Showing papers in "Classical and Quantum Gravity in 2023"

Graviton scattering in self-dual radiative space-times

Abstract: The construction of amplitudes on curved space-times is a major challenge, particularly when the background has non-constant curvature. We give formulae for all tree-level graviton scattering amplitudes in curved self-dual (SD) radiative space-times; these are chiral, source-free, asymptotically flat spaces determined by free characteristic data at null infinity. Such space-times admit an elegant description in terms of twistor theory, which provides the powerful tools required to exploit their underlying integrability. The tree-level S-matrix is written in terms of an integral over the moduli space of holomorphic maps from the Riemann sphere to twistor space, with the degree of the map corresponding to the helicity configuration of the external gravitons. For the MHV sector, we derive the amplitude directly from the Einstein–Hilbert action of general relativity, while other helicity configurations arise from a natural family of generating functionals and pass several consistency checks. The amplitudes in SD radiative space-times exhibit many novel features that are absent in Minkowski space, including tail effects. There remain residual integrals due to the functional degrees of freedom in the background space-time, but our formulae have many fewer such integrals than would be expected from space-time perturbation theory. In highly symmetric special cases, such as SD plane waves, the number of residual integrals can be further reduced, resulting in much simpler expressions for the scattering amplitudes.

Alleviating the cosmological constant problem from particle production

Abstract: We explore a toy model mechanism of geometric cancellation, alleviating the (classical) cosmological constant problem. To do so, we assume at primordial times that vacuum energy fuels an inflationary quadratic hilltop potential nonminimally coupled to gravity through a standard Yukawa-like interacting term, whose background lies on a perturbed Friedmann–Robertson–Walker metric. We demonstrate how vacuum energy release transforms into geometric particles, adopting a quasi-de Sitter phase where we compute the expected particle density and mass ranges. Perturbations are introduced by means of the usual external-field approximation, so that the back-reaction of the created particles on the geometry is not considered here. We discuss the limitations of this approach and we also suggest possible refinements. We then propose the most suitable dark matter candidates, showing under which circumstances we can interpret dark matter as constituted by geometric quasiparticles. We confront our predictions with quantum particle production and constraints made using a Higgs portal. In addition, the role of the bare cosmological constant is reinterpreted to speed up the Universe today. Thus, consequences on the standard ΛCDM paradigm are critically highlighted, showing how both coincidence and fine-tuning issues can be healed requiring the Israel–Darmois matching conditions between our involved inhomogeneous and homogeneous phases.

Static neutron stars perspective of quadratic and induced inflationary attractor scalar-tensor theories

Abstract: This study focuses on the static neutron star perspective for two types of cosmological inflationary attractor theories, namely the induced inflationary attractors and the quadratic inflationary attractors. The two cosmological models can be discriminated cosmologically, since one of the two does not provide a viable inflationary phenomenology, thus in this paper we investigate the predictions of these theories for static neutron stars, mainly focusing on the mass and radii of neutron stars. We aim to demonstrate that although the models have different inflationary phenomenology, the neutron star phenomenology predictions of the two models are quite similar. We solve numerically the Tolman–Oppenheimer–Volkoff equations in the Einstein frame using a powerful double shooting numerical technique, and after deriving the mass-radius graphs for three types of polytropic equations of state, we derive the Jordan frame mass and radii. With regard the equations of state we use polytropic equation of state with the small density part being either the Wiringa–Fiks–Fabrocini, the Akmal–Pandharipande–Ravenhall or the intermediate stiffness equation of state Skyrme–Lyon (SLy). The results of our models will be confronted with quite stringent recently developed constraints on the radius of neutron stars with specific mass. As we show, the only equation of state which provides results compatible with the constraints is the SLy, for both the quadratic and induced inflation attractors. Thus nowadays, scalar-tensor descriptions of neutron stars are quite scrutinized due to the growing number of constraining observations, which eventually may also constrain theories of inflation.

