Papers

In this paper, we generalize the covariant phase space formalism conjugate to field dependent vectors to include internal gauge transformations when gauge fields are present. In our formalism, the symmetry generators are combination of diffeomorphisms plus internal gauge transformations and depend on the field configuration. When the field dependence of the symmetry generators is considered in the covariant phase space formalism, the first law of black hole thermodynamics is a direct result for generally invariant gravitational theories. To check the validity of our formalism, we investigate the conserved charges and the first laws of thermodynamics for a torus-like black hole in Einstein-Maxwell theory and a charged Einstein-Euler-Heisenberg AdS black hole in Einstein-Euler-Heisenberg nonlinear electrodynamics.

This paper investigates a self-consistent effective-one-body (EOB) theory developed to describe the dynamics of spinning binary systems. We systematically derive, using field-theoretic principles, all expressions and quantities entering Hamilton's equations, which govern the dynamical evolution of the system. Based on the effective rotating metric up to fifth post-Minkowskian (PM) order recently obtained by us, we construct the Hamiltonian and the stress-energy tensor. We then derive a decoupled, separable Teukolsky-like equation with a source term for the Newman–Penrose Weyl scalar $\psi_4^B$ and present its formal solution. Finally, using this solution, we obtain the energy flux, radiation-reaction force, and gravitational waveforms for the “plus” and “cross” polarizations generated by spinning binaries. The EOB theory applies to systems with arbitrary mass ratio, which filling the gap between comparable mass ratios and extreme mass ratios.

We show, analytically, that a static sine-Gordon soliton cannot exist in 1 + 1 non-dynamical de Sitter spacetime if $\alpha := (m/H)^2 < 2$, where $m$ is the mass parameter of the sine-Gordon theory and $H$ is the Hubble constant. Conversely, we also show that static sine-Gordon solitons exist in 1 + 1 non-dynamical de Sitter spacetime if $\alpha > 2$. The above threshold is explained—qualitatively and to within an O(1) factor—using a heuristic argument involving the interplay of tensile force in the Lorentzian sine-Gordon soliton and the tidal force in de Sitter spacetime. A similar heuristic argument, which remains to be confirmed analytically, also suggests the existence of a threshold, $ (m_V/H)^2 \sim O(1)$, below which the tidal forces are too strong to permit the existence of a static `t Hooft–Polyakov monopole in non-dynamical 3 + 1 de Sitter spacetime; $m_V$ is the mass of the vector boson. Linde has suggested that new inflation could have triggered secondary inflation at the core of a GUT (Grand Unified Theory) monopole even if the Hubble constant at or after the GUT phase transition was significantly smaller than the mass of the $X$ boson. We present a heuristic argument, which suggests that the $SO(3)$ `t Hooft–Polyakov monopole does not allow secondary inflation at its core when the inflationary background is weak. Based on the above, as yet analytically unconfirmed, heuristic argument for the $SO(3)$ `t Hooft–Polyakov monopole, we conjecture that secondary inflation at the core of a GUT monopole is infeasible.

We construct gauge-covariant unintegrated vertex operators in an antighost-independent subcomplex of the bosonic ambitwistor string. For a linearized gauge field, a world-sheet ghost-derivative term completes the standard vertex so that BRST closure imposes $\p^nF_{nmI}=0$ without the Lorenz condition. In the rank-two sector we use an antighost-free ansatz that is sufficient to isolate a diffeomorphism-invariant spin-two subsector. After eliminating auxiliary fields and consistently setting the antisymmetric and scalar combinations to zero, BRST closure gives $R_{mn}=0$ without imposing transversality. We distinguish this construction from the full relative BRST cohomology of the bosonic ambitwistor string, whose additional antighost-dependent states lead to the known higher-derivative spectrum.

