In this paper, we introduce ubergravity based on the idea of the ensemble average theory of f (R) gravity models. This model has interesting properties including its universality. Another property of this model is its curvature dependency: In high curvatures, ubergravity is reduced to standard Einstein-Hilbert action, while in low curvatures, it vanishes. This transition happens at a scale of R0. It is possible to show that this dimensionful scale plays the role of the cosmological constant at late times. To consider the behavior of the non-linear structure formation, we need to start with the spherical collapse; hence, here we study the spherically symmetric solutions. We show that the radius dependency of these solutions is totally different from the Schwarzchild solution. Interestingly, the solutions looks like the Reissner-Nordstrom in the absence of any electrical charge.

In this paper, we study a family of dynamical wormhole solutions in an inhomogeneous spherically symmetric space time by considering a specific radial dependent redshift function. Using a generalized Friedmann-Robertson-Walker spacetime, we derive analytical evolving wormhole geometries by assuming a particular equation of state for energy density and pressure profiles. We calculate these classes of solutions for zero separation constant and their scale factor. The rate of expansion of these evolving wormholes is determined only by the standard Friedmann equation in cosmology. We introduce exact asymptotically flat solutions that respect energy conditions at throat. Finally, we investigate the weak energy condition for these solutions with detail.

In this paper, a combination of the braneworld scenario and covariant de Rham-Gabadadze-Tolley (dRGT) massive Gravity theory is proposed. In this setup, the Five-dimensional bulk graviton is considered to be massive. The Five dimensional nonlinear ghost-free massive gravity theory affects the 3-brane dynamics and the gravitational potential on the brane. Following the solutions with spherical symmetry on the brane, the full Field equations together with the generalized Israel-Darmois junction conditions on the brane and their weak field limits are presented in details. Generally, the theory has four Stuckelberg fields along with the components of physical metric. Although analytical solutions of these equations are impossible in general, by considering some simplifying assumptions, two classes of four-dimensional spherically symmetric solutions on the brane with different background Stuckelberg fields are obtained.

Considering an action in modified gravity, the static spherically symmetric solutions in vacuum are investigated. Introducing the Lagrangian multipliers α , we obtained the Lagrangian and equations of motion. For the constant Gauss-Bonnet invariant, the metric leads to de sitter solutions with and. Then for a large class of these models we obtain the exact solutions. Finally we study the thermodynamical quantities of these solutions. we obtain two type solutions for these models. The first case leads to Schwarzschild-de Sitter (anti de Sitter) solution and the other one, results in a new metric. The layout of the paper is the following. The action of gravity is considered and the field quations are derived, then the effect of modified gravity is considered as an effective stress-energy tensor. For the static spherically symmetric metric and using the method of Lagrangian multipliers to obtain the lagrangian and equations of motion is discussed. Then, the static spherically symmetric vacuum solutions for a large class of these metrics are investigated and the exact solutions are obtained.

