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This paper explores time-varying black holes within the framework of the Einstein-Gauss-Bonnet theory with two scalar fields, examining the propagation of gravitational waves (GW). In reconstructed models, ghosts frequently emerge but can be eliminated by applying certain constraints. We investigate the behavior of high-frequency gravitational waves by examining the effects of varying Gauss-Bonnet coupling during their propagation. The speed of transmission is altered by the coupling in the creation of black holes. The speed of gravitational waves varies as they enter a black hole compared to when they exit.

Physically based changes to general relativity (GR) often predict significant differences in how spacetime behaves near massive neutron stars. One of these modifications is represented by $f(\mathcal{Q}, { \mathcal{T}})$, with $\mathcal{Q}$ being the non-metricity and ${ \mathit{T}}$ representing the energy-momentum tensor trace. This theory is viewed as a neutral expansion of GR. Neutron stars weighing more than 1.8 times the mass of the Sun, when observed as radio pulsars, provide valuable opportunities to test fundamental physics under extreme conditions that are rare in the observable universe and cannot be replicated in experiments conducted on land. We derive an exact solution through utilizing the form $f(\mathcal{Q}, { \mathcal{T}})=\mathcal{Q}+\psi { \mathcal{T}}$, where $\psi$ represents a dimensional expression. We elucidate that all physical quantities within the star can be expressed using the dimensional parameter $\psi$ and the compactness, which is defined as $C=\frac{ 2GM}{Rc^2}$. We set $\psi$ to a maximum value of $\psi_1=\frac{\psi}{\kappa^2}=-0.04$ in the negative range, based on observational constraints related to radius and mass of the pulsar ${\textit SAX J1748.9-2021}$. Here, ${\mathrm \kappa^2}$ represents the coupling constant of Einstein, defined as ${\mathrm \kappa^2=\frac{8\pi G}{c^4}}$. Unlike in GR, the solution we derived results in a stable compact object without violating the conjectured sound speed condition $c_s^2\leq\frac{c^2}3$.It is crucial to mention that no equations of state were assumed in this investigation. Nevertheless, our model fits nicely with linear form. Generally, when $\psi$ is negative, the theory predicts a star with a slightly larger size than GR for the same mass. The difference in predicted size between the theory with a negative $\psi$ and GR for the same mass is attributed to an additional force., Comment: 16 pages and 7 figures will appear in EPJC

In the course of this research, we employ the Gauss-Bonnet equation of motion alongside the scalar field and potential to acquire a fresh solution for a spherically symmetrical charged black hole. Specifically, we derive this black hole solution by employing a metric potential where the components are equal, that is, $g_{tt}=g_{rr}$. In our research, we achieve several accomplishments, including fixing the characteristics of the scalar field, and the Gauss-Bonnet term. We thoroughly examine the physical properties associated with such black hole and show that we have supplementary terms when compared to the Reissner-Nordstr\"om black hole solution. These additional terms are of the order $O(\frac{1}{r^6})$ and $O(\frac{1}{r^9})$. The presence of these supplementary terms can be attributed to the impact of the scalar function denoted as $\xi$. Such expressions play a crucial role in generating the multi-horizon black hole solution. The presence of these extra terms facilitates the derivation of a modified first law of thermodynamics and the corresponding Smarr relation., Comment: 18 pages, 4 figures

We revisit slow rotating black hole (BH) solutions in Chern-Simons modified gravity (CSMG) by considering perturbative solution about Schwarzschild BH. In particular, the case when nondynamical CSMG with noncanonical CS scalar is considered. We provide a new solution different from the previously obtained one \cite{Konno:2007ze} which we refer to as KMT model. The present solution accounts for frame dragging effect which includes not only radial dependence as in the KMT. Nevertheless, it reduces to KMT as a particular case. We show that the tidal gravitational force (Kretschmann invariant) associated to the present solution contains a term of order $1/r^3$ additional to Schwarzschild but absent from directional divergence, unlike KMT model which diverges along the axis of symmetry. We derive the corresponding circular velocity of a massive test particle in which the KMT velocity is recovered in addition to an extra term $\propto r$. We investigate possible constraints on KMT and the present solutions from the observed rotation curve of UGC11455 galaxy as an example. We show that perturbation solutions cannot physically explain the flattening of galactic rotation curves., Comment: 13 pages, 2 figures, match the version that will appear in Phys. Lett. B

