arXiv subjects

Pawel O. Mazur

Publications and source records attributed to Pawel O. Mazur.

At least 19 recordsLinked to original sources

arXiv2023

Gravitational Condensate Stars: An Alternative to Black Holes

A new solution for the endpoint of gravitational collapse is proposed. By extending the concept of Bose-Einstein condensation to gravitational systems, a cold, compact object with an interior de Sitter condensate phase and an exterior Schwarzschild geometry of arbitrary total mass M is constructed. These are separated by a phase boundary with a small but finite thickness of fluid with eq. of state p= +rho, replacing both the Schwarzschild and de Sitter classical horizons. The new solution has no singularities, no event horizons, and a global time. Its entropy is maximized under small fluctuations and is given by the standard hydrodynamic entropy of the thin shell, instead of the Bekenstein-Hawking entropy. Unlike black holes, a collapsed star of this kind is thermodynamically stable and has no information paradox.

gr-qc↗

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

Superfluid Picture for Rotating Space-Times

A new prescription, in the framework of condensate models for space-times, for physical stationary gravitational fields is presented. We show that the spinning cosmic string metric describes the gravitational field associated with the single vortex in a superfluid condensate model for space-time outside the vortex core. This metric differs significantly from the usual acoustic metric for the Onsager-Feynman vortex. We also consider the question of what happens when many vortices are present, and show that on large scales a Gödel-like metric emerges. In both the single and multiple vortex cases the failure of general relativity exemplified by the presence of closed time-like curves is attributed to the breakdown of superfluid rigidity.

gr-qc↗

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↗

arXiv2011

An Optical Geometry Perspective on the Emerging Conformal Field Theory Behavior on the Cosmological Event Horizon: Massless Fermions on de Sitter Space

We have investigated the emerging conformal field theory behavior on the interior interface of the region near the cosmological event horizon on an example of massless Dirac fermions. Indeed, we have constructed and verified the emerging de Sitter/CFT correspondence for the near cosmological event horizon region. It is in this near horizon region where the infinitely thin shell of matter with the stiffest equation of state (Zeldovich's matter) is placed in the model for a thermodynamically stable `would be black hole' which is sometimes called a gravastar or a dark energy star. We put forward the hypothesis to the effect that the Zeldovich matter consists of the strongly correlated quanta which are best described by the emerging conformal field theory in the near `would be horizon' region of a gravastar/dark energy star.

gr-qc↗

arXiv2009

Superfluidity and Stationary Space-Times

A connection between superfluidity and gravitation is established for physical stationary gravitational fields. We show that the spinning cosmic string metric describes the gravitational field associated with the single vortex in a superfluid condensate model for space-time outside the vortex core. This metric differs significantly from the usual acoustic metric for the Onsager-Feynman vortex. We also consider the question of what happens when many vortices are present, and show that on large scales a Gödel-like metric emerges. In both the single and multiple vortex cases the presence of closed time-like curves is attributed to the breakdown of superfluid rigidity.

hep-th↗

arXiv2009

Stability of Exponential Tails in the Scattering on Wedges and Impurities

We study a simple exactly solvable 2D model describing the interaction of a localized particle with an impurity. The localization potential $V(x)=-αδ(x)$ causes the particle to be trapped in the y-axis, and the `impurity' is modeled by a straight impenetrable edge extending along the positive x-axis. We show that the problem described can be treated as the Sommerfeld diffraction from an infinite edge. We use the model to present qualitative arguments on the nature of interaction of polarized light traveling along an optical fiber with external impurities.