A conventional interaction-driven Weyl density wave is a complex scalar and supports vortex lines, but no topologically stable point defects. We show that two Weyl flavors do not merely duplicate this order. Starting from the matrix-valued internode coherence, a local flavor-symmetric repulsion selects a traceless adjoint condensate within the density-wave sector, while the fermionic ground-state energy locks its complex components into the collinear form $\mathbf{\Delta}=\Phi_0\mathbf{n} e^{i\theta}$. The resulting order-parameter manifold, $(S^2\times S^1)/\mathbb Z_2$, supports both unit hedgehogs and half-quantum Alice strings of the same electronic mass that gaps the Weyl fermions. An elementary hedgehog binds a single normalizable zero mode whose empty and occupied sectors carry charges $-e/2$ and $+e/2$ at neutrality. An elementary Alice string carries a single chiral electronic mode despite its $\pi$ phase winding, and transporting a hedgehog around it reverses the hedgehog winding, $N\rightarrow-N$. Flavor therefore converts spontaneous translation breaking into a route to point-defect fractionalization and intertwines the point- and line-defect sectors of an interaction-generated electronic mass.

We investigate the maximal total quantum dimension at a bounded categorical rank cutoff $R$ in three-dimensional Dijkgraaf–Witten theories. This optimization problem physically governs the maximal state-optimized torus topological entanglement entropy at a fixed torus ground-state degeneracy, while providing a quantitative constraint on the search space required to classify these topological order phases. We analyze how topological twists (3-cocycles) and gauge-group structures independently govern this trade-off. For elementary-Abelian gauge groups at a fixed prime $p$, we prove that introducing cocycle twists elevates the maximum total quantum dimension from square-root growth $\Theta_p(R^{1/2})$ to linear growth $\Theta_p(R)$ in the rank cutoff, driven by the geometric protection of cyclic holonomies. For untwisted theories, we establish sharp envelopes for symmetric and alternating gauge groups, and derive group-theoretic bounds across almost-simple, solvable, and radical-free families. In particular, almost-simple groups and their direct products obey a quadratic-logarithmic upper envelope: $\log\mathcal{D} = O((\log R)^2)$. Finally, we compare these scales against WZW models and discuss the status of the general quadratic-logarithmic envelope conjecture.

We develop a non-Abelian Hodge-theoretic refinement of asymptotic limits in type-$A$ class-$\mathcal S$ theories, enriching the geometric description of the degenerating UV curve with gauge-theoretic data encoded by the associated Hitchin system. A degeneration of the UV curve produces a long plumbing tube, which we equip with the local monodromy data of a Hitchin-Simpson flat connection admitting a regular-singular logarithmic model. The semisimple and unipotent parts of the monodromy govern, respectively, the power-law and logarithmic growth of flat sections through the tube. Combining this non-Abelian holonomy with the geometric Picard-Lefschetz monodromy yields a decorated cusp label that incorporates Higgs-bundle information and extends tube-wise to intersections of boundary divisors. For each tube, we require the weak gauge algebra specified by the fixture and gluing data to lie in the reductive monodromy centralizer. In type $A$, we organize the local monodromy labels into discrete types specified by the eigenspace multiplicities of the semisimple part and the Jordan type of the nilpotent logarithm of the unipotent part. Finally, we illustrate the construction for $SL(3,\mathbb C)$ on the four-punctured sphere and $SL(4,\mathbb C)$ on the two-punctured torus.

We study the high-temperature vacua of the Standard Model from the perspective of generalized symmetries and the global structure of the gauge group. We analyze the one-loop effective potential for Polyakov loop holonomies, incorporating the gauge identifications induced by gauging discrete subgroups of the electric one-form symmetry. This provides a classification of physically inequivalent vacua for each gauge-group quotient. We further comment on the effects of additional center-charged matter on the residual one-form symmetry and the vacuum structure.