The objective of this research is to explore compact celestial objects while considering the framework of an extended gravitational theory known as $\mathcal{R}+f(\mathcal{G})$ gravity. The notations $\mathcal{R}$ and $\mathcal{G}$ denote the Ricci scalar and the Gauss-Bonnet invariant, respectively. Radio pulsars, which are neutron stars with masses greater than 1.8 times that of the Sun ($M_\odot$), provide exceptional opportunities for delving into fundamental physics in extraordinary environments unparalleled in the observable universe and surpassing the capabilities of experiments conducted on Earth. Through the utilization of both the linear and quadratic expressions of the function { $f(\mathcal{G}) = \alpha_1 \mathcal{G}^2$, where $\alpha_1$ (with dimensional units of [${\textit length}^6$]) are incorporated}, we have achieved an accurate analytical solution for anisotropic perfect-fluid spheres in a state of hydrostatic equilibrium. By integrating the dimensional parameters $\alpha_1$ and the compactness factor, defined as ${\mathcal C=\frac{2GM}{Rc^2}}$, we showcase our capacity to encompass and depict all physical characteristics within the stellar structure. We illustrate that the model is capable of producing a stable arrangement encompassing its physical and geometric properties. We illustrate that by utilizing the quadratic form of $\mathcal{G}$ in the $\mathcal{R}+f(\mathcal{G})$ framework, the ansatz of Krori-Barua establishes connection between pressure in the radial direction ($p_r$) using semi-analytical methods, pressure in the tangential direction ($p_t$), and density ($\rho$)., Comment: 19 pages 9 Figures

We discuss spherically symmetric dynamical systems in the framework of a general model of $f({\cal R})$ gravity, i.e. $f({\cal R})={\cal R}e^{\zeta {\cal R}}$, where $\zeta$ is a dimensional quantity in squared length units [L$^2$]. We initially assume that the internal structure of such systems is governed by the Krori-Barua ansatz, alongside the presence of fluid anisotropy. By employing astrophysical observations obtained from the pulsar {\textit SAX J1748.9-2021}, derived from bursting X-ray binaries located within globular clusters, we determine that $\zeta$ is approximately equal to $\pm 5$ km$^2$. In particular, the model can create a stable configuration for {\textit SAX J1748.9-2021}, encompassing its geometric and physical characteristics. In $f({\cal R})$ gravity, the Krori-Barua approach links $p_r$ and $p_t$, which represent the components of the pressures, to ($\rho$), representing the density, semi-analytically. These relations are described as $p_r\approx v_r^2 (\rho-\rho_{I})$ and $p_t\approx v_t^2 (\rho-\rho_{II})$. Here, the expression $v_r$ and $v_t$ represent the radial and tangential sound speeds, respectively. Meanwhile, $\rho_I$ pertains to the surface density and $\rho_{II}$ is derived using the parameters of the model. Notably, within the frame of $f({\cal R})$ gravity where $\zeta$ is negative, the maximum compactness, denoted as $C$, is inherently limited to values that do not exceed the Buchdahl limit. This contrasts with general relativity or with $f({\cal R})$ with positive $\zeta$, where $C$ has the potential to reach the limit of the black hole asymptotically. The predictions of such model suggest a central energy density which largely exceeds the saturation of nuclear density, which has the value $\rho_{\text{nuc}} = 3\times 10^{14}$ g/cm$^3$. Also, the density at the surface $\rho_I$ surpasses $\rho_{\text{nuc}}$., Comment: 28 pages, 8 figures, Will appear in EPJC

In this paper, we investigate the gravitational collapse to form the black hole in the acceleratingly expanding universe in the frame of Einstein--Gauss-Bonnet theory having two scalar fields and we study the propagation of the gravitational wave (GW). This may describe the creation of the primordial black holes in the early stages of the universe and the impact of their creation on the propagation of primordial gravitational waves. The collapsing spacetime can be obtained by using the formulation of the ``reconstruction'', that is, we find a model that realises the desired or given geometry. In the reconstructed models, ghosts often appear, which could be eliminated by imposing constraints. We show that the standard cosmological solutions or self-gravitating objects such as a planet, the Sun, various types of stars, etc., in Einstein's gravity, are also solutions in this model. Using the dynamical value of the Gauss-Bonnet coupling, the propagation of the high-frequency GW is investigated. The propagating speed changes due to the coupling during the period of the black hole formation. The speed of the GW propagation going into the black hole is different from that of the wave going out., Comment: 24 pages, no figure, the title is changed, the version to appear in Physical Review D