Spin Hall effects in the sky

Abstract: In many areas of physics, the propagation of wave packets carrying intrinsic angular momentum is generally influenced by spin–orbit interactions. This is the main mechanism behind spin Hall effects, which result in wave packets following spin-dependent trajectories. Spin Hall effects have been observed in several experiments for electrons in condensed matter systems and for light propagating in inhomogeneous optical media. Similar effects have also been predicted for wave packets propagating in inhomogeneous gravitational fields. We give a brief introduction to gravitational spin Hall effects, emphasizing the analogies with the spin Hall effect of light in optics. Furthermore, we review the most promising astrophysical avenues that could lead to experimental observations of the gravitational spin Hall effect.

Photon rings around warped black holes

Abstract: The black hole photon ring is a prime target for upcoming space-based VLBI missions seeking to image the fine structure of astrophysical black holes. The classical Lyapunov exponents of the corresponding nearly bound null geodesics control the quasinormal ringing of a perturbed black hole as it settles back down to equilibrium, and they admit a holographic interpretation in terms of quantum Ruelle resonances of the microstate dual to the Kerr black hole. Recent work has identified a number of emergent symmetries related to the intricate self-similar structure of the photon ring. Here, we explore this web of interrelated phenomena in an exactly soluble example that arises as an approximation to the near-extremal Kerr black hole. The self-dual warped AdS$_3$ geometry has a photon ring as well as $\mathsf{SL}(2,\mathbb{R})$ isometries and an exactly calculable quasinormal mode (QNM) spectrum. We show explicitly that the geometric optics approximation reproduces the eikonal limit of the exact QNM spectrum, as well as the approximate "near-ring" wavefunctions. The $\mathsf{SL}(2,\mathbb{R})$ isometries are directly related to the emergent conformal symmetry of the photon ring in black hole images but are distinct from a recently discussed conformal symmetry of the eikonal QNM spectrum. The equivalence of the classical QNM spectrum -- and thus the photon ring -- to the quantum Ruelle resonances in the context of a spacetime with a putative holographic dual suggests that the photon ring of a warped black hole is indeed part of the black hole hologram.

Observational constraints in accelerated emergent f(Q) gravity model

Abstract: In this study, the non-metricity scalar Q, which characterizes the gravitational interaction, is used to analyze the Universe’s rapid expansion within the context of the f(Q) gravity theory. We suggest an emergent scale factor, which produces the deceleration parameter in redshift form which determines the solution of the field equations in the FLRW Universe. We evaluate the appropriate values of the model parameters by considering SNIa from Pantheon, CMB from Planck 2018, BAO, and 36 data points from Hubble datasets using Markov Chain Monte Carlo approach. The deceleration parameter’s development suggests that the Universe is moving from its deceleration phase into its acceleration phase. Furthermore, we analyze the statefinder (r, s) diagnostic parameter. We also use some different forms of f(Q) gravity models to study some other cosmological parameters, i.e. f(Q)=α1Q , f(Q)=α2Qm and f(Q)=α3Qm+Q , where α 1, α 2, α 3 and m all are free model parameters. Finally, we concluded that all f(Q) models predict that at z = 0, Universe is in the phase of accelerating and behaves like the quintessence models and at z=−1 , approaches to ΛCDM models.

Gravitational duality, Palatini variation and boundary terms: a synopsis

Abstract: We consider f(R) gravity and Born–Infeld–Einstein (BIE) gravity in formulations where the metric and connection are treated independently and integrate out the metric to find the corresponding models solely in terms of the connection, the archetypical treatment being that of Eddington–Schrödinger (ES) duality between cosmological Einstein and Eddington theories. For dimensions D≠2 , we find that this requires f(R) to have a specific form which makes the model Weyl invariant, and that its Eddington reduction is then equivalent to that of BIE with certain parameters. For D = 2 dimensions, where ES duality is not applicable, we find that both models are Weyl invariant and equivalent to a first order formulation of the bosonic string. We also discuss the form of the boundary terms needed for the variational principle to be well defined on manifolds with non-null boundaries. This requires a modification of the Gibbons–Hawking–York (GHY) boundary term for gravity. This modification also means that the dualities between metric and connection formulations are consistent and include the boundary terms.