Motivated by the anticipated data rates of the high-luminosity phase of the Large Hadron Collider, we report the first predictions up to next-to-leading order in quantum chromodynamics with parton-shower matching for the production and decay of scalars and heavy neutrinos from the Scotogenic model for neutrino masses and dark matter at $\sqrt{s}=14$ TeV and $\sqrt{s}=100$ TeV. We carry out our simulations using the FeynRules+MadGraph5\_aMC@NLO+Pythia8 pipeline. As a byproduct, we report the public release of the SM\_Scoto Universal FeynRules Object libraries for modeling the Scotogenic model in high-energy processes. We comment on prospects of observing new rare $Z$ decays at future $e^+e^-$ collider facilities as well as on the production of new particles at a multi-TeV $\mu^+\mu^-$ collider.

We present a two-step construction to violate the classical third law of black hole thermodynamics for charged black holes in four dimensions. A near-extremal black hole with an $\mathrm{AdS}_2\times X$ throat is first prepared and then driven to extremality in finite time by a charged shell. This construction suggests that the second step is universal for near-extremal black holes, and can be used to construct violations of the third law for Kerr black holes. The same description allows us to study the process in quantum gravity. The classical collapse condition selects a BF-violating matter sector, for which we construct a holographic dictionary and derive the quantum transition amplitude. Quantum effects replace the classical extremal endpoint by a probability distribution that vanishes at extremality and peaks at positive energy. This obstruction is consistent with the absence of non-supersymmetric extremal black hole states in quantum gravity. We show that driving the peak close enough to extremality for quantum gravity to become important requires a preparation time that scales with the black hole entropy.

The high-energy nuclear-recoil candidate reported by LUX-ZEPLIN could point to dark matter beyond the reach of the LHC. We examine how future colliders could test this interpretation, starting with the thermal Higgsino and extending to a broad class of electroweak multiplets containing neutral and charged particles. We assume an approximately pure multiplet protected by an exact stabilizing symmetry, with dominant inelastic Z exchange and the full dark-matter abundance set by gauge-dominated thermal freeze-out, where mixing and additional interactions affecting production or freeze-out are negligible. In this setting, heavy thermal masses, rare production and invisible neutral transitions make the Higgsino's main collider obstacles generic across the class, independently of supersymmetry. Charged lifetimes vary, but the benchmark spectra studied, including radiative doublet splittings, remain beyond the projected HL-LHC reach. We show how FCC-hh and a high-energy muon collider can overcome these obstacles. Our FCC-hh estimates show sensitivity to the doublets and several larger multiplets through disappearing charged tracks and complementary channels that do not depend on the charged lifetime. Muon-collider projections cover the fermionic doublet and triplet at 10 TeV and the full fermionic family considered here at 30 TeV, subject to the stated spectrum and systematic assumptions. This connects a possible underground signal to a concrete program for testing thermal electroweak dark matter at future colliders.

Single-field models of inflection point inflation experience a phase of ultra-slow roll (USR), leading to amplified curvature perturbations. Recently, Lorenzoni et al. modified the scenario by adding a light spectator field, showing that it ruins USR by setting a floor for the first slow-roll parameter $\epsilon$. Mixing with isocurvature perturbations still amplifies the curvature power spectrum. We offer an alternative point of view, arguing that the inflaton still undergoes effective USR. The spectator lifts the potential by a constant amount, and the inflaton perturbations follow single-field dynamics in the lifted inflection point potential, decoupling from the spectator perturbations. Mode mixing only affects the power spectrum dip, making it milder. We demonstrate this effective single-field behavior numerically for example models. Our results offer a simple way to study the models' parameter dependence.