This study looks into regular solutions in a theory of gravity called $f(R)$ gravity, which also involves a scalar field. The $f(R)$ theory changes Einstein's ideas by adding a new function related to something called the Ricci scalar. This lets us tweak the equations that describe how gravity works. Adding a scalar field makes the theory more interesting, giving us more ways to investigate and understand it. { The main goal of this research is to create regular black holes using a combination of $f(R)$ gravitational theory and a scalar field.} Regular solutions don't have any singularities, which are points where certain physical quantities, like invariants, become really big or undefined. { In this context, we find two regular black hole solutions by using a spherical space with either an equal or unequal approach.} For the solutions where we use the equal approach, we figure out the shape of $f(R)$ and how it changes, along with its first and second derivatives. We demonstrate that Hayward's solution in this theory stays steady because all the shapes of $f(R)$ and their first and second derivatives are positive. Next, we focus on the case where the metric isn't equal and figure out the black hole solution. We also find out what $f(R)$ and the scalar field look like in this situation. We demonstrate that the solution in this case is a broader version of the Hayward solution. When certain conditions are met, we end up back at the scenario where the metrics are equal. We also prove that this model is stable because $f(R)$, along with its first and second derivatives, are all positive. { We analyze the trajectories of these black hole solutions and determine the forms of their conserved quantities that remain same along those trajectories., Comment: 23 pages, four figures

In this paper, we propose a model including four scalar fields coupled with general gravity theories, which is a generalization of the two-scalar model proposed in Phys. Rev. D \textbf{103} (2021) no.4, 044055, where it has been shown that any given spherically symmetric static/time-dependent spacetime can be realized by using the two-scalar model. We show that by using the four-scalar model, we can construct a model that realizes any given spacetime as a solution even if the spacetime does not have a spherical symmetry or any other symmetry. We also show that by imposing constraints on the scalar fields by using the Lagrange multiplier fields, the scalar fields become non-dynamical and they do not propagate. This tells that there does not appear any sound which is usually generated by the density fluctuation of the fluid. In this sense, the model with the constraints is a most general extension of the mimetic theory in JHEP \textbf{11} (2013), 135, where there appears an effective dark matter. The dark matter is non-dynamical and it does not collapse even under gravitational force. Our model can be regarded as a general extension of any kind of fluid besides dark matter. We may consider the case that the potential of the scalar fields vanishes and the model becomes a non-linear $\sigma$ model. Then our formulation gives a mapping from the geometry of the spacetime to the geometry of the target space of the non-linear $\sigma$ model via gravity theory although the physical meaning has not been clear. We also consider the application of the model to $f(Q)$ gravity theory, which is based on a non-metricity tensor and $Q$ is a scalar quantity constructed from the non-metricity tensor. ..., Comment: LaTeX 12 pages, version to appear in Physics of the Dark Universe

Due to the absence of spherically symmetric black hole solutions in $f(\mathbb{Q})$ because of the constraint derived from its field equations, which yields either $\mathbb{Q}=0 $ or $f_{\mathbb{Q} \mathbb{Q}}=0 $ \cite{Heisenberg:2023lru,Maurya:2023muz}. We are going to introduce a tours solutions for charged anti-de-Sitter black holes in $N$-dimensions within the framework of the quadratic form of $f(\mathbb{Q})$ gravity, where the coincident gauge condition is applied \cite{Heisenberg:2023lru}. Here, $f(\mathbb{Q})=\mathbb{Q}+\frac{1}2\alpha \mathbb{Q}^2-2\Lambda$, and the condition $N \geq 4$ is satisfied. These black hole solutions exhibit flat or cylindrical horizons as their distinctive features. An intriguing aspect of these black hole solutions lies in the coexistence of electric monopole and quadrupole components within the potential field, which are indivisible and exhibit interconnected momenta. This sets them apart from the majority of known charged solutions in the linear form of the non-metricity theory and its extensions. Moreover, the curvature singularities in these solutions are less severe compared to those found in known charged black hole solutions within the characteristic can be demonstrated by computing certain invariants of the curvature and non-metricity tensors. Finally, we calculate thermodynamic parameters, including entropy, Hawking temperature, and Gibbs free energy. These thermodynamic computations affirm the stability of our model., Comment: 13 pages, 3 figures