Gravitational wave hints black hole remnants as dark matter

Abstract: The end state of Hawking evaporation of a black hole is uncertain. Some candidate quantum gravity theories, such as loop quantum gravity and asymptotic safe gravity, hint towards Planck sized remnants. If so, the Universe might be filled with remnants of tiny primordial black holes, which formed with mass $M<10^9\,{\rm g}$. A unique scenario is the case of $M\sim 5\times10^5\,{\rm g}$, where tiny primordial black holes reheat the universe by Hawking evaporation and their remnants dominate the dark matter. Here, we point out that this scenario leads to a cosmological gravitational wave signal at frequencies $\sim 100{\rm Hz}$. Finding such a particular gravitational wave signature with, e.g., the Einstein Telescope, would suggest black hole remnants as dark matter.

Angular correlations on causally-coherent inflationary horizons

Abstract: We develop a model for correlations of cosmic microwave background (CMB) anisotropy on the largest angular scales, based on standard causal geometrical relationships in slow-roll inflation. Unlike standard models based on quantized field modes, it describes perturbations with nonlocal directional coherence on spherical boundaries of causal diamonds. Causal constraints reduce the number of independent degrees of freedom, impose new angular symmetries, and eliminate cosmic variance for purely angular 2-point correlations. Distortions of causal structure from vacuum fluctuations are modeled as gravitational memory from randomly oriented outgoing and incoming gravitational null shocks, with nonlocally coherent directional displacements on curved surfaces of causal diamonds formed by standard inflationary horizons. The angular distribution is determined by axially symmetric shock displacements on circular intersections of the comoving sphere that represents the CMB photosphere with other inflationary horizons--- those centered on it, and those that pass through an observer's world line. Displacements on thin spheres at the end of inflation have a unique angular power spectrum $C_\ell$ that approximates the standard expectation on small angular scales, but differs substantially at large angular scales due to horizon curvature. For a thin sphere, the model predicts a universal angular correlation function $C(\Theta)$ with an exact ``causal shadow'' symmetry, $C(\pi/4<\Theta<3\pi/4)= 0$, and significant large-angle parity violation. We apply a rank statistic to compare models with {\sl WMAP} and {\sl Planck} satellite data, and find that a causally-coherent model with no shape parameters or cosmic variance agrees with the measured $C(\Theta)$ better than a large fraction ($> 0.9999$) of standard model realizations. Model-independent tests of holographic causal symmetries are proposed.

A linear response relation for perturbed Einstein’s equations with a Langevin source: applications to perturbations in compact stars

Abstract: A new linear response relation for the perturbed Einstein’s equation is introduced. We give the idea of considering the metric perturbations as a linear response to the fluid (matter) perturbations in strong gravity regions. This can be meaningful when the perturbations in the system are driven by sources internal to the fluid (matter) in the relativistic star. The aim is to study the strong regions embedding the compact matter like that of the internal structure of relativistic stars, with this new framework. The formulations are specifically done to address the generalized stochastic perturbations which can arise in the dense matter at intermediate scales. These internally sourced perturbations lead to the possibility of equilibrium and non-equilibrium (dynamical or thermal) statistical analysis for the properties of compact matter at the sub-hydro mesoscopic scales, which are yet unexplored. A general relativistic Langevin formalism, defining a random driving source and its analytical solutions for a simple example are given. With a first principles approach, this new framework and its potential towards building up a theme of research in asteroseismology is discussed.

Continuous charge management scheme for TianQin

Abstract: TianQin is a proposed Chinese space-borne gravitational wave detection mission, which will consist of three earth-orbiting spacecraft in equilateral triangle constellation. Due to the ‘3 months on + 3 months off’ observation scheme, the continuous scientific observation period of TianQin is much shorter than LISA, it is highly preferred that other on-board operations, such as charge management, will not interrupt gravitational wave detection. This paper presents a torsion pendulum system on the ground to investigate the continuous discharge method in detail. It is found that the difference in surface characteristics between the test mass and the surrounding housing is the most critical to the success of continuous discharge method. Consequently, the effect of this difference on the continuous discharge process was evaluated in ground simulation experiments, and based on the research results, we also proposed a more feasible spatial continuous charge management strategy for TianQin.

