A New Family of Gauges in Linearized General Relativity

For vacuum Maxwell theory in four dimensions, a supplementary condition exists (due to Eastwood and Singer) which is invariant under conformal rescalings of the metric, in agreement with the conformal symmetry of the Maxwell equations. Thus, starting from the de Donder gauge, which is not conformally invariant but is the gravitational counterpart of the Lorenz gauge, one can consider, led by formal analogy, a new family of gauges in general relativity, which involve fifth-order covariant derivatives of metric perturbations. The admissibility of such gauges in the classical theory is first proven in the cases of linearized theory about flat Euclidean space or flat Minkowski space-time. In the former, the general solution of the equation for the fulfillment of the gauge condition after infinitesimal diffeomorphisms involves a 3-harmonic 1-form and an inverse Fourier transform. In the latter, one needs instead the kernel of powers of the wave operator, and a contour integral. The analysis is also used to put restrictions on the dimensionless parameter occurring in the DeWitt supermetric, while the proof of admissibility is generalized to a suitable class of curved Riemannian backgrounds. Eventually, a non-local construction is obtained of the tensor field which makes it possible to achieve conformal invariance of the above gauges.Comment: 28 pages, plain Tex. In the revised version, sections 4 and 5 are completely ne

Conformally invariant bending energy for hypersurfaces

The most general conformally invariant bending energy of a closed four-dimensional surface, polynomial in the extrinsic curvature and its derivatives, is constructed. This invariance manifests itself as a set of constraints on the corresponding stress tensor. If the topology is fixed, there are three independent polynomial invariants: two of these are the straighforward quartic analogues of the quadratic Willmore energy for a two-dimensional surface; one is intrinsic (the Weyl invariant), the other extrinsic; the third invariant involves a sum of a quadratic in gradients of the extrinsic curvature -- which is not itself invariant -- and a quartic in the curvature. The four-dimensional energy quadratic in extrinsic curvature plays a central role in this construction.Comment: 16 page

Vacuum polarization in Schwarzschild space-time by anomaly induced effective actions

The characteristic features of $$ in the Boulware, Unruh and Hartle-Hawking states for a conformal massless scalar field propagating in the Schwarzschild space-time are obtained by means of effective actions deduced by the trace anomaly. The actions are made local by the introduction of auxiliary fields and boundary conditions are carefully imposed on them in order to select the different quantum states.Comment: 20 pages, latex; misprints corrected and references adde

Logarithmic correction to BH entropy as Noether charge

We consider the role of the type-A trace anomaly in static black hole solutions to semiclassical Einstein equation in four dimensions. Via Wald's Noether charge formalism, we compute the contribution to the entropy coming from the anomaly induced effective action and unveil a logarithmic correction to the Bekenstein-Hawking area law. The corrected entropy is given by a seemingly universal formula involving the coefficient of the type-A trace anomaly, the Euler characteristic of the horizon and the value at the horizon of the solution to the uniformization problem for Q-curvature. Two instances are examined in detail: Schwarzschild and a four-dimensional massless topological black hole. We also find agreement with the logarithmic correction due to one-loop contribution of conformal fields in the Schwarzschild background.Comment: 14 pages, JHEP styl

Quantum Interaction ϕ44\phi^4_4: the Construction of Quantum Field defined as a Bilinear Form

We construct the solution $\phi(t,{\bf x})$ of the quantum wave equation $\Box\phi + m^2\phi + \lambda:\!\!\phi^3\!\!: = 0$ as a bilinear form which can be expanded over Wick polynomials of the free $in$-field, and where $:\!\phi^3(t,{\bf x})\!:$ is defined as the normal ordered product with respect to the free $in$-field. The constructed solution is correctly defined as a bilinear form on $D_{\theta}\times D_{\theta}$, where $D_{\theta}$ is a dense linear subspace in the Fock space of the free $in$-field. On $D_{\theta}\times D_{\theta}$ the diagonal Wick symbol of this bilinear form satisfies the nonlinear classical wave equation.Comment: 32 pages, LaTe

Causal structures and causal boundaries

We give an up-to-date perspective with a general overview of the theory of causal properties, the derived causal structures, their classification and applications, and the definition and construction of causal boundaries and of causal symmetries, mostly for Lorentzian manifolds but also in more abstract settings.Comment: Final version. To appear in Classical and Quantum Gravit

Building a successful minimally invasive mitral valve repair program before introducing the robotic approach: The Massachusetts General Hospital experience

BackgroundPatients with mitral valve prolapse (MVP) requiring surgical repair (MVr) are increasingly operated using minimally invasive strategies. Skill acquisition may be facilitated by a dedicated MVr program. We present here our institutional experience in establishing minimally invasive MVr (starting in 2014), laying the foundation to introduce robotic MVr.MethodsWe reviewed all patients that had undergone MVr for MVP via sternotomy or mini-thoracotomy between January 2013 and December 2020 at our institution. In addition, all cases of robotic MVr between January 2021 and August 2022 were analyzed. Case complexity, repair techniques, and outcomes are presented for the conventional sternotomy, right mini-thoracotomy and robotic approaches. A subgroup analysis comparing only isolated MVr cases via sternotomy vs. right mini-thoracotomy was conducted using propensity score matching.ResultsBetween 2013 and 2020, 799 patients were operated for native MVP at our institution, of which 761 (95.2%) received planned MVr (263 [34.6%] via mini-thoracotomy) and 38 (4.8%) received planned MV replacement. With increasing proportions of minimally invasive procedures (2014: 14.8%, 2020: 46.5%), we observed a continuous growth in overall institutional volume of MVP (n = 69 in 2013; n = 127 in 2020) and markedly improved institutional rates of successful MVr, with 95.4% in 2013 vs. 99.2% in 2020. Over this period, a higher complexity of cases were treated minimally-invasively and increased use of neochord implantation ± limited leaflet resection was observed. Patients operated minimally invasively had longer aortic cross-clamp times (94 vs. 88 min, p = 0.001) but shorter ventilation times (4.4 vs. 4.8 h, p = 0.002) and hospital stays (5 vs. 6 days, p < 0.001) than those operated via sternotomy, with no significant differences in other outcome variables. A total of 16 patients underwent robotically assisted MVr with successful repair in all cases.ConclusionA focused approach towards minimally invasive MVr has transformed the overall MVr strategy (incision; repair techniques) at our institution, leading to a growth in MVr volume and improved repair rates without significant complications. On this foundation, robotic MVr was first introduced at our institution in 2021 with excellent outcomes. This emphasizes the importance of building a competent team to perform these challenging operations, especially during the initial learning curve