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Papers by Jerzy Lewandowski

Physical review, Dec 28, 2020

All the Lie point symmetries of the near extremal horizon geometry equation, in the case of 4-dim... more 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.

Classical and Quantum Gravity, Aug 15, 2022

We start a systematic investigation of possible isometries of the asymptotically de Sitter soluti... more We start a systematic investigation of possible isometries of the asymptotically de Sitter solutions to Einstein equations. We reformulate the Killing equation as conformal equations for the initial data at mathcalI+\mathcal{I}^+mathcalI+. This allows for partial classification of possible symmetry algebras. In particular, if they are not maximal, they may be at most 444-dimensional. We provide several examples. As a simple collorary it is shown that the only spacetime in which the Killing horizon intersects mathcalI+\mathcal{I}^+mathcalI+ (after a conformal completion) is locally the de Sitter universe.

arXiv (Cornell University), May 20, 2013

Quantum theory of a scalar field is developed on the LQC Bianchi I space-time. By comparing the t... more Quantum theory of a scalar field is developed on the LQC Bianchi I space-time. By comparing the the quantum field theory for a single mode on classical and quantum background geometries we find that an effective Bianchi I space-time emerges. We show that by disregarding the back-reaction no Lorentz-violation is present, despite the effective metric being different than the classical Bianchi I one.

arXiv (Cornell University), Nov 15, 2021

It is well-known that blackhole and cosmological horizons in equilibrium situations are well-mode... more It is well-known that blackhole and cosmological horizons in equilibrium situations are well-modeled by non expanding horizons (NEHs) [1-3]. In the first part of the paper we introduce multipole moments to characterize their geometry, removing the restriction to axisymmetric situations made in the existing literature [4]. We then show that the symmetry group G of NEHs is a 1-dimensional extension of the BMS group B. These symmetries are used in a companion paper [5] to define charges and fluxes on NEHs, as well as perturbed NEHs. They have physically attractive properties. Finally, it is generally not appreciated that I ± of asymptotically flat space-times are NEHs in the conformally completed space-time. Forthcoming papers will (i) show that I ± have a small additional structure that reduces G to the BMS group B, and the BMS charges and fluxes can be recovered from the NEH framework; and, (ii) develop gravitational wave tomography for the late stage of compact binary coalescences: reading-off the dynamics of perturbed NEHs in the strong field regime (via evolution of their multipoles), from the waveform at I + .

Journal of High Energy Physics, Apr 1, 2015

In this addendum we clarify a point which strengthens one of the results from [1]. Namely, we sho... more In this addendum we clarify a point which strengthens one of the results from [1]. Namely, we show that the algebra of the observables F (r, θ) is yet simpler then it was described in [1]. This is an important point, because with this simplification an important subalgebra becomes canonical, allowing for a natural reduction of the phase space.

Physical Review D

In a previous article we have introduced an operator representing the three-dimensional scalar cu... more In a previous article we have introduced an operator representing the three-dimensional scalar curvature in loop quantum gravity. In this article we examine the new curvature operator in the setting of quantumreduced loop gravity. We derive the explicit form of the curvature operator as an operator on the Hilbert space of the quantum-reduced model. As a simple practical example, we study the expectation values of the operator with respect to basis states of the reduced Hilbert space.

arXiv (Cornell University), Feb 6, 2023

In this chapter we take up the quantum Riemannian geometry of a spatial slice of spacetime. While... more In this chapter we take up the quantum Riemannian geometry of a spatial slice of spacetime. While researchers are still facing the challenge of observing quantum gravity, there is a geometrical core to loop quantum gravity that does much to define the approach. This core is the quantum character of its geometrical observables: space and spacetime are built up out of Planck-scale quantum grains. The interrelations between these grains are described by spin networks, graphs whose edges capture the bounding areas of the interconnected nodes, which encode the extent of each grain. We explain how quantum Riemannian geometry emerges from two different approaches: in the first half of the chapter we take the perspective of continuum geometry and explain how quantum geometry emerges from a few principles, such as the general rules of canonical quantization of field theories, a classical formulation of general relativity in which it appears embedded in the phase space of Yang-Mills theory, and general covariance. In the second half of the chapter we show that quantum geometry also emerges from the direct quantization of the finite number of degrees of freedom of the gravitational field encoded in discrete geometries. These two approaches are complimentary and are offered to assist readers with different backgrounds enter the compelling arena of quantum Riemannian geometry.