A ‘black hole theorem,’ and its implications

Abstract: A general formulation of the basic conflict of the information problem is given, encapsulated in a "black hole theorem." This is framed in a more general context than the usual one of quantum field theory on a background, and is based on describing a black hole as a quantum subsystem of a larger system, including its environment. This sharpens the limited set of possible consistent options; as with the Coleman-Mandula theorem, the most important point is probably the loophole in the "theorem," and what this tells us about the fundamental structure of quantum gravity. This "theorem" in particular involves the general question of how to define quantum subsystems in quantum gravity. If black holes do behave as quantum subsystems, at least to a good approximation, evolve unitarily, and do not leave remnants, the "theorem" implies the presence of interactions between a black hole and its environment that go beyond a description based on local quantum fields. This provides further motivation for and connects to previous work giving a principled parameterization of these interactions, and investigating their possible observational signatures via electromagnetic or gravitational wave observations of black holes.

Nonsingular black holes from conformal symmetries

Abstract: We derive the form of the metric for static, nonsingular black holes with a de Sitter core, representing a deformation of the Schwarzschild solution, by assuming that the gravitational sources describe a flow between two conformal points, at small and great distances. The resulting black-hole metric turns out to be a particular case of the Fan & Wang metric, whose parameters have been recently constrained by using the data of the S2 star orbits around the galactic center SgrA ∗ .

Gravastar-like black hole solutions in q-theory

Abstract: We present a stationary spherically symmetric solution of the Einstein equations, with a source generated by a scalar field of q-theory. In this theory Riemannian gravity, as described by the Einstein - Hilbert action, is coupled to a three - form field that describes the dynamical vacuum. Formally it behaves like a matter field with its own stress - energy tensor, equivalent to a scalar field minimally coupled to gravity. The asymptotically flat solutions obtained to the field equations represent black holes. For a sufficiently large horizon radius the energy density is localized within a thin spherical shell situated just outside of the horizon, analogous to a gravastar. The resulting solutions to the field equations, which admit this class of configurations, satisfy existence conditions that stem from the Black Hole no - hair theorem, thanks to the presence of a region in space in which the energy density is negative.

Waveform uncertainty quantification and interpretation for gravitational-wave astronomy

Abstract: We demonstrate how to quantify the frequency-domain amplitude and phase accuracy of waveform models, δA and δφ, in a form that could be marginalized over in gravitational-wave inference using techniques currently applied for quantifying calibration uncertainty. For concreteness, waveform uncertainties affecting neutron-star inspiral measurements are considered, and post-hoc error estimates from a variety of waveform models are made by comparing time-domain and frequency-domain analytic models with multiple-resolution numerical simulations. These waveform uncertainty estimates can be compared to GW170817 calibration envelopes or to Advanced LIGO and Virgo calibration goals. Signal-specific calibration and waveform uncertainties are compared to statistical fluctuations in gravitational-wave observatories, giving frequency-dependent modeling requirements for detectors such as Advanced LIGO Plus, Cosmic Explorer, or Einstein Telescope. Finally, the distribution of waveform error for the GW170817 posterior is computed from tidal models and compared to the constraints on δφ or δA from GWTC-1 by Edelman et al. In general, δφ and δA can also be interpreted in terms of unmodeled astrophysical energy transfer within or from the source system.

High-accuracy numerical models of Brownian thermal noise in thin mirror coatings

Abstract: Abstract Brownian coating thermal noise in detector test masses is limiting the sensitivity of current gravitational-wave detectors on Earth. Therefore, accurate numerical models can inform the ongoing effort to minimize Brownian coating thermal noise in current and future gravitational-wave detectors. Such numerical models typically require significant computational resources and time, and often involve closed-source commercial codes. In contrast, open-source codes give complete visibility and control of the simulated physics, enable direct assessment of the numerical accuracy, and support the reproducibility of results. In this article, we use the open-source SpECTRE numerical relativity code and adopt a novel discontinuous Galerkin numerical method to model Brownian coating thermal noise. We demonstrate that SpECTRE achieves significantly higher accuracy than a previous approach at a fraction of the computational cost. Furthermore, we numerically model Brownian coating thermal noise in multiple sub-wavelength crystalline coating layers for the first time. Our new numerical method has the potential to enable fast exploration of realistic mirror configurations, and hence to guide the search for optimal mirror geometries, beam shapes and coating materials for gravitational-wave detectors.

