arXiv subjects

Grzegorz Plewa

Publications and source records attributed to Grzegorz Plewa.

12 recordsLinked to original sources

arXiv2023

On extra dimensions and the cosmological constant problem

We consider a massive scalar field with a coordinate-dependent mass in higher-dimensional spacetime. The field satisfies Dirichlet boundary conditions on a brane representing the four-dimensional world. Despite being massive, the theory is scale-invariant. We quantize the theory calculating the zero-point energy. We find the lower bound for the uncertainty product in the uncertainty principle. We show that the zero-point energy density could be small if large extra dimensions exist. Identifying the zero-point energy as a source of dark energy, we extract the four-dimensional cosmological constant from higher-dimensional theory, considering quantum fluctuations close to the brane surface. We examine numerically ten- and eleven-dimensional spaces. The resulting zero-point energy is parameterized by the number of extra dimensions and the additional dimensionless {\it saturation parameter}, expressing the deviation from perfect saturation of the uncertainty principle. Letting the parameter to be small and of order of the fine-structure constant, we reproduce the experimental value of the cosmological constant in four dimensions.

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arXiv2021

Hunting for gravitational quantum spikes

We present the result of our examination of quantum structures called quantum spikes. The classical spikes, that are known in gravitational systems, occur in the evolution of the inhomogeneous spacetimes. Different kind of spikes, which we name strange spikes, can be seen in the dynamics of the homogeneous sector of the Belinski-Khalatnikov-Lifshitz scenario. They can be made visible if the so-called inhomogeneous initial data are used. The question to be explored is whether the strange spikes may survive quantization. The answer is in the affirmative. However, this is rather a subtle effect that needs further examination using sophisticated analytical and numerical tools. The spikes seem to be of fundamental importance, both at classical and quantum levels, as they may serve as seeds of real structures in the universe.

gr-qc↗

arXiv2020

Quantum origin of the Minkowski space

We show that D=4 Minkowski space is an emergent concept related to a class of operators in extended Hilbert space with no positive-definite scalar product. We start with the idea of position-like and momentum-like operators (Plewa 2019 J. Phys. A: Math. Theor. 52 375401), introduced discussing a connection between quantum entanglement and geometry predicted by ER=EPR conjecture. We examine eigenequations of the simplest operators and identify D=4 Minkowski space as to be spanned by normalized eigenvectors corresponding to the zero eigenvalue. Both spacetime dimension and signature of the metric are fixed by the regularization procedure. We generalize the result to the case of more general operators, being analogues to quantum fields. We reproduce the Minkowski space again, however, now in a holographic way, as being identified with the conformal boundary of $AdS_5$. We observe an interesting analogy to string theory and, in particular, to AdS/CFT correspondence.

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arXiv2019

Quantum harmonic oscillator, entanglement in the vacuum and its geometric interpretation

Inspired by ER=EPR conjecture we present a mathematical tool providing a link between quantum entanglement and the geometry of spacetime. We start with the idea of operators in extended Hilbert space which, by definition, has no positive definite scalar product. Adopting several simple postulates we show that a quantum harmonic oscillator can be constructed as a positive definite sector in that space. We discuss the two-dimensional oscillator constructed in such a way that the ground state is maximally entangled. Being a vector in the Hilbert space, it has also a non-trivial expansion in a bigger extended space. On one hand, the space is not free of negative norm states. On the other hand, it allows one to interpret the ground state geometrically in terms of $AdS_3$. The interpretation is based solely on the form of the expansion, revealing certain structures at the boundary and in the bulk of $AdS_3$. The former correspond to world lines of massless particles at the boundary. The latter resemble interacting closed strings.

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arXiv2019

Quantum Belinski-Khalatnikov-Lifshitz scenario

We present the quantum model of the asymptotic dynamics underlying the Belinski-Khalatnikov-Lifshitz (BKL) scenario. The symmetry of the physical phase space enables making use of the affine coherent states quantization. Our results show that quantum dynamics is regular in the sense that during quantum evolution the expectation values of all considered observables are finite. The classical singularity of the BKL scenario is replaced by the quantum bounce that presents a unitary evolution of considered gravitational system. Our results suggest that quantum general relativity is free from singularities.

