Searcharxiv⌕ Search

arXiv subjects

Jerzy Lewandowski

Publications and source records attributed to Jerzy Lewandowski.

At least 37 records · Page 2Linked to original sources
arXiv2022

Rainbow Black Hole From Quantum Gravitational Collapse

Quantum evolution of a scalar field's modes propagating on quantum spacetime of a collapsing homogeneous dust ball is written effectively, as an evolution of the same quantum modes on a (semiclassical) dressed geometry. When the backreaction of the field is discarded, the classical spacetime singularity is resolved due to quantum gravity effects and is replaced by a quantum bounce on the dressed collapse background. In the presence of backreaction, the emergent (interior) dressed geometry becomes mode dependent and the energy density associated with the backreaction of each mode scales as a radiation fluid. Semiclassical dynamics of this so-called {\em rainbow} dressed background is analyzed. It turns out that the backreaction effects speed up the occurrence of the bounce in comparison to the case where only a dust fluid is present. By matching the interior and exterior regions at the boundary of dust, a mode-dependent black hole geometry emerges as the exterior spacetime. Properties of such a rainbow black hole are discussed. That mode dependence causes, in particular, a chromatic aberration in the gravitational lensing process of which maximal magnitude is estimated via calculation of the so-called Einstein angle.

gr-qc↗
arXiv2022

Loop representation and r-Fock measures for $SU(N)$ gauge theories

In this article we continue the work on translating elements of the perturbative quantum field theory defined on Minkowski spacetime into the background independent framework of Loop Quantum Gravity. We present the construction of r-Fock measures for $SU(N)$ gauge theories and provide a relation between these new r-Fock measures and the difeomorphism invariant measure used in loop quantum gravity.

gr-qc↗
arXiv2022

Charges and Fluxes on (Perturbed) Non-expanding Horizons

In a companion paper we showed that the symmetry group $\mathfrak{G}$ of non-expanding horizons (NEHs) is a 1-dimensional extension of the Bondi-Metzner-Sachs group $\mathfrak{G}$ at $\mathcal{I}^{+}$. For each infinitesimal generator of $\mathfrak{G}$, we now define a charge and a flux on NEHs as well as perturbed NEHs. The procedure uses the covariant phase space framework in presence of internal null boundaries $\mathcal{N}$. However, $\mathcal{N}$ is required to be an NEH or a perturbed NEH. Consequently, charges and fluxes associated with generators of $\mathfrak{G}$ are free of physically unsatisfactory features that can arise if $\mathcal{N}$ is allowed to be a general null boundary. In particular, all fluxes vanish if $\mathcal{N}$ is an NEH, just as one would hope; and fluxes associated with symmetries representing `time-translations' are positive definite on perturbed NEHs. These results hold for zero as well as non-zero cosmological constant. In the asymptotically flat case, as noted in \cite{akkl1}, $\mathcal{I}^\pm$ are NEHs in the conformally completed space-time but with an extra structure that reduces $\mathfrak{G}$ to $\mathfrak{B}$. The flux expressions at $\mathcal{N}$ reflect this synergy between NEHs and $\mathcal{I}^{+}$. In a forthcoming paper, this close relation between NEHs and $\mathcal{I}^{+}$ will be used to develop gravitational wave tomography, enabling one to deduce horizon dynamics directly from the waveforms at $\mathcal{I}^{+}$.

gr-qc↗
arXiv2022

Extremal horizons stationary to the second order: new constraints

We consider non-expanding shear free (NE-SF) null surface geometries embeddable as extremal Killing horizons to the second order in Einstein vacuum spacetimes. A NE-SF null surface geometry consists of a degenerate metric tensor and a consistent torsion free covariant derivative. We derive the constraints implied by the existence of an embedding. The first constraint is well known as the near horizon geometry equation. The second constraint we find is new. The constraints lead to a complete characterization of those NE-SF null geometries that are embeddable in the extremal Kerr spacetime. Our results are also valid for spacetimes with a cosmological constant.