Reflecting boundary conditions in numerical relativity as a model for black hole echoes

Abstract: Recently, there has been much interest in black hole echoes, based on the idea that there may be some mechanism (e.g., from quantum gravity) that waves/fields falling into a black hole could partially reflect off of an interface before reaching the horizon. There does not seem to be a good understanding of how to properly model a reflecting surface in numerical relativity, as the vast majority of the literature avoids the implementation of artificial boundaries, or applies transmitting boundary conditions. Here, we present a framework for reflecting a scalar field in a fully dynamical spherically symmetric spacetime, and implement it numerically. We study the evolution of a wave packet in this situation and its numerical convergence, including when the location of a reflecting boundary is very close to the horizon of a black hole. This opens the door to model exotic near-horizon physics within full numerical relativity.

Pitfalls in applying gravitomagnetism to galactic rotation curve modelling

Abstract: The flatness of galaxy rotation curves at large radii is generally considered to be a significant piece of evidence in support of the existence of dark matter. Several studies have claimed that post-Newtonian corrections to the Newtonian equations of galaxy dynamics may remove (at least to some degree) the need for dark matter. A few recent studies have examined these claims, and identified errors in their reasoning. We add to this critique by giving what we consider to be particularly simple and transparent description of the errors made in these post-Newtonian calculations, some of which were of a rather technical nature, others more fundamental, e.g. the loss of the correct relativistic scaling, promoting small corrections to order unity changes. Our work reinforces the orthodoxy that post-Newtonian effects are indeed too small to significantly alter galactic rotation curves, and will hopefully serve as a useful guide for others, pointing out subtle errors that one might inadvertently make in such calculations.

Gluing variations

Abstract: We establish several results on gluing/embedding/extending geometric structures in vacuum spacetimes with a cosmological constant in any spacetime dimensions d ≥ 4, with emphasis on characteristic data. A useful tool is provided by the notion of submanifold-data of order k. As an application of our methods we prove that vacuum Cauchy data on a spacelike Cauchy surface with boundary can always be extended to vacuum data defined beyond the boundary.

Linearised conformal Einstein field equations

Abstract: The linearisation of a second-order formulation of the conformal Einstein field equations (CEFEs) in Generalised Harmonic Gauge (GHG), with trace-free matter is derived. The linearised equations are obtained for a general background and then particularised for the study linear perturbations around a flat background —the inversion (conformal) representation of the Minkowski spacetime— and the solutions discussed. We show that the generalised Lorenz gauge (defined as the linear analogue of the GHG-gauge) propagates. Moreover, the equation for the conformal factor can be trivialised with an appropriate choice for the gauge source functions; this permits a scri-fixing strategy using gauge source functions for the linearised wave-like CEFE-GHG, which can in principle be generalised to the nonlinear case. As a particular application of the linearised equations, the far-field and compact source approximation is employed to derive quadrupole-like formulae for various conformal fields such as the perturbation of the rescaled Weyl tensor.

Further observations on the definition of global hyperbolicity under low regularity

Abstract: The definitions of global hyperbolicity for closed cone structures and topological preordered spaces are known to coincide. In this work we clarify the connection with definitions of global hyperbolicity proposed in recent literature on Lorentzian length spaces and Lorentzian optimal transport, suggesting possible corrections for the terminology adopted in these works. It is found that in Kunzinger-Saemann's Lorentzian length spaces the definition of global hyperbolicity coincides with that valid for closed cone structures and, more generally, for topological preordered spaces: the causal relation is a closed order and the causally convex hull operation preserves compactness. In particular, it is independent of the metric, chronological relation or Lorentzian distance.