Quasinormal modes (QNMs) of black hole perturbations in the large overtone limit, namely, asymptotic QNMs, are highly sensitive to a black hole's interior geometry. We probe the singularity structure of a class of exact (2+1)-dimensional quantum black hole solutions to semi-classical gravity by computing their asymptotic QNM spectra. We do this using methods of complex analysis in which the radial coordinate is analytically continued to the complex plane. The leading order QNM frequencies all fit the generic form $\omega=(\text{offset})+n(\text{gap})$, for overtone number $n$, which we also confirm numerically. Under a general assumption about the global Stokes topology of the complexified radial coordinate, we show how to reconstruct the scaling exponent of more general (spacelike or timelike) black hole singularities from the offset. We then compute subleading corrections to the asymptotic QNMs, from which we provide a robust method for extracting the scaling of the metric function near the singularity. Our findings exemplify the transition between "Kasner eons", successive regimes encountered on approach to a spacelike singularity, as non-perturbative quantum effects become dominant. For charged quantum black holes, the asymptotic QNMs exhibit a crossover between two regimes in which the neutral and charge contributions to the metric function dominate, respectively. Within the crossover region, the QNMs develop an oscillatory behavior that may be a signature of the inner horizon.

We compute the linear magnetoelectric conductivity of a two-band vortex nodal-ring (VNR) semimetal and a three-band Hopf semimetal (HSM) within the semiclassical Boltzmann formalism in the relaxation-time approximation. We consider three inequivalent planar-Hall configurations, in which the electric ($\boldsymbol E$) and magnetic ($\boldsymbol B$) fields are oriented differently with respect to the nodal-ring plane and the BC-dipole axis. Unlike Weyl and multifold semimetals, where Berry-curvature (BC) flux originates from monopole-like sources, both systems host dipole-like BC sources and vanishing Chern numbers. Working consistently to cubic order in the magnetic field, we evaluate the Drude, BC, orbital-magnetic-moment (OMM), anomalous-Hall, and Lorentz-force contributions to the conductivity. In both systems, the dipolar BC and OMM generate odd powers of $|\boldsymbol B|$ in in-plane response channels that are symmetry-forbidden in systems with monopole-like BC sources. For the HSM, the internode-scattering contribution to the conductivity vanishes identically. By comparing the VNR with a $\mathcal{PT}$-broken gapped nodal ring and the HSM with a pseudospin-1 triple-point semimetal, we demonstrate that the dipolar nature of the BC gives rise to distinctive features in magnetoelectric response that are absent in semimetals with monopole-like BC flux.

We study the leading probe-flavour contribution to equal-time spatial entanglement entropy in a homogeneous 3+1-dimensional strongly coupled conductor at finite temperature and charge density, realised holographically by the D3-D7 system and driven by a constant DC electric field. We compare slab-shaped subregions that are extended in two spatial directions and have finite width parallel or transverse to the field. The difference between the corresponding entropy corrections isolates a homogeneous, spatially traceless response and exhibits a density-driven sign reversal. Over the investigated parameter range, the crossover density increases with the electric-field magnitude and decreases with the strip width. Mutual information shows the same qualitative reversal and provides an ultraviolet-finite check. We trace the effect to a radial sign competition in the full Dirac-Born-Infeld stress anisotropy. The reversal is a smooth response crossover rather than a thermodynamic phase transition.

We consider the canonical quantization of the Schwarzschild geometry in a minisuperspace description based on a foliation with leaves labeled by the radial variable. This formulation remains regular across the Killing horizon. In this way, the resulting quantum theory admits a physical Hilbert space of states that solve the radial constraint equation and simultaneously describe the exterior and interior regions of the black hole. We discuss the construction of quantum relational observables, which act as gauge-invariant symmetric operators on the physical Hilbert space. In order to analyze quantum effects on the geometry, we construct a family of semiclassical intelligent states that saturate the Robertson-Schrödinger uncertainty relation for both the black-hole mass and the asymptotic Killing norm, while exhibiting small relative fluctuations. The expectation values of relational observables in these states admit a clear geometric interpretation, and they lead to an effective, quantum-corrected spacetime. In particular, we find that the position of the horizon may be shifted, depending on the correlation of the state. In addition, both the proper acceleration of a static observer and the horizon surface gravity are enhanced with respect to a classical Schwarzschild black hole with the same horizon area. Using the relation between surface gravity and temperature, we then obtain corrections to the thermodynamic properties of the black hole, leading to a logarithmically corrected Bekenstein-Hawking entropy. Finally, we discuss the definition of a state of minimal energy that could be interpreted as a stable remnant characterized by a finite horizon radius, suggesting a possible mechanism for preventing the complete evaporation of the black hole.

