Annales Henri Poincaré最新文献

We investigate the interior of a dynamical black hole as described by the Einstein–Maxwell-charged-Klein–Gordon system of equations with a cosmological constant, under spherical symmetry. In particular, we consider a characteristic initial value problem where, on the outgoing initial hypersurface, interpreted as the event horizon (mathcal {H}^+) of a dynamical black hole, we prescribe: (a) initial data asymptotically approaching a fixed sub-extremal Reissner–Nordström–de Sitter solution and (b) an exponential Price law upper bound for the charged scalar field. After showing local well-posedness for the corresponding first-order system of partial differential equations, we establish the existence of a Cauchy horizon (mathcal{C}mathcal{H}^+) for the evolved spacetime, extending the bootstrap methods used in the case (Lambda = 0) by Van de Moortel (Commun Math Phys 360:103–168, 2018. https://doi.org/10.1007/s00220-017-3079-3). In this context, we show the existence of (C^0) spacetime extensions beyond (mathcal{C}mathcal{H}^+). Moreover, if the scalar field decays at a sufficiently fast rate along (mathcal {H}^+), we show that the renormalized Hawking mass remains bounded for a large set of initial data. With respect to the analogous model concerning an uncharged and massless scalar field, we are able to extend the known range of parameters for which mass inflation is prevented, up to the optimal threshold suggested by the linear analyses by Costa–Franzen (Ann Henri Poincaré 18:3371–3398, 2017. https://doi.org/10.1007/s00023-017-0592-z) and Hintz–Vasy (J Math Phys 58(8):081509, 2017. https://doi.org/10.1063/1.4996575). In this no-mass-inflation scenario, which includes near-extremal solutions, we further prove that the spacetime can be extended across the Cauchy horizon with continuous metric, Christoffel symbols in (L^2_{text {loc}}) and scalar field in (H^1_{text {loc}}). By generalizing the work by Costa–Girão–Natário–Silva (Commun Math Phys 361:289–341, 2018. https://doi.org/10.1007/s00220-018-3122-z) to the case of a charged and massive scalar field, our results reveal a potential failure of the Christodoulou–Chruściel version of the strong cosmic censorship under spherical symmetry.

We give a simple and self-contained construction of the (P(Phi )) Euclidean quantum field theory in the plane and verify the Osterwalder–Schrader axioms: translational and rotational invariance, reflection positivity and regularity. In the intermediate steps of the construction, we study measures on spheres. In order to control the infinite volume limit, we use the parabolic stochastic quantization equation and the energy method. To prove the translational and rotational invariance of the limit measure, we take advantage of the fact that the symmetry groups of the plane and the sphere have the same dimension.

The spherical Sherrington–Kirkpatrick (SSK) model and its bipartite analog both exhibit the phenomenon that their free energy fluctuations are asymptotically Gaussian at high temperature but asymptotically Tracy–Widom at low temperature. This was proved in two papers by Baik and Lee, for all non-critical temperatures. The case of the critical temperature was recently computed for the SSK model in two separate papers, one by Landon and the other by Johnstone, Klochkov, Onatski, Pavlyshyn. In the current paper, we derive the critical temperature result for the bipartite SSK model. In particular, we find that the free energy fluctuations exhibit a transition when the temperature is in a window of size (n^{-1/3}sqrt{log n}) around the critical temperature, the same window as for the SSK model. Within this transitional window, the asymptotic fluctuations of the free energy are the sum of independent Gaussian and Tracy–Widom random variables.

We study the Schrödinger operator describing a two-dimensional quantum particle moving in the presence of ( N geqslant 1) Aharonov–Bohm magnetic fluxes. We classify all the self-adjont realizations of such an operator, providing an explicit characterization of their domains and actions. Moreover, we examine their spectral and scattering properties, proving in particular the existence and completeness of wave operators in relation with the free dynamics.

We introduce a dually-weighted multi-matrix model that for a suitable choice of weights reproduce two-dimensional Causal Dynamical Triangulations (CDT) coupled to the Ising model. When Ising degrees of freedom are removed, this model corresponds to the CDT-matrix model introduced by Benedetti and Henson (Phys Lett B 678:222, 2009). We present exact as well as approximate results for the Gaussian averages of characters of a Hermitian matrix A and (A^2) for a given representation and establish the present limitations that prevent us to solve the model analytically. This sets the stage for the formulation of more sophisticated matter models coupled to two-dimensional CDT as dually weighted multi-matrix models providing a complementary view to the standard simplicial formulation of CDT-matter models.

In this paper we make a detailed analysis of conservation principles in the context of a family of fourth-order gravitational theories generated via a quadratic Lagrangian. In particular, we focus on the associated notion of energy and start a program related to its study. We also exhibit examples of solutions which provide intuitions about this notion of energy which allows us to interpret it, and introduce several study cases where its analysis seems tractable. Finally, positive energy theorems are presented in restricted situations.

While it has become widely appreciated that (higher) gauge theories need, besides their variational phase space data, to be equipped with “flux quantization laws” in generalized differential cohomology, there used to be no general prescription for how to define and construct the resulting flux-quantized phase space stacks. In this short note, we observe that all higher Maxwell-type equations have solution spaces given by flux densities on a Cauchy surface subject to a higher Gauß law and no further constraint: The metric duality-constraint is all absorbed into the evolution equation away from the Cauchy surface. Moreover, we observe that the higher Gauß law characterizes the Cauchy data as flat differential forms valued in a characteristic (L_infty )-algebra. Using the recent construction of the non-abelian Chern–Dold character map, this implies that compatible flux quantization laws on phase space have classifying spaces whose rational Whitehead (L_infty )-algebra is this characteristic one. The flux-quantized higher phase space stack of the theory is then simply the corresponding (generally non-abelian) differential cohomology moduli stack on the Cauchy surface. We show how this systematic prescription reproduces existing proposals for flux-quantized phase spaces of vacuum Maxwell theory and of the chiral boson and its higher siblings, but reveals that there are other choices of (non-abelian) flux quantization laws even in these basic cases, further discussed in a companion article (Sati and Schreiber in Quantum observables on quantized fluxes. arXiv:2312.13037). Moreover, for the case of NS/RR-fields in type II supergravity/string theory, the traditional “Hypothesis K” of flux quantization in topological K-theory is naturally implied, without the need, on phase space, of the notorious further duality constraint. Finally, as a genuinely non-abelian example we consider flux quantization of the C-field in 11d supergravity/M-theory given by unstable differential 4-Cohomotopy (“Hypothesis H”) and emphasize again that, implemented on Cauchy data, this qualifies as the full phase space without the need for a further duality constraint.

We show that for a unitary modular invariant 2D CFT with central charge (c>1) and having a nonzero twist gap in the spectrum of Virasoro primaries, for sufficiently large spin J, there always exist spin-J operators with twist falling in the interval ((frac{c-1}{12}-varepsilon ,frac{c-1}{12}+varepsilon )) with (varepsilon =O(J^{-1/2}log J)). We establish that the number of Virasoro primary operators in such a window has a Cardy-like, i.e., (exp left( 2pi sqrt{frac{(c-1)J}{6}}right) ) growth. A similar result is proven for a family of holographic CFTs with the twist gap growing linearly in c and a uniform boundedness condition, in the regime (Jgg c^3gg 1). From the perspective of near-extremal rotating BTZ black holes (without electric charge), our result is valid when the Hawking temperature is much lower than the “gap temperature.”