On the non-linear stability of the Cosmological region of the Schwarzschild-de Sitter spacetime

Abstract: The non-linear stability of the sub-extremal Schwarzschild-de Sitter spacetime in the stationary region near the conformal boundary is analysed using a technique based on the extended conformal Einstein field equations and a conformal Gaussian gauge. This strategy relies on the observation that the Cosmological stationary region of this exact solution can be covered by a non-intersecting congruence of conformal geodesics. Thus, the future domain of dependence of suitable spacelike hypersurfaces in the Cosmological region of the spacetime can be expressed in terms of a conformal Gaussian gauge. A perturbative argument then allows to prove existence and stability results close to the conformal boundary and away from the asymptotic points where the Cosmological horizon intersects the conformal boundary. In particular, we show that small enough perturbations of initial data for the sub-extremal Schwarzschild-de Sitter spacetime give rise to a solution to the Einstein field equations which is regular at the conformal boundary. The analysis in this article can be regarded as a first step towards a stability argument for perturbation data on the Cosmological horizons.

ArchEnemy: removing scattered-light glitches from gravitational wave data

Abstract: Data recorded by gravitational wave detectors includes many non-astrophysical transient noise bursts, the most common of which is caused by scattered-light within the detectors. These so-called ‘glitches’ in the data impact the ability to both observe and characterize incoming gravitational wave signals. In this work we use a scattered-light glitch waveform model to identify and characterize scattered-light glitches in a representative stretch of gravitational wave data. We identify 2749 scattered-light glitches in 5.96 days of LIGO-Hanford data and 1306 glitches in 5.93 days of LIGO-Livingston data taken from the third LIGO-Virgo observing run. By subtracting identified scattered-light glitches we demonstrate an increase in the sensitive volume of a gravitational wave search for binary black hole signals by ∼1% .

Entanglement islands, fire walls and state paradox from quantum teleportation and entanglement swapping

Abstract: Recent discovery of the fine-grained entropy formula in gravity succeeded in reconstructing the Page curves that are compatible with unitary evolution. The formula of generalized entropy derived from the gravitational path integration, nevertheless, does not provide a concrete insight on how information comes out from a black hole. In this paper, we start from a qubit model and provide a quantum informational interpretation of entanglement islands. We propose an identification of entanglement islands with quantum measurements and remark on the parallel between the black hole information problem and the old problem of quantum measurements. We show that the Page curve can still be realized even if information is lost so that the information paradox can be explained as one manifestation of measurement problem. We show that such interpretation is necessary for a quantum informational model if smooth horizons and bulk reconstruction are assumed, and demonstrate explicitly that Page curves of solvable 2D gravity can be obtained through teleportation and entanglement swapping. We argue that the similarities between the black hole information problem and the measurement problem suggest links in the origins of the two problems.

On the non-minimal coupling of magnetic fields with gravity in Schwarzschild spacetime

Abstract: Abstract In this work we study the effects of non-minimal coupling between electromagnetism and gravity, which are motivated by quantum effects such as vacuum polarization. We investigate the modification of both asymptotically dipole and uniform magnetic fields around a Schwarzschild black hole that come as the result of non-minimal coupling. While in both cases the magnetic field gets enhanced or suppressed with respect to the case of minimal coupling, depending on the sign of non-minimal coupling parameter, in the case of a background uniform magnetic field the direction of the magnetic field also alters in the vicinity of the black hole horizon. We have discussed the possible astrophysical and cosmological sources for which the vacuum polarization may be at play, while also discussing the observational effects, in particular the possibility of synchrotron radiation from the vicinity of a black hole. We conclude that such observations could be used to constrain the value of the non-minimal coupling parameter.

Relativistic elasticity II

Abstract: This paper is based on a series of talks given at the Erwin Schr\odinger International Institute for Mathematics and Physics (ESI) program on ‘Mathematical Perspectives of Gravitation Beyond the Vacuum Regime’ in February 2022. It is meant to be an introduction to the field of relativistic elasticity for readers with a good base in the mathematics of general relativity with no necessary previous of knowledge of elasticity either in the classical or relativistic domain. Despite its introductory purpose, the present work has new material, in particular related to the formal structure of the theory.