We study Witten's induced gauge theory associated with the D1-D5 Higgs-branch CFT${}_2$, in which the non-dynamical vector multiplet becomes reanimated by integrating out the fundamental hypermultiplets. We propose a BRST quantisation of this theory and derive its induced propagators. We show that the ghost sector first contributes at subleading order, that the induced $A\phi^2$ vertex satisfies the Slavnov-Taylor identity and that gauge-invariant correlators are independent of the gauge parameter. Together with our chosen regularization prescription, this gives a perturbative framework for computing observables in the induced theory.

Appell functions are a large class of multi-variable quasi-elliptic functions, which are also instances of higher depth mock modular forms. A central aspect of these functions is their non-holomorphic modular completion. Our previous work developed Appell functions for a general positive definite lattice $\Lambda$, and expressed the non-holomorphic completion in terms of the generalized error functions $M_P$, which are integrals over a $P$-dimensional hyperplane in $\Lambda\otimes \mathbb{C}$. In this sequel, we express $M_P$ as a $P$-dimensional iterated integral of variables $w_j\in \mathbb{H}$, such that the completion of the Appell function takes the form of an iterated Eichler integral of modular forms. We apply this to the case of the root lattice of the $A_N$ Lie algebra, which is of particular interest because of their appearance in partition functions of topological twisted Yang-Mills theories.

We consider a dilatonic dyon black hole solution with a gravitational radius of $2 \mu$ and two charges, $Q_1$ (electric) and $Q_2$ (magnetic), within the framework of a four-dimensional gravitational model comprising one scalar field and one 2-form. The dilaton coupling constant $\lambda$ is fixed by $\lambda^2 = \frac{3}{2}$. This solution is related to the $A_2$ Toda chain. The circular orbits of null geodesics are explored, and the fifth-order polynomial master equation governing the photon sphere radius $R_0$ is analyzed. It is shown to admit a unique solution satisfying $R_0 > 2 \mu$. The circular null geodesics are proven to be unstable. Finally, the black hole shadow is examined, yielding relations for the shadow angle and the critical impact parameter.

We construct the Super-Composite Higgs, a scenario designed to stabilize the Higgs mass and generate the flavor structure within a single dynamical framework. The basic idea is to combine supersymmetry and compositeness, where the Higgs mass is protected by supersymmetry and Yukawa couplings are generated through partial compositeness. This combination offers mutual advantages and ameliorates several drawbacks of each individual theory. The Super-Composite Higgs makes experimentally testable predictions across three different areas of fundamental physics. At the precision frontier, the electron EDM is predicted to be within reach of future experiments. At the observational cosmology frontier, measurable effects in CMB and large-scale structures are expected from an ultra-light gravitino. At the high-energy frontier, an upper bound on supersymmetric particle masses, derived from cosmological considerations, indicates that squarks should be lighter than about 10 TeV, which is within reach of the FCC-hh.

We provide the first compact examples of type-changing generalized Calabi–Yau manifolds using Fei's construction of non-Kähler Calabi–Yau manifolds on branched covers of twistor spaces \cite{Fei16}. The structure, which is generically of type 1 and changes to type 3, is constructed on the product of a hyperelliptic surface of genus three and a four-torus, $\Sigma_3 \times \mathbb{T}^4$, with starting point a non-Kähler Calabi–Yau structure.

In this paper, it is shown that in spacetimes of maximal proper acceleration, there is a reduction of the mean lifetime of the muon. We consider several candidates for the maximal proper acceleration. For all of them, the induced corrections are small, but for the case when the maximal proper acceleration is identified with the Schwinger's acceleration, the effect is detectable in future muon collider facilities.