arXiv (Cornell University), Feb 24, 2023

It is known that a source-free Yang-Mills theory with the normal conformal Cartan connection used... more It is known that a source-free Yang-Mills theory with the normal conformal Cartan connection used as the gauge potential gives rise to equations of motion equivalent to the vanishing of the Bach tensor. We investigate the conformally invariant presymplectic potential current obtained from this theory and find that on the solutions to the Einstein field equations, it can be decomposed into a topological term derived from the Euler density and a part proportional to the potential of the standard Einstein-Hilbert Lagrangian. The pullback of our potential to the asymptotic boundary of an asymptotically de Sitter spacetime turns out to coincide with the current obtained from the holographically renormalized gravitational action. This provides an alternative derivation of a symplectic structure on scri without resorting to holographic techniques. We also calculate our current at the null infinity of an asymptotically flat spacetime and in particular show that it vanishes for variations induced by the Bondi-Metzner-Sachs group of asymptotic symmetries. In addition, we calculate the Noether currents and charges corresponding to gauge transformations and diffeomorphisms.

Physical Review D

It is known that a source-free Yang-Mills theory with the normal conformal Cartan connection used... more It is known that a source-free Yang-Mills theory with the normal conformal Cartan connection used as the gauge potential gives rise to equations of motion equivalent to the vanishing of the Bach tensor. We investigate the conformally invariant presymplectic potential current obtained from this theory and find that on the solutions to the Einstein field equations, it can be decomposed into a topological term derived from the Euler density and a part proportional to the potential of the standard Einstein-Hilbert Lagrangian. The pullback of our potential to the asymptotic boundary of an asymptotically de Sitter spacetime turns out to coincide with the current obtained from the holographically renormalized gravitational action. This provides an alternative derivation of a symplectic structure on scri without resorting to holographic techniques. We also calculate our current at the null infinity of an asymptotically flat spacetime and in particular show that it vanishes for variations induced by the Bondi-Metzner-Sachs group of asymptotic symmetries. In addition, we calculate the Noether currents and charges corresponding to gauge transformations and diffeomorphisms.

General Relativity and Gravitation, 1997

]. All the details and other results are to be found in joint papers of the author with Abhay Ash... more ]. All the details and other results are to be found in joint papers of the author with Abhay Ashtekar.) The projective limit technics derived for spaces of connections are extended to a new framework which for the associated projective limit plays a role of the differential geometry. It provides us with powerfull technics for construction and studding various operators. In particular, we introduce the commutator algebra of `vector fields', define a divergence of a vector field and find for them a quantum representation. Among the vector fields, there are operators which we identify as regularised Rovelli-Smolin loop operators linear in momenta. Another class of operators which comes out naturally are Laplace operators.

General Relativity and Gravitation, 2005

Physics Letters A, 1987

ABSTRACT

Letters in Mathematical Physics, 1983

ABSTRACT

Journal of Geometry and Physics, 1990

4-dimensional Lorentzian geometries admitting a shearfree optical geometry are considered. Cartan... more 4-dimensional Lorentzian geometries admitting a shearfree optical geometry are considered. Cartan's chains defined on a 3-dimensional CR manifold are lifted to null curves. It is proved that all of them are geodesic iff the lCeyl tensor is of Petrov type N and the metric admits a twisting null conformal-Killing vector field. Such metrics are shown to be Fefferman's metries. In another case, there exist at most two congruences of null geodesic chains.