The gravito-electromagnetic approximation to the gravimagnetic dipole and its velocity rotation curve

Abstract: In view of the observed flat rotation curves of spiral galaxies and motivated by the simple fact that within Newtonian gravity a stationary axisymmetric mass distribution or dark matter vortex of finite extent readily displays a somewhat flattened out velocity rotation curve up to distances comparable to the extent of such a vortex transverse to the galaxy’s disk, the possibility that such a flattening out of rotation curves may rather be a manifestation of some stationary axisymmetric space-time curvature of purely gravitational character, without the need of some dark matter particles, is considered in the case of the gravimagnetic dipole carrying opposite Newman–Unti–Tamburino charges and in the tensionless limit of its Misner string, as an exact vacuum solution to Einstein’s equations. Aiming for a first assessment of the potential of such a suggestion easier than a full-fledged study of its geodesics, the situation is analysed within the limits of weak field gravito-electromagnetism and nonrelativistic dynamics. Thereby leading indeed to interesting and encouraging results.

Quantization of a black-hole gravity: geometrodynamics and the quantum

Abstract: Abstract Quantum gravity is effective in domains where both quantum effects and gravity are essential, such as in the vicinity of space-time singularities. This paper will investigate the quantization of a black-hole gravity, particularly the region surrounding the singularity at the origin of the coordinate system. Describing the system with a Hamiltonian formalism, we apply the covariant integral quantization method to find the Wheeler–DeWitt equation of the model. We find that the quantized system has a discrete energy spectrum in the region inside the event horizon. Through the Kantowski–Sachs metric, it is possible to correlate the entropic time, which gives the dynamics for this model, to the cosmic time in a non-trivial way. Different configurations for the phase space of a Schwarzschild black hole are obtained in a semi-classical analysis. For lower-energy states, the quantum corrections result in singularity removal and wormhole formation.

Adaptive charge control for the space inertial sensor

Abstract: Inertial sensors are key components of gravitational wave observations and Earth geodesy missions. An inertial sensor includes an isolated free-floating test mass (TM) surrounded by capacitive electrodes and a housing frame (EH) to perform the relative-position measurement and control the TM in six degrees of freedom. Owing to galactic cosmic rays and solar energetic particles, many additional accelerations are introduced through the Coulomb interaction between charged TMs and their surrounding conducting surfaces. Thus, the TM charge control is critical in space-based missions. A contact-free and ultraviolet light-based charge management system (CMS) was developed to reduce charge-induced noises acting on the TMs and minimize force disturbances that can perturb measurements or interrupt science tasks. However, the operating environment for space charge control is full of uncertainties and disturbances. Physical parameters in the discharging process are rarely measured and will vary owing to changes in solar activity, temperature, and so on. The unpredictability and variability of these parameters affects the CMS performance in long-term space missions and must be evaluated or eliminated. This paper presents a simplified physical model for the discharge process based on electron exchange between the TM and the opposing EH. Subsequently, a model reference adaptive control (MRAC) is proposed for the CMS with parametric uncertainties to maintain the TM charge below a certain level and improve its robustness. The simulation results show that the MRAC can automatically adjust control parameters to eliminate the effect of the variability of the aforementioned physical parameters, and the control precision can reach 0.1 mV under uncertainties, which is superior to that of a classic proportional–integral–derivative controller. This study demonstrated the effects of adaptive charge control and its potential for actual applications.

Some remarks on relativistic fluids of divergence type

Abstract: Relativistic fluids of divergence type constitute a special class of fluids whose states are determined from the knowledge of a scalar generating function χ and a dissipation tensor Iμν i.e. a second rank, symmetric and traceless tensor. Both (χ,Iμν) depend upon fourteen variables, known in the literature as Lagrange multipliers, and these multipliers satisfy a symmetric, quasilinear, first order system determined by (χ,Iμν) . For particular choices of the generating function χ, this system can be symmetric-hyperbolic and causal. We show in this work that this characteristic property of fluids of divergence type originates in the overdetermined nature of their dynamical equations. Combining their overdetermined nature with the work of Friedrichs on overdetermined system of conservation laws with more recent work by Boillat, Ruggeri and coworkers, we prove that fluids of divergence type are locally determined by a vector potential depending upon the Lagrange multipliers. For the case where the dynamical variables describing fluid states contain a symmetric energy momentum tensor, this vector potential is the gradient of a scalar field and this field is precisely the generating function χ introduced by Pennisi and independently by Geroch and Lindblom. Examples of scalar generating functions χ are discussed where this system is a symmetric hyperbolic and causal system in an open vicinity of equilibrium states.