trace anomaly provides a general algorithm for approximating the expectation value of the stress tensor of conformal matter fields in arbitrary curved spacetimes. In static, spherically symmetric spacetimes, the algorithm involves solving a fourth order linear differential equation in the radial coordinate r for the two scalar auxiliary fields appearing in the anomaly action, and its corresponding stress tensor. By appropriate choice of the homogeneous solutions of the auxiliary field equations, we show that it is possible to obtain finite stress tensors on all Reissner-Nordstrom event horizons, including the extreme Q=M case. We compare these finite results to previous analytic approximation methods, which yield invariably an infinite stress-energy on charged black hole horizons, as well as with detailed numerical calculations that indicate the contrary. The approximation scheme based on the auxiliary field effective action reproduces all physically allowed behaviors of the quantum stress tensor, in a variety of quantum states, for fields of any spin, in the vicinity of the entire family (0 le Q le M) of RN horizons.

gr-qc↗

arXiv2006

Cosmological Dark Energy: Prospects for a Dynamical Theory

We present an approach to the problem of vacuum energy in cosmology, based on dynamical screening of Lambda on the horizon scale. We review first the physical basis of vacuum energy as a phenomenon connected with macroscopic boundary conditions, and the origin of the idea of its screening by particle creation and vacuum polarization effects. We discuss next the relevance of the quantum trace anomaly to this issue. The trace anomaly implies additional terms in the low energy effective theory of gravity, which amounts to a non-trivial modification of the classical Einstein theory, fully consistent with the Equivalence Principle. We show that the new dynamical degrees of freedom the anomaly contains provide a natural mechanism for relaxing Lambda to zero on cosmological scales. We consider possible signatures of the restoration of conformal invariance predicted by the fluctuations of these new scalar degrees of freedom on the spectrum and statistics of the CMB, in light of the latest bounds from WMAP. Finally we assess the prospects for a new cosmological model in which the dark energy adjusts itself dynamically to the cosmological horizon boundary, and therefore remains naturally of order H^2 at all times without fine tuning.

gr-qc↗

arXiv2006

Macroscopic Effects of the Quantum Trace Anomaly

The low energy effective action of gravity in any even dimension generally acquires non-local terms associated with the trace anomaly, generated by the quantum fluctuations of massless fields. The local auxiliary field description of this effective action in four dimensions requires two additional scalar fields, not contained in classical general relativity, which remain relevant at macroscopic distance scales. The auxiliary scalar fields depend upon boundary conditions for their complete specification, and therefore carry global information about the geometry and macroscopic quantum state of the gravitational field. The scalar potentials also provide coordinate invariant order parameters describing the conformal behavior and divergences of the stress tensor on event horizons. We compute the stress tensor due to the anomaly in terms of its auxiliary scalar potentials in a number of concrete examples, including the Rindler wedge, the Schwarzschild geometry, and de Sitter spacetime. In all of these cases, a small number of classical order parameters completely determine the divergent behaviors allowed on the horizon, and yield qualitatively correct global approximations to the renormalized expectation value of the quantum stress tensor.

gr-qc↗