Classical and Quantum Gravity, 1992

ABSTRACT

Classical and Quantum Gravity, 1991

Classical and Quantum Gravity, 1991

ABSTRACT

Physical review, Dec 28, 2020

All the Lie point symmetries of the near extremal horizon geometry equation, in the case of 4-dim... more 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.

Classical and Quantum Gravity, Aug 15, 2022

We start a systematic investigation of possible isometries of the asymptotically de Sitter soluti... more We start a systematic investigation of possible isometries of the asymptotically de Sitter solutions to Einstein equations. We reformulate the Killing equation as conformal equations for the initial data at mathcalI+\mathcal{I}^+mathcalI+. This allows for partial classification of possible symmetry algebras. In particular, if they are not maximal, they may be at most 444-dimensional. We provide several examples. As a simple collorary it is shown that the only spacetime in which the Killing horizon intersects mathcalI+\mathcal{I}^+mathcalI+ (after a conformal completion) is locally the de Sitter universe.

arXiv (Cornell University), May 20, 2013

Quantum theory of a scalar field is developed on the LQC Bianchi I space-time. By comparing the t... more Quantum theory of a scalar field is developed on the LQC Bianchi I space-time. By comparing the the quantum field theory for a single mode on classical and quantum background geometries we find that an effective Bianchi I space-time emerges. We show that by disregarding the back-reaction no Lorentz-violation is present, despite the effective metric being different than the classical Bianchi I one.

arXiv (Cornell University), Nov 15, 2021

It is well-known that blackhole and cosmological horizons in equilibrium situations are well-mode... more It is well-known that blackhole and cosmological horizons in equilibrium situations are well-modeled by non expanding horizons (NEHs) [1-3]. In the first part of the paper we introduce multipole moments to characterize their geometry, removing the restriction to axisymmetric situations made in the existing literature [4]. We then show that the symmetry group G of NEHs is a 1-dimensional extension of the BMS group B. These symmetries are used in a companion paper [5] to define charges and fluxes on NEHs, as well as perturbed NEHs. They have physically attractive properties. Finally, it is generally not appreciated that I ± of asymptotically flat space-times are NEHs in the conformally completed space-time. Forthcoming papers will (i) show that I ± have a small additional structure that reduces G to the BMS group B, and the BMS charges and fluxes can be recovered from the NEH framework; and, (ii) develop gravitational wave tomography for the late stage of compact binary coalescences: reading-off the dynamics of perturbed NEHs in the strong field regime (via evolution of their multipoles), from the waveform at I + .

Journal of High Energy Physics, Apr 1, 2015

In this addendum we clarify a point which strengthens one of the results from [1]. Namely, we sho... more In this addendum we clarify a point which strengthens one of the results from [1]. Namely, we show that the algebra of the observables F (r, θ) is yet simpler then it was described in [1]. This is an important point, because with this simplification an important subalgebra becomes canonical, allowing for a natural reduction of the phase space.

Physical Review D

In a previous article we have introduced an operator representing the three-dimensional scalar cu... more In a previous article we have introduced an operator representing the three-dimensional scalar curvature in loop quantum gravity. In this article we examine the new curvature operator in the setting of quantumreduced loop gravity. We derive the explicit form of the curvature operator as an operator on the Hilbert space of the quantum-reduced model. As a simple practical example, we study the expectation values of the operator with respect to basis states of the reduced Hilbert space.

arXiv (Cornell University), Feb 6, 2023

In this chapter we take up the quantum Riemannian geometry of a spatial slice of spacetime. While... more In this chapter we take up the quantum Riemannian geometry of a spatial slice of spacetime. While researchers are still facing the challenge of observing quantum gravity, there is a geometrical core to loop quantum gravity that does much to define the approach. This core is the quantum character of its geometrical observables: space and spacetime are built up out of Planck-scale quantum grains. The interrelations between these grains are described by spin networks, graphs whose edges capture the bounding areas of the interconnected nodes, which encode the extent of each grain. We explain how quantum Riemannian geometry emerges from two different approaches: in the first half of the chapter we take the perspective of continuum geometry and explain how quantum geometry emerges from a few principles, such as the general rules of canonical quantization of field theories, a classical formulation of general relativity in which it appears embedded in the phase space of Yang-Mills theory, and general covariance. In the second half of the chapter we show that quantum geometry also emerges from the direct quantization of the finite number of degrees of freedom of the gravitational field encoded in discrete geometries. These two approaches are complimentary and are offered to assist readers with different backgrounds enter the compelling arena of quantum Riemannian geometry.