We describe a phase-retrieval-based imaging method to directly spatially resolve the vector lattice distortions in an extended crystalline sample by explicit coupling of independent Bragg ptychography data sets into the reconstruction process. Our method addresses this multi-peak Bragg ptychography (MPBP) inverse problem by explicit gradient descent optimization of an objective function based on modeling of the probe-lattice interaction, along with corrective steps to address spurious reconstruction artifacts. Robust convergence of the optimization process is ensured by computing exact gradients with the automatic differentiation capabilities of high-performance computing software packages. We demonstrate MPBP reconstruction with simulated ptychography data mimicking diffraction from a single crystal membrane containing heterogeneities that manifest as phase discontinuities in the diffracted wave. We show the superior ability of such an optimization-based approach in removing reconstruction artifacts compared to existing phase retrieval and lattice distortion reconstruction approaches.

Solutions pertaining to a Kerr black hole with a flat horizon undergoing gradual rotation are explored in the context of gravitational theories modified by dynamical Chern-Simons terms with cylindrical metrics, which approach asymptotically the anti de Sitter spacetime. It is shown that the cross-term of a metric component is unaffected by the perturbations of the Chern-Simons scalar independently of whether the dynamical Chern-Simons field equation is uncharged or charged with an electric field. From this result, it is ensured that the Chern-Simons scalar field can affect the spaces of the metric that approach asymptotically the flat spacetime only., Comment: 10 pages

We propose a class of models, in which stable gravastar with large surface redshift becomes a solution. In recent decades, gravastars have become a plausible substitute for black holes. Researchers have explored stable gravastar models in various alternative gravity theories, in addition to the conventional framework of general relativity. In this paper, we present a stellar model within the framework of Einstein's gravity with two scalar fields, in accordance with the conjecture proposed by Mazur and Mottola [Proc. Nat. Acad. Sci. \textbf{101} (2004), 9545-9550]. In the model, the two scalar fields become non-dynamical by imposing constraints in order to avoid ghosts. The gravastar comprises two distinct regions, namely: (a) the interior region and (b) the exterior region. We assume the interior region consists of the de Sitter spacetime, and the exterior region is the Schwarzschild one. The two regions are connected with each other by the shell region. On the shell, we assume that the metric is given by a polynomial function of the radial coordinate $r$. The function has six constants. These constants are fixed by the smooth junction conditions, i.e., the interior region with the interior layer of the shell and the exterior region with the exterior layer of the shell. From these boundary conditions, we are able to write the coefficients of the scalar fields in terms of the interior radius and exterior radius. To clarify the philosophy of this study, we also give two examples of spacetimes that asymptote as the de Sitter spacetime for small $r$ and as the Schwarzschild spacetime for large $r$. Exploration is focused on the physical attribute of the shell region, specifically, its proper length., Comment: 18 pages, 8 Figures, will appear in JCAP

In this paper, we construct models that admit the traversable wormhole geometries in the framework of Einstein's gravity with two scalar fields. As well known, the energy conditions are broken and we show that there appears a ghost. The ghost can be, however, eliminated by imposing a constraint on the ghost field, which is a scalar. The constraint is similar to the mimetic one proposed by Chamseddine and Mukhanov to construct an alternative description of cold dark matter. We explicitly show that there does not appear any unstable mode although the energy conditions are broken. Therefore we obtain a model that realizes the traversable and stable wormhole., Comment: 11 pages, one figure

We derive a novel class of four-dimensional black hole solutions in Gauss-Bonnet gravity coupled with a scalar field in presence of Maxwell electrodynamics. In order to derive such solutions, we assume the ansatz $ g_{tt}\neq g_{rr}{}^{-1}$ for metric potentials. Due to the ansatz for the metric, the Reissner Nordstr\"om gauge potential cannot be recovered because of the presence of higher-order terms ${\cal O}\left(\frac{1}{r}\right)$ which are not allowed to be vanishing. Moreover, the scalar field is not allowed to vanish. If it vanishes, a function of the solution results undefined. For this reason, the solution cannot be reduced to a Reissner Nordstr\"om space-time in any limit. Furthermore, it is possible to show that the electric field is of higher-order in the monopole expansion: this fact explicitly comes from the contribution of the scalar field. Therefore, we can conclude that the Gauss-Bonnet scalar field acts as non-linear electrodynamics creating monopoles, quadrupoles, etc. in the metric potentials. We compute the invariants associated with the black holes and show that, when compared to Schwarzschild or Reissner-Nordstr\"om space-times, they have a soft singularity. Also, it is possible to demonstrate that these black holes give rise to three horizons in AdS space-time and two horizons in dS space-time. Finally, thermodynamic quantities can be derived and we show that the solution can be stable or unstable depending on a critical value of the temperature., Comment: 28 pages three figures, will appear in Class.& Quant. Grav