gr-qc↗
arXiv2021

Non-singular extension of the Kerr-NUT-(anti) de Sitter spacetimes

In 1963 Ezra Ted Newman and his two students Louis A. Tamburino, and Theodore W. J. Unti, proposed a deformation of the Shwarzschild spacetime that made it twisting. In the cosmological context, an equivalent solution had been found earlier, in 1951, by Abraham Haskel Taub. The problem that these solutions have is a conical singularity along the symmetry axis at all distances from the origin. In 1969 Misner proposed a non-singular interpretation of Taub-NUT spacetimes. We extend and refine his method to include a broader family of solutions and completely solve the outstanding issue of a non-singular extension of the Kerr-NUT- (anti) de Sitter solutions to Einstein's equations. Our approach relies on an observation that in 2 dimensional algebra of Killing vector fields there exist 2 distinguished vector fields that may be used to define $U(1)$-principal bundle structure over the non-singular spaces of non-null orbits. For all admissible parameters we derive appropriate Killing vector fields and discuss limits to spacetimes with less parameters. The global structure of spacetime, together with non-singular conformal geometry of the infinities is presented and (possibly also projectively non-singular) Killing horizons is presented.

gr-qc↗
arXiv2021

Axisymmetric, extremal horizons in the presence of a cosmological constant

All axisymmetric solutions to the near-horizon geometry equation with a cosmological constant defined on a topological $2$-sphere were derived. The regularity conditions preventing cone singularity at the poles were accounted for. The one-to-one correspondence of the solutions with the extremal horizons in the Kerr-(anti-)de Sitter spacetimes was found. A solution corresponding to the triply degenerate horizon was identified and characterized. The solutions were also identified among the solutions to the Petrov type D equation.

gr-qc↗
arXiv2021

Hamiltonian charges in the asymptotically de Sitter spacetimes

We generalize a notion of 'conserved' charges given by Wald and Zoupas to the asymptotically de Sitter spacetimes. Surprisingly, our construction is less ambiguous than the one encountered in the asymptotically flat context. An expansion around exact solutions possessing Killing vectors provides their physical meaning. In particular, we discuss a question of how to define energy and angular momenta of gravitational waves propagating on Kottler and Carter backgrounds. We show that obtained expressions have a correct limit as $Λ\to 0$. We also comment on the relation between this approach and the one based on the canonical phase space of initial data at $\mathcal{I}^+$.

gr-qc↗
arXiv2020

Projectively non-singular horizons in Kerr-NUT-de Sitter spacetimes

It was recently discovered that Killing horizons in the generic Kerr-NUT-(anti) de Sitter spacetimes are projectively singular, i.e. their spaces of the null generators have singular geometry. Only if the cosmological constant takes the special value determined by the Kerr and NUT parameters, and the radius of the horizon, then the corresponding horizon does not suffer that problem. In the current paper, the projectively non-singular horizons are investigated. They are found to be cosmological and non-extremal. Every projectively non-singular horizon can be used to define a global completion of the Kerr-NUT-de Sitter spacetime it is contained in. The resulting spacetime extends from $\mathcal{I}^-$ to $\mathcal{I}^+$, has the topology of $\mathbb{R}\times S_3$ and is smooth except for a possible Kerr-like singularity.

gr-qc↗
arXiv2020

Energy of gravitational radiation in the de Sitter universe at the scri and at a horizon

In this note we investigate outcomes of a symplectic formula for the gravitational waves charges in the general relativity linearized around the de Sitter spacetime. We derive their explicit form at {\it scri} in the Bondi frame, compare with the connected Noether expression and analyze their gauge dependence which allows us to fix unambiguously boundary terms. We also discuss minimal requirements needed to impose on initial data to have finite values of charges. Furthermore, we analyze transformation laws of the energy upon the action of the de Sitter group and discuss its physical interpretation. Finally, we calculate its flux through a cosmological horizon instead of {\it scri}. We show that in the limit $Λ\to 0$, one recovers Trautman--Bondi formula strengthening recent proposal that one should choose a~null surface as a more natural boundary for the astrophysical systems in the presence of the cosmological constant.