arXiv (Cornell University), Feb 24, 2023

It is known that a source-free Yang-Mills theory with the normal conformal Cartan connection used... more It is known that a source-free Yang-Mills theory with the normal conformal Cartan connection used as the gauge potential gives rise to equations of motion equivalent to the vanishing of the Bach tensor. We investigate the conformally invariant presymplectic potential current obtained from this theory and find that on the solutions to the Einstein field equations, it can be decomposed into a topological term derived from the Euler density and a part proportional to the potential of the standard Einstein-Hilbert Lagrangian. The pullback of our potential to the asymptotic boundary of an asymptotically de Sitter spacetime turns out to coincide with the current obtained from the holographically renormalized gravitational action. This provides an alternative derivation of a symplectic structure on scri without resorting to holographic techniques. We also calculate our current at the null infinity of an asymptotically flat spacetime and in particular show that it vanishes for variations induced by the Bondi-Metzner-Sachs group of asymptotic symmetries. In addition, we calculate the Noether currents and charges corresponding to gauge transformations and diffeomorphisms.

Physical Review D

It is known that a source-free Yang-Mills theory with the normal conformal Cartan connection used... more It is known that a source-free Yang-Mills theory with the normal conformal Cartan connection used as the gauge potential gives rise to equations of motion equivalent to the vanishing of the Bach tensor. We investigate the conformally invariant presymplectic potential current obtained from this theory and find that on the solutions to the Einstein field equations, it can be decomposed into a topological term derived from the Euler density and a part proportional to the potential of the standard Einstein-Hilbert Lagrangian. The pullback of our potential to the asymptotic boundary of an asymptotically de Sitter spacetime turns out to coincide with the current obtained from the holographically renormalized gravitational action. This provides an alternative derivation of a symplectic structure on scri without resorting to holographic techniques. We also calculate our current at the null infinity of an asymptotically flat spacetime and in particular show that it vanishes for variations induced by the Bondi-Metzner-Sachs group of asymptotic symmetries. In addition, we calculate the Noether currents and charges corresponding to gauge transformations and diffeomorphisms.

General Relativity and Gravitation, 1997

]. All the details and other results are to be found in joint papers of the author with Abhay Ash... more ]. All the details and other results are to be found in joint papers of the author with Abhay Ashtekar.) The projective limit technics derived for spaces of connections are extended to a new framework which for the associated projective limit plays a role of the differential geometry. It provides us with powerfull technics for construction and studding various operators. In particular, we introduce the commutator algebra of `vector fields', define a divergence of a vector field and find for them a quantum representation. Among the vector fields, there are operators which we identify as regularised Rovelli-Smolin loop operators linear in momenta. Another class of operators which comes out naturally are Laplace operators.

General Relativity and Gravitation, 2005

Physics Letters A, 1987

ABSTRACT

Letters in Mathematical Physics, 1983

ABSTRACT

Journal of Geometry and Physics, 1990

4-dimensional Lorentzian geometries admitting a shearfree optical geometry are considered. Cartan... more 4-dimensional Lorentzian geometries admitting a shearfree optical geometry are considered. Cartan's chains defined on a 3-dimensional CR manifold are lifted to null curves. It is proved that all of them are geodesic iff the lCeyl tensor is of Petrov type N and the metric admits a twisting null conformal-Killing vector field. Such metrics are shown to be Fefferman's metries. In another case, there exist at most two congruences of null geodesic chains.

Classical and Quantum Gravity, 1992

ABSTRACT

Classical and Quantum Gravity, 1991

Classical and Quantum Gravity, 1991

ABSTRACT