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arXiv2018

Structures arising in the asymptotic dynamics of the Bianchi IX model

We present the analyses of the asymptotic evolution of the general Bianchi IX spacetime using Hamiltonian formulation. The dynamics reveals the existence of special structures, which we call wiggles, in the physical phase space. The wiggles are different from the spikes known in the context of evolution of some spacetime models towards gravitational singularities. Our results may be used as starting point in the examination of wiggles at the quantum level.

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arXiv2017

Dynamical structures specific to strong gravitational field: Quantum formalism

The dynamics of the general Bianchi IX spacetime, near the gravitational singularity, underlies the Belinskii, Khalatnikov and Lifshitz scenario. Asymptotically, near the singularity, the oscillations of the directional scale factors (defining the spacetime metric) are freezed so the evolution of the Bianchi IX model is devoid of chaotic features. However, it includes special structures, that we call the wiggles, which change their properties in the asymptotic regime. We propose the formalism, based on an affine quantization scheme, to examine the fate of the wiggles at the quantum level. We present the way of comparing the classical wiggles with their quantum counterparts. We expect that our work may contribute towards understanding some quantum aspects of the BKL scenario.

gr-qc↗

arXiv2015

Linearized nonequilibrium dynamics in nonconformal plasma

We investigate the behaviour of the lowest nonhydrodynamic modes in a class of holographic models which exhibit an equation of state closely mimicking the one determined from lattice QCD. We calculate the lowest quasinormal mode frequencies for a range of scalar self-interaction potentials and find that the damping of the quasinormal modes at the phase transition/crossover falls off by a factor of around two from conformality after factoring out standard conformal temperature dependence. The damping encoded in the imaginary part of the frequencies turns out to be correlated with the speed of sound and is basically independent of the UV details of the model. We also find that the dynamics of the nonhydrodynamic degrees of freedom remains ultralocal, even to a higher degree, as we deviate from conformality. These results indicate that the role of nonhydrodynamic degrees of freedom in the vicinity of the crossover transition may be enhanced.

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arXiv2014

Statistics of thermalization in Bjorken Flow

The apparent early thermalization of quark-gluon plasma produced at RHIC and LHC has motivated a number of studies of strongly coupled ${\mathcal N}=4$ supersymmetric Yang-Mills theory using the AdS/CFT correspondence. Here we present the results of numerical simulations of Bjorken flow aimed at establishing typical features of the dynamics. This is done by evolving a large number of far from equilibrium initial states well into the hydrodynamic regime. The results strongly suggest that early thermalization is generic in this theory, taking place at proper times around $0.6$ in units of inverse local temperature. We also find that the scale which determines the rate of hydrodynamic cooling is linearly correlated with the entropy of initial states defined by the area of the apparent horizon in the dual geometry. Our results also suggest that entropy production during the hydrodynamic stage of evolution is not negligible despite the low value of $η/s$.

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arXiv2013

On the gravity dual of strongly coupled charged plasma

Locally asymptotically AdS solutions of Einstein equations coupled with a vector field with a weakly curved boundary metric are found within the fluid-gravity gradient expansion up to second order in gradients. This geometry is dual to 1+3 dimensional hydrodynamics with a conserved current in a weakly curved background. The causal structure of the bulk geometry is determined and it is shown that the black brane singularity is shielded by an event horizon.

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arXiv2013

Entropy currents from holography in hydrodynamics with charge

The holographic interpretation of the hydrodynamic entropy current is developed for the case of hydrodynamics with a conserved charge. This is carried out within a framework developed in earlier work, which showed how to associate entropy currents with horizons in the dual geometry. The entropy current defined by the event horizon in the dual bulk geometry is calculated. It is also shown that to second order in the gradient expansion the dual geometry possesses a unique Weyl-invariant apparent horizon which also defines an admissable entropy current. At first order both currents coincide with the result obtained on the basis of a purely hydrodynamic analysis.

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arXiv2011

On the apparent horizon in fluid-gravity duality

This article develops a computational framework for determining the location of boundary-covariant apparent horizons in the geometry of conformal fluid-gravity duality in arbitrary dimensions. In particular, it is shown up to second order and conjectured to hold to all orders in the gradient expansion that there is a unique apparent horizon which is covariantly expressible in terms of fluid velocity, temperature and boundary metric. This leads to the first explicit example of an entropy current defined by an apparent horizon and opens the possibility that in the near-equilibrium regime there is preferred foliation of apparent horizons for black holes in asymptotically-AdS spacetimes.

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