Holographic is Hamiltonian, relatively
We show that a relative holographic energy coincides with the relative Hamiltonian energy.
gr-qc↗
arXiv subjects
Piotr T. Chruściel
Publications and source records attributed to Piotr T. Chruściel.
Static vacuum metrics in (4 + 1) dimensions with Λ < 0 and squashed conformal infinity
We construct numerically two families of static five-dimensional Lorentzian metrics, solutions of vacuum Einstein equations with a negative cosmological constant, one with and one without a black hole region, with a metric at sections of conformal infinity which is conformal to any squashed three-dimensional sphere.
gr-qc↗
Positivity of holographic energy
We prove positivity of a weighted holographic energy for four-dimensional spacetimes with negative cosmological constant whose conformal boundary at infinity is conformally static and admits either spherical sections, or toroidal sections with compatible spin structure.
gr-qc↗
The hyperbolic positive energy theorem
We show that the causal-future-directed character of the energy-momentum vector of $n$-dimensional asymptotically hyperbolic Riemannian manifolds with spherical conformal infinity, $n\ge 3$, can be traced back to that of asymptotically Euclidean general-relativistic initial data sets satisfying the dominant energy condition.
math.DG↗
Who's afraid of a negative lapse?
We rederive the Arnowitt-Deser-Misner equations in a framework in which the zeros of the lapse are innocuous, whether with or without changes of sign. We further develop and analyse a covariantized version of the Anderson-York equations, which provide a well posed system of tensorial evolution equations with freely prescribable shift vector and densitised lapse. The causality properties of the resulting equations are explored. We show how to relate solutions of the Anderson-York equations to the maximal globally hyperbolic development of the initial data.
gr-qc↗
Characteristic Gluing with $Λ$: III. High-differentiability nonlinear gluing
We prove a nonlinear characteristic $C^k$-gluing theorem for vacuum gravitational fields in Bondi gauge for a class of characteristic hypersurfaces near static vacuum $n$-dimensional backgrounds, $n\ge 3$, with any finite $k$, with cosmological constant $ Λ\in \mathbb{R}$, near Birmingham-Kottler backgrounds. This generalises the $C^2$-gluing of Aretakis, Czimek and Rodnianski, carried-out near light cones in four-dimensional Minkowski spacetime.
gr-qc↗
Kerr-AdS type higher dimensional black holes with non-spherical cross-sections of horizons
We construct, in even spacetime dimensions, a family of singularity-free Kerr-Anti-de Sitter-like black holes with negatively curved cross-sections of conformal infinity and non-spherical cross-sections of horizons.
gr-qc↗
50-km fiber interferometer for testing gravitational signatures in quantum interference
Quantum mechanics and general relativity are the foundational pillars of modern physics, yet experimental tests that combine the two frameworks remain rare. Measuring optical phase shifts of massless photons in a gravitational potential provides a unique quantum platform to probe gravity beyond Newtonian descriptions, but laboratory-based interferometers have not yet reached the sensitivity needed to access this regime. Here, we report the realization of a 50-km table-top Mach-Zehnder fiber interferometer operating at the single-photon level, achieving a phase sensitivity of $4.42\times10^{-6}$ rad root-mean-square (RMS) within the frequency range of 0.01 Hz to 5 Hz. We demonstrate that this sensitivity is sufficient to resolve a phase-shift signal of $(6.18 \pm 0.44)\times10^{-5}$ rad RMS at 0.1 Hz, associated with a modulated gravity-induced signal. Our results establish a milestone for quantum sensing with large-scale optical interferometry, demonstrating the capability to detect gravitational redshifts in a local laboratory, thereby paving the way for testing quantum phenomena within general relativistic frameworks.
quant-ph↗
Cauchy problems for Einstein equations in three-dimensional spacetimes
We analyze existence and properties of solutions of two-dimensional general relativistic initial data sets with a negative cosmological constant, both on spacelike and characteristic surfaces. A new family of such vacuum, spacelike data parameterised by poles at the conformal boundary at infinity is constructed. We review the notions of global Hamiltonian charges, emphasising the difficulties arising in this dimension, both in a spacelike and characteristic setting. One or two, depending upon the topology, lower bounds for energy in terms of angular momentum, linear momentum, and center of mass are established.