Liquid argon time projection chambers (LArTPCs) are widely used in particle detection for their tracking and calorimetric capabilities. The particle physics community actively builds and improves high-quality simulators for such detectors in order to develop physics analyses in a realistic setting. The fidelity of these simulators relative to real, measured data is limited by the modeling of the physical detectors used for data collection. This modeling can be improved by performing dedicated calibration measurements. Conventional approaches calibrate individual detector parameters or processes one at a time. However, the impact of detector processes is entangled, making this a poor description of the underlying physics. We introduce a differentiable simulator that enables a gradient-based optimization, allowing for the first time a simultaneous calibration of all detector parameters. We describe the procedure of making a differentiable simulator, highlighting the challenges of retaining the physics quality of the standard, non-differentiable version while providing meaningful gradient information. We further discuss the advantages and drawbacks of using our differentiable simulator for calibration. Finally, we provide a starting point for extensions to our approach, including applications of the differentiable simulator to physics analysis pipelines.

By utilizing the field equations of the modified teleparallel equivalent of general relativity, denoted as $\mathit{f(T)}$, we obtain an exact solution for a static charged black hole in n-dimensions, without imposing any constraints. The black hole possesses two distinctive dimensional constants: $m$ and $v$ with unit {\textit length}. The first constant is associated with the mass, while the second constant represents the electric charge. The existence of this electrical charge causes the black hole to diverge from the expectations of the teleparallel equivalent of general relativity (TEGR). Our analysis demonstrates that $\mathit{f(T)}$ is reliant on the parameter $v$ and transforms into a constant expression when $v$ is assigned a value of zero. A captivating aspect of this particular black hole is its absence of singularities in the quantities formed using torsion and curvature, given that the dimension $n$ falls within the interval of $4 \leq n \leq 6$ as $r$ approaches zero. However, for $n\geq7$, the singularity becomes milder in comparison to the case of TEGR. Furthermore, By utilizing the conserved n-momentum vector, we calculate the energy of this solution and confirm its correspondence with the ADM mass, accurate to the order of $O\Big(\frac{1}{r}\Big)$. Otherwise, we observe higher-order contributions arising from the electric charge terms. Through the application of a coordinate transformation to the black hole, we derive a precise solution describing a stationary rotating black hole. This solution showcases significant readings of the torsion scalar and the analytical function $\mathit{f(T)}$. In order to gain insight into the physics of this black hole, we calculate various physical quantities related to thermodynamics, such as entropy, Hawking temperature, and heat capacity. The analysis reveals that the black hole exhibits thermal stability., Comment: 17 pages and four figures

Many physically inspired general relativity (GR) modifications predict significant deviations in the properties of spacetime surrounding massive neutron stars. Among these modifications is $f(\mathcal{R}, \mathbb{T})$, where $\mathcal{R}$ is the Ricci scalar, $\mathbb{T}$ represents the trace of the energy-momentum tensor, the gravitational theory that is thought to be a neutral extension of GR. Neutron stars with masses above 1.8 $M_\odot$ expressed as radio pulsars are precious tests of fundamental physics in extreme conditions unique in the observable universe and unavailable to terrestrial experiments. We obtained an exact analytical solution for spherically symmetric anisotropic perfect-fluid objects in equilibrium hydrostatic using the frame of the form of $f(\mathcal{R},\mathbb{T})=\mathcal{R}+\beta \mathbb{T}$ where $\beta$ is a dimensional parameter. We show that the dimensional parameter $\beta$ and the compactness, $C=\frac{ 2GM}{Rc^2}$ can be used to express all physical quantities within the star. We fix the dimensional parameter $\beta$ to be at most. (Here ${\mathrm \kappa^2}$ is the coupling constant of Einstein which is figured as $\kappa^2=\frac{8\pi G}{c^4}$, the Newtonian constant of gravitation is denoted as $G$ while $c$ represents the speed of light.) $\beta_1=\frac{\beta}{\kappa^2}= 0.1$ in positive values through the use of observational data from NICER and X-ray Multi-Mirror telescopes on the pulsar PSR J0740+6620, which provide information on its mass and radius., Comment: 22 pages 10 figures