gr-qc↗
arXiv2020

Lie point symmetries of near-horizon geometry equation

All the Lie point symmetries of the near extremal horizon geometry equation, in the case of 4-dimensional Einstein vacuum spacetime with cosmological constant, are the diffeomorphisms of the space of the null generators of the horizon. This result is also generalised to the Maxwell-Einstein spacetime.

gr-qc↗
arXiv2020

Non-singular Kerr-NUT-de Sitter spacetimes

We study Killing horizons and their neighbourhoods in the Kerr-NUT-(anti-)de Sitter and the accelerated Kerr-NUT-(anti-)de Sitter spacetimes. The geometries of the horizons have an irremovable singularity at one of the poles, unless the parameters characterising the spacetimes satisfy the constraint we derive and solve in the current paper. In the Kerr-NUT-de Sitter case, the constraint relates the cosmological constant of spacetime and the horizon area, leaving 3 parameters free. In the accelerated case the acceleration becomes a 4th parameter that allows the cosmological constant to take arbitrary value, independently of the area. We find that the neighbourhoods of the non-singular horizons are non-singular too, at least in the non-extremal case. Finally, we compare the embedded horizons with previously unembedded horizons provided by the local theory of type D Killing horizons to the second order.

gr-qc↗
arXiv2020

Petrov type D equation on horizons of nontrivial bundle topology

We consider $3$-dimensional isolated horizons (IHs) generated by null curves that form nontrivial $U(1)$ bundles. We find a natural interplay between the IH geometry and the $U(1)$-bundle geometry. In this context we consider the Petrov type D equation introduced and studied in previous works \cite{DLP1,DLP2,LS,DKLS1}. From the $4$-dimensional spacetime point of view, solutions to that equation define isolated horizons embeddable in vacuum spacetimes (with cosmological constant) as Killing horizons to the second order such that the spacetime Weyl tensor at the horizon is of the Petrov type D. From the point of view of the $U(1)$-bundle structure, the equation couples a $U(1)$-connection, a metric tensor defined on the base manifold and the surface gravity in a very nontrivial way. We focus on the $U(1)$-bundles over $2$-dimensional manifolds diffeomorphic to $2$-sphere. We have derived all the axisymmetric solutions to the Petrov type D equation. For a fixed value of the cosmological constant they set a $3$-dimensional family as one could expect. A surprising result is, that generically our horizons are not embeddable in the known exact solutions to Einstein's equations. It means that among the exact type D spacetimes there exists a new family of spacetimes that generalize the properties of the Kerr- (anti) de Sitter black holes on one hand and the Taub-NUT spacetimes on the other hand.

gr-qc↗
arXiv2019

Towards the self-adjointness of a Hamiltonian operator in loop quantum gravity

Although the physical Hamiltonian operator can be constructed in the deparameterized model of loop quantum gravity coupled to a scalar field, its property is still unknown. This open issue is attacked in this paper by considering an operator $\hat{H}_v$ representing the square of the physical Hamiltonian operator acting nontrivially on two-valent spin networks. The Hilbert space $\mathcal{H}_v$ preserved by the graphing changing operator $\hat{H}_v$ is consist of spin networks with a single two-valent non-degenerate vertex. The matrix element of $\hat{H}_v$ are explicitly worked out in a suitable basis. It turns out that the operator $\hat{H}_v$ is essentially self-adjoint, which implies a well-defined physical Hamiltonian operator in $\mathcal{H}_v$ for the deparameterized model.