gr-qc↗
Elastically induced phase-shift and birefringence in optical fibers
We compute how elastic deformations of optical fibers affect light propagation therein. Specifically, we consider differences in wave-guiding properties of straight fibers subject to different external temperatures, pressures, and gravitational fields. This is done by solving, perturbatively to first order, the Maxwell equations in deformed and anisotropic fibers using a multiple-scales approximation scheme. We derive explicit expressions for the induced phase shift and birefringence. The phase shift can be expressed in terms of the average radial pressure, longitudinal tension, and change in temperature, while birefringence depends on the quadrupole of the external pressure distribution and the stresses on the axis of the fiber.
physics.optics↗
Thomas-Wigner rotation via Clifford algebras
We derive Macfarlane's formula for the Thomas-Wigner angle of rotation using Clifford-algebra methods. The presentation is pedagogical and elementary, suitable for students with some basic knowledge of special relativity; no prior knowledge of Clifford algebras is required.
math-ph↗
A Bogovskiǐ-type operator for Corvino-Schoen hyperbolic gluing
We construct a solution operator for the linearized constant scalar curvature equation at hyperbolic space in space dimension larger than or equal to two. The solution operator has good support propagation properties and gains two derivatives relative to standard norms. It can be used for Corvino-Schoen-type hyperbolic gluing, partly extending the recently introduced Mao-Oh-Tao gluing method to the hyperbolic setting.
gr-qc↗
Gluing-at-infinity of two-dimensional asymptotically locally hyperbolic manifolds
We review notions of mass of asymptotically locally Anti-de Sitter three-dimensional spacetimes, and apply them to some known solutions. For two-dimensional general relativistic initial data sets the mass is not invariant under asymptotic symmetries, but a unique mass parameter can be obtained either by minimisation, or by a monodromy construction, or both. We give an elementary proof of positivity, and of a Penrose-type inequality, in a natural gauge. We apply the "Maskit gluing construction" to time-symmetric asymptotically locally hyperbolic vacuum initial data sets and derive mass/entropy formulae for the resulting manifolds. Finally, we show that all mass aspect functions can be realised by constant scalar curvature metrics on complete manifolds which are smooth except for at most one conical singularity.
gr-qc↗
Characteristic Gluing with $Λ$ 1. Linearised Einstein equations on four-dimensional spacetimes
We establish a gluing theorem for linearised vacuum gravitational fields in Bondi gauge on a class of characteristic surfaces in static vacuum four-dimensional backgrounds with cosmological constant $Λ\in \mathbb{R}$ and arbitrary topology of the compact cross-sections of the null hypersurface. This generalises and complements, in the linearised case, the pioneering analysis of Aretakis, Czimek and Rodnianski, carried-out on light-cones in Minkowski spacetime.
gr-qc↗
Characteristic Gluing with $Λ$: II. Linearised equations in higher dimensions
We prove a gluing theorem for linearised vacuum gravitational fields in Bondi gauge on a class of characteristic hypersurfaces in static vacuum $(n+1)$-dimensional backgrounds with cosmological constant $ Λ\in \mathbb{R}$, $n\ge 4$. This generalises, in the linearised case, the pioneering analysis of Aretakis, Czimek and Rodnianski, carried-out on light cones in four-dimensional Minkowski spacetime.
gr-qc↗
On elastic deformations of cylindrical bodies under the influence of the gravitational field
We analyse the deformations of a cylindrical elastic body resulting from displacements in a varying gravitational field.
gr-qc↗
Asymptotic flatness in higher dimensions
We show that $(n+1)$-dimensional Myers-Perry metrics, $n\geq4$, have a conformal completion at spacelike infinity of $C^{n-3,1}$ differentiability class, and that the result is optimal in even spacetime dimensions. The associated asymptotic symmetries are presented.
gr-qc↗
On staticity of bifurcate Killing horizons
We show that bifurcate Killing horizons with closed torsion form, in spacetimes of arbitrary dimension satisfying a Ricci-structure condition, arise from static Killing vectors. The result applies in particular to $Λ$-vacuum spacetimes.
gr-qc↗