quant-ph↗

arXiv2007

Quantum Theory and the Nature of Gravitation

This is an essay sketching the line of thinking which has led the present author to propose the constituent or atomic model of gravitation more than a decade ago. It turns out that viewing the problem of gravitation as a quantum many body problem could be quite useful when addressing some old unsolved problems such as the cosmological constant problem. I have applied this idea in 1996 to the problem of the largest cold gravitating system, the finite Universe itself. The result was the prediction of a small, positive vacuum energy density, now known, after its experimental discovery in 1998, as `dark energy'. The smallness of this quantity was understood as the finite size effect in the cold quantum many body system, and I quote here from \cite{Ma96}, {\it `` The smallness of the cosmological constant in natural Planck units is a result of an almost perfect thermodynamical limit. This is to say that the smallness of the cosmological constant is an effect due to an enormous number $N$ of hypothetical \textsf{gravitational} \textsf{atoms}. The present upper bound on the cosmological constant $Λ$ allows us to draw the conclusion about the lower bound on a number of \textsf{gravitational} \textsf{atoms} in the observed Universe, $N\sim 10^{122}$. ...''}. The old cosmological constant problem is a man-made problem because the vacuum energy density has nothing to do with the quartic divergences (zero point energies) in the interacting relativistic quantum field theories (i.e. in the Standard Model of elementary particles). The actual value of the vacuum energy density of the vacuum finite size de Sitter Universe is $\frac{E_{0}}{V}$, where $E_{0}$ is the ground state energy of $N$ \textsf{gravitational} \textsf{atoms}, which are spin-zero bosons of mass $M\sim M_{_{Pl}}$, contained in the finite volume $V$.

astro-ph↗

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↗

arXiv2005

De Sitter Invariant Vacuum States, Vertex Operators, and Conformal Field Theory Correlators

We show that there is only one physically acceptable vacuum state for quantum fields in de Sitter space-time which is left invariant under the action of the de Sitter-Lorentz group $SO(1,d)$ and supply its physical interpretation in terms of the Poincare invariant quantum field theory (QFT) on one dimension higher Minkowski spacetime. We compute correlation functions of the generalized vertex operator $:e^{i\hat{S}(x)}:$, where $\hat{S}(x)$ is a massless scalar field, on the $d$-dimensional de Sitter space and demonstrate that their limiting values at timelike infinities on de Sitter space reproduce correlation functions in $(d-1)$-dimensional Euclidean conformal field theory (CFT) on $S^{d-1}$ for scalar operators with arbitrary real conformal dimensions. We also compute correlation functions for a vertex operator $e^{i\hat{S}(u)}$ on the Łobaczewski space and find that they also reproduce correlation functions of the same CFT. The massless field $\hat{S}(u)$ is the nonlocal transform of the massless field $\hat{S}(x)$ on de Sitter space introduced by one of us.

hep-th↗

arXiv2005

Tommy Gold Revisited: Why Does Not The Universe Rotate?

Understanding gravitational collapse requires understanding how $\sim 10^{58}$ nucleons can be destroyed in $\sim 10^{-5}$ seconds. The recent proposal that the endpoint of gravitational collapse can be a "dark energy star" implies that the mass-energy of the nucleons undergoing gravitational collapse can be converted to vacuum energy when one gets near to conditions where classical general relativity predicts that a trapped surface would form. The negative pressure associated with a large vacuum energy prevents an event horizon from forming, thus resolving the long-standing puzzle as to why gravitational collapse always leads to an explosion. An indirect consequence is that the reverse process - creation of matter from vacuum energy - should also be possible. Indeed this process may be responsible for the "big bang". In this new cosmology the observable universe began as a fluctuation in an overall steady state universe. The fluctuations in the CMB in this picture are the result of quantum turbulence associated with vorticity. This explanation for the CMB fluctuations is superior to inflationary scenarios because there is a natural explanation for both the level of CMB fluctuations and the deviation from a scale invariant spectrum at large scales.

astro-ph↗

arXiv2004

Gravitational Vacuum Condensate Stars

A new final state of gravitational collapse is proposed. By extending the concept of Bose-Einstein condensation to gravitational systems, a cold, dark, compact object with an interior de Sitter condensate $p_{_V} = -ρ_{_V}$ and an exterior Schwarzschild geometry of arbitrary total mass $M$ is constructed. These are separated by a shell with a small but finite proper thickness $\ell$ of fluid with equation of state $p=+ρ$, replacing both the Schwarzschild and de Sitter classical horizons. The new solution has no singularities, no event horizons, and a global time. Its entropy is maximized under small fluctuations and is given by the standard hydrodynamic entropy of the thin shell, which is of order $k_{_B}\ell Mc/\hbar$, instead of the Bekenstein-Hawking entropy formula, $S_{_{BH}}= 4πk_{_B} G M^2/\hbar c$. Hence unlike black holes, the new solution is thermodynamically stable and has no information paradox.