We focus on the problem of estimating the average vector $\text{\boldmath$\text{\boldmath$\theta$}$}= ( \theta_{1} ,\ldots,\theta_{d} )$ of a random vector $\mathbf{X} \in \mathbb{R}^{d }$ which follows a spherically symmetric distribution. We consider modified balanced loss functions of the form:\\$ \textbf{(i)}\ \ L_{\omega,\text{\boldmath$\text{\boldmath$\delta$}$}_0,\rho}(\text{\boldmath$\text{\boldmath$\delta$}$},\text{\boldmath$\text{\boldmath$\theta$}$})=\omega \rho(\|\text{\boldmath$\text{\boldmath$\delta$}$} - \text{\boldmath$\text{\boldmath$\delta$}$}_ {0 }\|^{2}) +(1-\omega)\rho(\|\text{\boldmath$\text{\boldmath$\delta$}$} - \text{\boldmath$\text{\boldmath$\theta$}$}\|^{2})\ \hbox{ and } \ \textbf{(ii)}\ \ \ell(\omega \ \|\text{\boldmath$\text{\boldmath$\delta$}$} - \text{\boldmath$\text{\boldmath$\delta$}$}_{0}\|^{2} +(1-\omega)\|\text{\boldmath$\text{\boldmath$\delta$}$}- \text{\boldmath$\text{\boldmath$\theta$}$}\|^{2}). $Here, $\text{\boldmath$\text{\boldmath$\delta$}$}_{0}$ represents a target estimator of $\text{\boldmath$\text{\boldmath$\theta$}$}$, $\omega \in [0,1]$ and $\rho$ and $\ell$ are increasing and concave functions. If $d \geq 4$ and the target estimator is $\text{\boldmath$\text{\boldmath$\delta$}$}_{0}(\mathbf{X})=\mathbf{X}$, we provide conditions on the parameter $a$ for Baranchik type estimators $\text{\boldmath$\text{\boldmath$\delta$}$}_{a,S} (\mathbf{X}) =\left(1-a(1-\omega) S(\| \mathbf{X}\|^2)/\|\mathbf{\mathbf{X}}\|^{2} \right)\mathbf{X}$ and reach the minimaxity. These conditions are derived using the radial properties of spherically symmetric distributions, which do not require the existence of a probability density for the random vector $\mathbf{X}$. Furthermore, we extend the obtained results to the case of robust shrinkage estimators of the form $\text{\boldmath$\delta$}_{\omega,g}(\mathbf{X})=\mathbf{X} + a(1-\omega)g(\mathbf{X})$, where $g(\cdot)$ is a weakly differentiable and satisfying some conditions. Additionally, we conduct a simulation study in order to show the effectiveness and the usefulness of the obtained results.

High temperatures are often encountered in almost all of the combustion systems, therefore, thermal radiation heat transfer can influence the droplets heat up rate and consequently their life time. In this paper, the effect of thermal radiation heat transfer is investigated for two cases of directional and spherically symmetric illuminations. The flow and temperature fields insdie and outside of the droplet are solved numerically using control volume approach in the presence of thermal radiation. Mie theory is used for the case of directionally illuminated droplet and Dombrovsky’s simplified model is employed for the spherically symmetric illumination to determine the amount and distribution of the absorbed thermal heat inside the droplet. Maximum absorption for a dodecane droplet occurs at the back of the droplet when subjected to directional illumination, while it happens on the surface of the droplet for spherically symmetric illumination. Results show that the heat up rate is less affected by directional radiation whereas spherically symmetric radiation enhances the heat up rate.

This model considers the impact of microscopic structure on a nonsimple thermoelastic hollow sphere with a spherically symmetry exposed to thermal shock-type heat supply on the inner and outer curved surface. The influence of temperature discrepancy factor and phase-lag in the context of a memory-dependent derivative are examined. The study utilizes the Fourier series Laplace inversion method to obtain numerical solutions across different physical domains, and graphically illustrates transient responses such as temperature, displacement, and stress. The study indicates that the memory-dependent derivative accurately represents the memory effect, which is the rate of change influenced by the previous state, potentially aiding in better heat management of nonsimple media. The study compares temperature distributions in non-Fourier and classical Fourier models, revealing wave-like phenomena in fractional heat transfer that are not observed in classical heat conduction. Based on the proposed model, we can derive specific previous thermoelasticity models as special cases. The article's physical viewpoints could be helpful in the development of novel materials for modeling nanoscale heat transport problems in various devices. This study aims to provide future researchers with a comprehensive understanding of nonsimple three-phase lags thermoelasticity, including a detailed analysis of the memory effect.

The purpose of this paper is to introduce the concept of a cone symmetric space and to investigate relationship between (cone) metric spaces and (cone) symmetric spaces. Among other things, we shall also extend some fixed point results from metric spaces to cone metric spaces (Theorem 3.3), and to symmetric spaces (Theorems 3.2 and 3.5) under some new contraction conditions.

A null thin shell immersed in a generic spherically symmetric space-time is studied within the distributional formalism. It has been shown that the distributional formalism leads to the same result as the conventional Barrabes-Israel formalism.