The slow rotation of Kerr-NUT spacetime is explored by taking into account the linear form of rotation and NUT parameters in the dynamical Chern-Simon gravity theory, which can be formulated from a scalar field describing the background. We show that in the absence of the potential scalar field, the metric potential does not respect the effect of the NUT parameter, although the scalar field is affected by the rotation and NUT parameters. Consequently, unlike the gradually spinning black hole solution outlined in \cite{Alexander:2009tp}, the mixed component of the metric potential, encompassing both rotational and NUT parameters, doesn't make a contribution at the primary level of the initial perturbation., Comment: 14 pages

Recently, the mimetic gravitational theory has gained much attention in the frame of cosmology as well as in the domain of astrophysics. In this study, we show that in the frame of mimetic gravitation theory we are not able to derive an isotropic model. As a result, our focus shifts towards combining mimetic gravitational theory with the Lagrangian multiplier. The field equations of a static isotropic gravitational system that controls the geometry and dynamics of star structure are studied in the frame of mimetic theory coupled with a Lagrangian multiplier using a non-linear equation of state. An energy density is assumed from where all the other unknowns are fixed and a new isotropic model is derived. The physical analysis of this model is studied from different viewpoints and consistent results compatible with a realistic isotropic star are investigated analytically and graphically. Ultimately, we demonstrate the stability of the model in question by employing the adiabatic index technique., Comment: 12 pages 6 figures

Meta reinforcement learning (meta-RL) methods such as RL$^2$ have emerged as promising approaches for learning data-efficient RL algorithms tailored to a given task distribution. However, they show poor asymptotic performance and struggle with out-of-distribution tasks because they rely on sequence models, such as recurrent neural networks or transformers, to process experiences rather than summarize them using general-purpose RL components such as value functions. In contrast, traditional RL algorithms are data-inefficient as they do not use domain knowledge, but they do converge to an optimal policy in the limit. We propose RL$^3$, a principled hybrid approach that incorporates action-values, learned per task through traditional RL, in the inputs to meta-RL. We show that RL$^3$ earns greater cumulative reward in the long term, compared to RL$^2$, while maintaining data-efficiency in the short term, and generalizes better to out-of-distribution tasks. Experiments are conducted on both custom and benchmark discrete domains from the meta-RL literature that exhibit a range of short-term, long-term, and complex dependencies.

In the framework of scalar-Einstein-Gauss-Bonnet gravity, we construct the model which realizes the Hayward black hole and discuss the absence of ghosts in this model. Because Hayward black hole has two horizons but no curvature singularity, it may solve the problem of the information loss that might be generated by black holes. The Gauss-Bonnet term appears as a stringy correction, and therefore, our results might indicate that the stringy correction would solve the information loss problem., Comment: 13 pages 2 figures, To appear in Phys. Rev. D

We apply quadratic $f(R)=R+\epsilon R^2$ field equations, where $\epsilon$ has a dimension [L$^2$], to static spherical stellar model. We assume the interior configuration is determined by Krori-Barua ansatz and additionally the fluid is anisotropic. Using the astrophysical measurements of the pulsar PSR J0740+6620 as inferred by NICER and XMM observations, we determine $\epsilon\approx \pm 3$ km$^2$. We show that the model can provide a stable configuration of the pulsar PSR J0740+6620 in both geometrical and physical sectors. We show that the Krori-Barua ansatz within $f(R)$ quadratic gravity provides semi-analytical relations between radial, $p_r$, and tangential, $p_t$, pressures and density $\rho$ which can be expressed as $p_r\approx v_r^2 (\rho-\rho_1)$ and $p_r\approx v_t^2 (\rho-\rho_2)$, where $v_r$ ($v_t$) is the sound speed in radial (tangential) direction, $\rho_1=\rho_s$ (surface density) and $\rho_2$ are completely determined in terms of the model parameters. These relations are in agreement with the best-fit equations of state as obtained in the present study. We further put the upper limit on the compactness, which satisfies the $f(R)$ modified Buchdahl limit. Interestingly, the quadratic $f(R)$ gravity with negative $\epsilon$ naturally restricts the maximum compactness to values lower than Buchdahl limit, unlike the GR or $f(R)$ gravity with positive $\epsilon$ where the compactness can arbitrarily approach the black hole limit $C\to 1$. The model predicts a core density a few times the saturation nuclear density $\rho_{\text{nuc}} = 2.7\times 10^{14}$ g/cm$^3$, and a surface density $\rho_s > \rho_{\text{nuc}}$. We provide the mass-radius diagram corresponding to the obtained boundary density which has been shown to be in agreement with other observations., Comment: 18 pages, 9 figures and one table