gr-qc↗

arXiv2004

Dark Energy and Condensate Stars: Casimir Energy in the Large

Vacuum fluctuations and the Casimir effect are considered in a cosmological setting. It is suggested that the dark energy, which recent observations suggest make up 73% of our universe, is vacuum energy due to a causal boundary effect at the cosmological horizon. After a discussion of the similarities and differences between material boundaries in flat spacetime and causal horizons in general relativity, a simple model with a purely vacuum energy de Sitter interior and Schwarzschild exterior, separated by a thin boundary layer is outlined. The boundary layer is a quantum transition region which replaces the event horizons of the classical de Sitter and Schwarzschild solutions, through which the vacuum energy changes.

gr-qc↗

arXiv2001

Weyl Cohomology and the Effective Action for Conformal Anomalies

We present a general method of deriving the effective action for conformal anomalies in any even dimension, which satisfies the Wess-Zumino consistency condition by construction. The method relies on defining the coboundary operator of the local Weyl group, and giving a cohomological interpretation to counterterms in the effective action in dimensional regularization with respect to this group. Non-trivial cocycles of the Weyl group arise from local functionals that are Weyl invariant in and only in the physical even integer dimension. In the physical dimension the non-trivial cocycles generate covariant non-local action functionals characterized by sensitivity to global Weyl rescalings. The non-local action so obtained is unique up to the addition of trivial cocycles and Weyl invariant terms, both of which are insensitive to global Weyl rescalings. These distinct behaviors under rigid dilations can be used to distinguish between infrared relevant and irrelevant operators in a generally covariant manner. Variation of the $d=4$ non-local effective action yields two new conserved geometric stress tensors with local traces. The method may be extended to any even dimension by making use of the general construction of conformal invariants given by Fefferman and Graham. As a corollary, conformal field theory behavior of correlators at the asymptotic infinity of either anti-de Sitter or de Sitter spacetimes follows, i.e. AdS$_{d+1}$ or deS$_{d+1}$/CFT$_d$ correspondence. The same construction naturally selects all infrared relevant terms (and only those terms) in the low energy effective action of gravity in any even integer dimension. The infrared relevant terms arising from the known anomalies in d=4 imply that the classical Einstein theory is modified at large distances.

hep-th↗

arXiv2000

Black Uniqueness Theorems

I review the black hole uniqueness theorem and the no hair theorems established for physical black hole stationary states by the early 80'. This review presents the original and decisive work of Carter, Robinson, Mazur and Bunting on the problem of no bifurcation and uniqueness of physical black holes. Its original version was written only few years after my proof of the Kerr-Newman et al. black hole uniqueness theorem has appeared in print. The proof of the black hole uniqueness theorem relies heavily on the positivity properties of nonlinear sigma models on the Riemannian noncompact symmetric spaces with negative sectional curvature. It is hoped that the first hand description of the original developments leading to our current understanding of the black hole uniqueness will be found useful to all interested in the subject.

hep-th↗

arXiv1998

On the $Θ$-term in electrodynamics

The term $Θε^{μνρσ}F_{μν}F_{ρσ}$, when added to the electromagnetic Lagrangian $-{1\over 16π}F^{μν}F_{μν}$, does not change the signature of the Lagrangian. Actually, it increases the part with negative kinetic energy term at the spatial infinity. For this reason it does not change the conclusion, that at the spatial infinity the magnetic part of the electromagnetic field should be absent.

hep-th↗

arXiv1998

Fractal Geometry of Quantum Spacetime at Large Scales

We compute the intrinsic Hausdorff dimension of spacetime at the infrared fixed point of the quantum conformal factor in 4D gravity. The fractal dimension is defined by the appropriate covariant diffusion equation in four dimensions and is determined by the coefficient of the Gauss-Bonnet term in the trace anomaly to be generally greater than 4. In addition to being testable in simplicial simulations, this scaling behavior suggests a physical mechanism for the screening of the effective cosmological `constant' and inverse Newtonian coupling at very large distance scales, which has implications for the dark matter content and large scale structure of the universe.

hep-th↗

arXiv1997

On Gravitation and Quanta

A slightly extended version, with a footnote added on December 19, 1997, of a contributed Abstract to the Eight Marcel Grossmann Meeting, Jerusalem, June 1997.

hep-th↗