The static Love numbers of four-dimensional Schwarzschild black holes vanish classically. We show that this is not true in the quantum theory. Working in the worldline effective field theory, we compute the leading quantum correction to the Compton amplitude for massless scalars and photons scattering off a Schwarzschild black hole at first post-Minkowskian order, and find logarithmic divergences associated with the renormalization of the static Love numbers. We conclude that renormalization-group running necessarily generates Love numbers suppressed by the square of the Planck length in units of the horizon radius, $\ell_{\rm pl}^{2}/r_{\rm h}^{2}$. This is consistent with the classical vanishing being a consequence of an accidental symmetry of static general relativity, broken by quantum loops. Extrapolated to gravitational perturbations, our results suggest that the quadrupolar static Love numbers of Schwarzschild are of size $\lambda \sim M r_{\rm h}^{2} \ell_{\rm pl}^{2}$.

We numerically construct the Sasaki–Einstein metric on the link of the cone over the second del Pezzo surface $\mathrm{dP}_2$ and two primitive harmonic basic $(1,1)$-forms at its irregular volume-minimizing Reeb vector. Being toric, the metric in symplectic coordinates is encoded in a single convex function on a polygon. We approximate the correction to the canonical Guillemin potential in two ways: polynomial expansion and neural networks. The polynomial fit achieves a held-out mean-squared Monge–Ampère residual below $10^{-13}$, in contrast to the $10^{-2}$ plateau for the non-volume-minimizing regular Reeb vector. We validate our method against closed-form metrics of $Y^{p,q}$ using curvature invariants, and also against the numerical result of Doran et al. (2007) for the Kähler–Einstein metric of $\mathrm{dP}_3$ using the Laplacian spectrum of low torus-invariant modes. The integrated Riemann-squared curvature of the $\mathrm{dP}_2$ link agrees to two parts in $10^{9}$ with the closed form conjectured from the dual field theory. Our data for the metric and harmonic forms can be used to study warped non-conformal holographic IIB backgrounds, the analogues of the Klebanov–Tseytlin solution on the conifold.

We study correlation functions of giant and dual giant gravitons in $\mathcal N=4$ super Yang–Mills theory. Although the two objects correspond to rather different D3 brane configurations in $AdS_5\times S^5$, their gauge theory operators are Schur polynomials associated with transposed Young diagrams. We show that this transposition is accompanied by a formal rank reflection $N\to -N$ at the level of correlation functions. For both $U(N)$ and $SU(N)$, the relation is exact for free correlators at finite $N$, and, using Lagrangian insertion, extends to separated point weak coupling integrands at every loop order. More generally, it applies to any number of Schur polynomial external operators, provided all Young diagrams are transposed. We illustrate the relation in several examples and also discuss evidence for its extension beyond perturbative integrands.

We study the thermal partition function of the critical large-$N$ $O(N)$ model on rotating $S^1\times S^2$. Rotation makes the saddle latitude dependent, with its leading profile governed by the local temperature. Using a Weyl-covariant hydrostatic expansion, we determine the partition function through four-derivative order in high-temperature and semi-universal limits. In the near-light-speed limit, the geometry around the equator reduces to a pp-wave and captures the expected semi-universal behavior of the partition function. We compute the corresponding theory-dependent residue directly on this limiting geometry, both at high and low temperatures. The high-temperature result agrees with the near-light-speed limit of the sphere calculation, while the low-temperature expansion reveals interaction-dependent corrections arising from the response of the saddle to the thermal source.