gr-qc↗
arXiv2019

Dressed metric predictions revisited

It was recently shown that the volume operator of loop quantum cosmology (LQC) and all its positive powers are ill-defined on physical states. In this paper, we investigate how it effects predictions of cosmic microwave background (CMB) power spectra obtained within dressed metric approach for which expectations values of $\hat{a}$ are the key element. We find that almost every step in the procedure is ill-defined and relies heavily upon a (seemingly premature) numerical truncation. Thus, it suggests that more care is needed in making predictions regarding pre-inflationary physics. We propose a new scheme which contains only well-defined quantities. The surprising agreement of the hitherto models with observational data, especially at low angular momenta $l$ is explained.

gr-qc↗
arXiv2019

Bouncing evolution in a model of loop quantum gravity

To understand the dynamics of loop quantum gravity, the deparametrized model of gravity coupled to a scalar field is studied in a simple case, where the graph underlying the spin network basis is one loop based at a single vertex. The Hamiltonian operator $\hat{H}_v$ is chosen to be graph-preserving, and the matrix elements of $\hat{H}_v$ are explicitly worked out in a suitable basis. The non-trivial Euclidean part $\hat{H}_v^E$ of $\hat{H}_v$ is studied in details. It turns out that by choosing a specific symmetrization of $\hat{H}_v^E$, the dynamics driven by the Hamiltonian gives a picture of bouncing evolution. Our result in the model of full loop quantum gravity gives a significant echo of the well-known quantum bounce in the symmetry-reduced model of loop quantum cosmology, which indicates a closed relation between singularity resolution and quantum geometry.

gr-qc↗
arXiv2018

Spacetime near Kerr isolated horizon

The theory of isolated horizon provides a quasi-local framework to study the spacetime geometry in the neighbourhood of the horizon of a black hole in equilibrium without any reference to structures far away from the horizon. While the geometric properties of the Kerr-(A)dS and more general algebraically special solutions have drawn substantial interest recently in the isolated horizon formalism, their horizon metrics have never been written down explicitly in the adapted Bondi-like coordinate system. Following the approach by Krishnan and assuming that the horizon symmetry extends to certain order in the bulk, we present in this note a general method to compute the metric functions order by order radially in Bondi-like coordinates in 4-dimensions from a small set of intrinsic data -- the connection and the Newman-Penrose spin coefficient $π$ specified on the horizon cross-section. Applying this general method, we then present the horizon metric of non-extremal Kerr-dS in Bondi-like coordinates. For the pure Kerr case without a cosmological constant, we also show explicitly the metric functions to the first order.

gr-qc↗
arXiv2018

Quantum Reference Frames via Transition Amplitudes in Timeless Quantum Gravity

We propose an algorithm of extracting Schrödinger theories under all viable physical time from the Einstein-Hilbert path integral, formulated as the timeless transition amplitudes $\hat{\mathbb{P}}:\mathbb{K} \to \mathbb{K}^*$ between the boundary states in a kinematic Hilbert space $\mathbb{K}$. Each of these Schrödinger theories refers to a certain set of quantum degrees of freedom in $\mathbb{K}$ as a background, with their given values specifying moments of the physical time. Restricted to these specified background values, the relevant elements of $\hat{\mathbb{P}}$ are transformed by the algorithm into the unitary propagator of a corresponding reduced phase space Schrödinger theory. The algorithm embodies the fundamental principle of quantum Cauchy surfaces, such that all the derived Schrödinger theories emerge from one timeless canonical theory defined by $\hat{\mathbb{P}}$ as a rigging map, via the relational Dirac observables referring to the corresponding backgrounds. We demonstrate its application to a FRW loop quantum cosmological model with a massless Klein-Gordon scalar field. Recovering the famous singularity-free quantum gravitational dynamics with the background of the scalar field, we also obtain in another reference frame a modified Klein-Gordon field quantum dynamics with the background of the spatial (quantum) geometry.

gr-qc↗