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We introduce a new approach to modified gravity which generalizes the recently proposed hybrid metric-Palatini gravity. The gravitational action is taken to depend on a general function of both the metric and Palatini curvature scalars. The…
This is a short note to announce the availability of some movies that may be useful in classroom discussions on the photographic appearance of objects moving at relativistic speeds. The images are based on special relativity with no account…
This chapter provides a comprehensive overview of weak gravitational lensing and its current applications in cosmology. We begin by introducing the fundamental concepts of gravitational lensing and derive the key equations for the…
We develop a formalism for General Relativistic N-body simulations in the weak field regime, suitable for cosmological applications. The problem is kept tractable by retaining the metric perturbations to first order, the first derivatives…
Examining the relativistic collapse of a spherical spacetime where gravity is coupled with a scalar field, this review provides a thorough analysis of some of the most relevant studies from both analytical and numerical perspectives. The…
A general approach to viable modified $f(R)$ gravity is developed in both the Jordan and the Einstein frames. A class of exponential, realistic modified gravities is introduced and investigated with care. Special focus is made on step-class…
The Euclidean interpretation of special relativity which has been suggested by the author is a formulation of special relativity in ordinary 4D Euclidean space-time geometry. The natural and geometrically intuitive generalization of this…
The weak field limit of scalar tensor theories of gravity is discussed in view of conformal transformations. Specifically, we consider how physical quantities, like gravitational potentials derived in the Newtonian approximation for the…
In this lecture I address the issue of possible large distance modification of gravity and its observational consequences. Although, for the illustrative purposes we focus on a particular simple generally-covariant example, our conclusions…
We consider the three dimensional gravitational Vlasov-Poisson (GVP) system in both classical and relativistic cases. The classical problem is subcritical in the natural energy space and the stability of a large class of ground states has…
This paper is based on a series of talks given at the 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…
We shall here propose a class of relativistic theories of gravitation, based on a foundational paper of Ehlers Pirani and Schild (EPS).All "extended theories of gravitation" (also known as f(R) theories) in Palatini formalism are shown to…
In the Regge-Teitelboim model, gravity is described by embedding the space-time manifold in a (usually flat) fixed higher-dimensional background, where the embedding coordinates, rather than the metric tensor, are the dynamical degrees of…
A general, iterative, method for the description of evolving self-gravitating relativistic spheres is presented. Modeling is achieved by the introduction of an ansatz, whose rationale becomes intelligible and finds full justification within…
From a previous paper where we proposed a description of general relativity within the gravito-electromagnetic limit, we propose an alternative modified gravitational theory. As in the former version, we analyze the vector and tensor…
The relativistic extension of non-relativistic hydrodynamics suffers from notorious difficulties. In non-relativistic hydrodynamics where difficulties also abound, it has proved a useful supplement to study lattice models which can imitate…
The relativistic time is different from the Newtonian one. We revisit some of these differences in Doppler effect, twin paradox, rotation, rigid rod, and constant proper acceleration. ------- La relativeca tempo estas malsama ol la Newtona.…
Experimental constraints on the gravitational inverse-square law at short range are presented, employing a consistent formalism across a wide range of length scales. We provide comprehensive updates from the past decade, building upon our…
Granular media are soft matter systems that exhibit some of the extreme behavior of complex fluids. Understanding of the natural formation of planetary bodies, landing on and exploring them, future engineering of structures beyond Earth and…
We study a general relativistic particle action obtained by incorporating the Hamiltonian constraints into the formalism as a toy model for general relativity and string theory. We show how a non-vanishing cosmological constant and a…