The possibility of describing neutrino masses through a single multiplet of modular forms in a modular symmetric framework is reanalysed. The minimal model achieving this is Feruglio's model based on modular $A_4$ symmetry, which contains a chiral flavon triplet $\phi$, with all neutrino masses and mixing determined by a superfield triplet of modular forms $Y(\tau)$. We point out that, in local supersymmetry, these superfields by themselves allow an additional $R$-parity-violating contribution to neutrino masses originating from the Kähler potential of the model. The $R$ violation manifests through a bilinear term $\epsilon_i L_i H_u$ in the effective superpotential, with parameters $\epsilon_i$ determined in terms of $Y(\tau)$ and its derivatives. The Kähler potential also mixes neutrinos with the fermionic component of $\phi$, leading to seesaw neutrino masses when these fermions are massive. Two separate cases are analysed, with neutrinos obtaining mass through the Weinberg operator or through the $\phi$-induced seesaw. Unlike the original model, adding the $R$-violating contribution allows accurate reproduction of neutrino mixing angles and mass ratios for both the normal and inverted orderings in either case, with the Weinberg operator predicting a sum of neutrino masses close to the cosmological limit and the seesaw mechanism predicting ones comfortably below it.

We study the holographic description of the RN-like black hole in bumblebee gravity, which is a vector-tensor theory with spontaneous Lorentz violation. By combining the first laws of the outer and inner horizons, the thermodynamics method yields the right- and left-moving entropies, temperatures, and chemical potentials of the dual two-dimensional conformal field theory (CFT), determines the central charges from the mass-independent entropy product, and reproduces the outer and inner horizon entropies through the Cardy formula. An independent dynamical test based on the hidden conformal symmetry of a charged scalar probe confirms these results. A central outcome is the equality of the right- and left-moving central charges, $c_R=c_L$, which we trace to the spontaneous character of Lorentz breaking. Because the action of bumblebee gravity preserves diffeomorphism and local Lorentz invariance, and the symmetry is broken only by a vector vacuum expectation value, no chirally asymmetric structure arises in the dual theory, in sharp contrast to topologically massive gravity in $(2+1)$ dimensions. All CFT data depend smoothly on the Lorentz-violating parameter and reduce to the known RN results when Lorentz violation is switched off.

We derive a Lipatov type effective action for the Reggeized gravitons. In place of the order by order construction of the effective currents from diffeomorphism invariance, we propose a current which is a single ordered exponential $W_{ij}$ along the light cone, generated by the optical tidal matrix integrated once. The nested ordering of it reproduces the known perturbative answer with some new terms added. These new terms are non-local along the light cone and have a structure which the diffeomorphism construction cannot produce, the form of the third order contribution to the current is also calculated. The effective action, the current to Reggeon vertex and the current to current interaction are obtained in closed form, in three equivalent writings, one of them covariant. Generally defined $W_{ij}$ reduces to four parameters of the ray bundle, its density, its shear, the orientation of the shear and a rotation of the image. The effective current uses three of them, being the second light cone derivative of a single scalar, it is not sensitive to the orientation. Comparing with the standard eikonal gravitational Wilson line, which is the phase, $W_{ij}$ is the Hessian of the same eikonal: it carries the shear and the focusing that the Abelian phase does not, and it is inverse to the Jacobi propagator of the congruence at first order in the field. A generalization of the proposed ordered operator is discussed as well as applications of the gravitational effective action.

Inspired by black hole thermodynamics and other results suggesting that general relativity has some intrinsic connection with thermodynamics, this work aims to establish a quasi-local thermodynamic formalism in general spacetimes. With this purpose, we generalize the Bondi-Sachs formalism to past light cones associated with an arbitrary worldline. From this generalization, we demonstrate the emission of Hawking radiation in a quasi-local context through a few examples, suggesting that it may occur under mild conditions. In addition, we argue that an "irreversible inequality" is satisfied in typical gravitational systems, indicating that an analogue of the second law may be established. Together with a definition of internal energy derived from the Landau-Lifshitz pseudotensor, these results are used to construct a postulational framework that generalizes classical thermodynamics in order to include the dynamics of spacetime. As a consequence, it is possible to define the rest-mass density from thermodynamic variables, decoupling it from the dynamics of constituent numbers.