Recent findings from the Neutron Star Interior Composition Explorer (NICER) have opened up opportunities to investigate the potential coupling between matter and geometry, along with its resulting physical implications. Millisecond pulsars serve as an ideal subject for conducting such tests and examining these phenomena. We apply the field equations of modified gravity, $f(R, T)=R+\alpha\, T$ to a spherically symmetric spacetime, where $R$ is the Ricci scalar, $\alpha$ is a dimensional parameter, and $T$ is the matter of the geometry. Five unknown functions are present in the output system of differential equations, which consists of three equations. To close the system, we make explicit assumptions about the anisotropy and the radial metric potential, $g_{rr}$. We then solve the output differential equations and derive the explicit forms of the components of the energy-momentum tensor, namely, density, radial, and tangential pressures., Comment: 22 pages, 10 figures, 3 tables

We investigate how to derive an isotropic stellar model in the framework of mimetic gravitational theory. Recently, this theory has gained big interest due to its difference from Einstein's general relativity (GR), especially in the domain non-vacuum solutions. In this regard, we apply the field equation of mimetic gravitational theory to a spherically symmetric ansatz and obtain an over determined system of non-linear differential equations in which differential equations are less than the unknown functions. To overcome the over determined system we suppose a specific form of the temporal component of the metric potential, $g_{tt}$, and assume the vanishing of the anisotropic condition to derive the form of the spatial component of the metric, $g_{rr}$. In this regard, we discuss the possibility to derive a stellar isotropic model that is in agreement with observed pulsars. To examine the stability of the isotropic model we use the Tolman-Oppenheimer-Volkoff equation and the adiabatic index. Furthermore, we assess the model's validity by evaluating its compatibility with a broad range of observed pulsar masses and radii. We demonstrate that the model provides a good fit to these observations., Comment: 13 pages, four figures and two tables

With the introduction of x-ray free electron laser sources around the world, new scientific approaches for visualizing matter at fundamental length and time-scales have become possible. As it relates to magnetism and "magnetic-type" systems, advanced methods are being developed for studying ultrafast magnetic responses on the time-scales at which they occur. We describe three capabilities which have the potential to seed new directions in this area and present original results from each: pump-probe x-ray scattering with low energy excitation, x-ray photon fluctuation spectroscopy, and ultrafast diffuse x-ray scattering. By combining these experimental techniques with advanced modeling together with machine learning, we describe how the combination of these domains allows for a new understanding in the field of magnetism. Finally, we give an outlook for future areas of investigation and the newly developed instruments which will take us there.

The observation and description of collective excitations in solids is a fundamental issue when seeking to understand the physics of a many-body system. Analysis of these excitations is usually carried out by measuring the dynamical structure factor, S(Q, $\omega$), with inelastic neutron or x-ray scattering techniques and comparing this against a calculated dynamical model. Here, we develop an artificial intelligence framework which combines a neural network trained to mimic simulated data from a model Hamiltonian with automatic differentiation to recover unknown parameters from experimental data. We benchmark this approach on a Linear Spin Wave Theory (LSWT) simulator and advanced inelastic neutron scattering data from the square-lattice spin-1 antiferromagnet La$_2$NiO$_4$. We find that the model predicts the unknown parameters with excellent agreement relative to analytical fitting. In doing so, we illustrate the ability to build and train a differentiable model only once, which then can be applied in real-time to multi-dimensional scattering data, without the need for human-guided peak finding and fitting algorithms. This prototypical approach promises a new technology for this field to automatically detect and refine more advanced models for ordered quantum systems., Comment: 12 pages, 7 figures

Neural networks functions are supposed to be able to encode the desired solution of an inverse problem very efficiently. In this paper, we consider the problem of solving linear inverse problems with neural network coders. First we establish some correspondences of this formulation with existing concepts in regularization theory, in particular with state space regularization, operator decomposition and iterative regularization methods. A Gauss-Newton's method is suitable for solving encoded linear inverse problems, which is supported by a local convergence result. The convergence studies, however, are not complete, and are based on a conjecture on linear independence of activation functions and its derivatives.

The Chern-Simons (CS) gravity is a modified theory of Einstein's general relativity (GR). The CS theory arises from the low energy limit of string theory which involves anomaly correction to the Einstein-Hilbert action. The CS term is given by the product of the Pontryagin density with a scalar field. In this study, we derive a charged slowly rotating black hole (BH) solution. The main incentives of this BH solution are axisymmetric and stationary and form distortion of the Kerr-Newman BH solution with a dipole scalar field. Additionally, we investigate the asymptotic correction of the metric with the inverse seventh power of the radial distance to the BH solution, This indicates that it will escape any meaningful constraints from weak-field experiments. To find this kind of BHs by observations, we investigate the propagation of the photon near the BH and we show that the difference between the left-rotated polarization and the right-handed one could be observed as stronger than the case of the Kerr-Newman BH. Finally, we derived the stability condition using the geodesic deviations., Comment: 20 pages 3 figures, will appear in Phys. Rev. D

One of the most crucial areas of gravity research, after the direct observation of gravitational waves, is the possible modification of General Relativity at ultraviolet and infrared scales. In particular, the possibility of parity violation should be considered in strong field regime. The Chern-Simons gravity takes into account parity violation in strong gravity regime. For all conformally flat spacetimes and spacetimes with a maximally symmetric two-dimensional subspace, Chern-Simons gravity is identical to General Relativity. Specifically, the Anti-de Sitter (A)dS-Kerr/Kerr black hole is not a solution for Chern-Simons gravity. The slow-rotating BH and the quadratic order in spin solutions are some of the known solutions to quadratic order in spin and they are rotating solutions in the frame of dynamical Chern-Simons gravity. In the present study, for the (A)dS slow-rotating situation (correct to the first order in spin), we derive the linear perturbation equations controlling the metric and the dynamical Chern-Simons field equation corrected to the linear order in spin and to the second order in the Chern-Simons coupling parameter. We show that the black hole of the (A)dS-Kerr solution is stronger (i.e. more compact and energetic) than the Kerr black hole solution and the reason for this feature comes form contributions at Planck scales. Moreover, we calculate the thermodynamical quantities related to this black hole. Finally, we calculate the geodesic equation and derive the effective potential of the black hole., Comment: 15 pages 3 figures, will appear in Phys. Rev D

As automated decision making and decision assistance systems become common in everyday life, research on the prevention or mitigation of potential harms that arise from decisions made by these systems has proliferated. However, various research communities have independently conceptualized these harms, envisioned potential applications, and proposed interventions. The result is a somewhat fractured landscape of literature focused generally on ensuring decision-making algorithms "do the right thing". In this paper, we compare and discuss work across two major subsets of this literature: algorithmic fairness, which focuses primarily on predictive systems, and ethical decision making, which focuses primarily on sequential decision making and planning. We explore how each of these settings has articulated its normative concerns, the viability of different techniques for these different settings, and how ideas from each setting may have utility for the other., Comment: 10 pages

Optical photons are used as signal in a wide variety of particle detectors. Modern neutrino experiments employ hundreds to tens of thousands of photon detectors to observe signal from millions to billions of scintillation photons produced from energy deposition of charged particles. These neutrino detectors are typically large, containing kilotons of target volume, with different optical properties. Modeling individual photon propagation in form of look-up table requires huge computational resources. As the size of a table increases with detector volume for a fixed resolution, this method scales poorly for future larger detectors. Alternative approaches such as fitting a polynomial to the model could address the memory issue, but results in poorer performance. Both look-up table and fitting approaches are prone to discrepancies between the detector simulation and the data collected. We propose a new approach using SIREN, an implicit neural representation with periodic activation functions, to model the look-up table as a 3D scene and reproduces the acceptance map with high accuracy. The number of parameters in our SIREN model is orders of magnitude smaller than the number of voxels in the look-up table. As it models an underlying functional shape, SIREN is scalable to a larger detector. Furthermore, SIREN can successfully learn the spatial gradients of the photon library, providing additional information for downstream applications. Finally, as SIREN is a neural network representation, it is differentiable with respect to its parameters, and therefore tunable via gradient descent. We demonstrate the potential of optimizing SIREN directly on real data, which mitigates the concern of data vs. simulation discrepancies. We further present an application for data reconstruction where SIREN is used to form a likelihood function for photon statistics.