We review recent developments in structural stability as applied to key topics in general relativity. For a nonlinear dynamical system arising from the Einstein equations by a symmetry reduction, bifurcation theory fully characterizes the set of all...
The equations of general relativity are recast in the form of a wave equation for the Weyl tensor. This allows reformulation of gravitational wave theory in terms of curvature waves, rather than metric waves. The existence of two transverse polarizat...
We endeavour to illustrate the physical relevance of the Landauer principle applying it to different important issues concerning the theory of gravitation. We shall first analyze, in the context of general relativity, the consequences derived from th...
The aim of this paper is to introduce the basic theoretical (both conceptual and technical) tenets of Mallios’s Abstract Differential Geometry (ADG), as well as to present and to summarise the main results from its applications in the last quar...
The relatively high abundance of fractal properties of complex systems on Earth and in space is considered an argument in support of the general relativity of the geometric theory of gravity. The fractality may be called the fractal symmetry of physi...
In this paper, we introduce Kluitenberg’s formulation of non-equilibrium thermodynamics with internal variables in the context of a Riemannian space, as required by Einstein’s general relativity. Using the formulation of the second law of...
The detections of gravitational-wave (GW) signals from compact binary coalescence by ground-based detectors have opened up the era of GW astronomy. These observations provide opportunities to test Einstein’s general theory of relativity at the...
We have built quasi-equilibrium models for uniformly rotating quark stars in general relativity. The conformal flatness approximation is employed and the Compact Object CALculator (cocal) code is extended to treat rotating stars with surface density...
An alternative approach to Einstein’s theory of General Relativity (GR) is reviewed, which is motivated by a range of serious theoretical issues inflicting the theory, such as the cosmological constant problem, presence of non-Machian solutions, prob...
The fact that real dissipative (entropy producing) processes may be detected by non-comoving observers (tilted), in systems that appear to be isentropic for comoving observers, in general relativity, is explained in terms of the information theory, a...
To get exact solutions to Einstein’s field equations in general relativity, one has to impose some symmetry requirements. Otherwise, the equations are too difficult to solve. However, sometimes, the imposition of too much extra symmetry can cau...
General relativity is one of the pillars of modern physics. For decades, the theory has been mainly tested in the weak-field regime with experiments in the solar system and radio observations of binary pulsars. Until 2015, the strong-field regime was...
In this paper, we review the physics of many bodies in the context of general relativity. Starting from the stress–energy tensor for one body and moving onto those for a swarm of bodies and for a perfect fluid, we review the relativistic hydrod...
HERO (Highly Eccentric Relativity Orbiter) is a space-based mission concept aimed to perform several tests of post-Newtonian gravity around the Earth with a preferably drag-free spacecraft moving along a highly elliptical path fixed in its plane unde...
In this paper the dynamical equation for propagating wave-fronts of gravitational signals in classical general relativity (GR) is determined. The work relies on the manifestly-covariant Hamilton and Hamilton–Jacobi theories underlying the Einst...
The metrics of general relativity generally fall into two categories: those which are solutions of the Einstein equations for a given source energy-momentum tensor and the “reverse engineered” metrics—metrics bespoke for a certain purpose. Their ener...
We present a brief review of the teleparallel equivalent of general relativity and analyse the expression for the centre of mass density of the gravitational field. This expression has not been sufficiently discussed in the literature. One motivation...
We elaborate on the similarities between the explanation of the well known Maxwell’s demon paradox, based on the theory of information, and the rationale behind the fact that real dissipative (entropy producing) processes may be detected by non–comov...
For the last 100 years, General Relativity (GR) has taken over the gravitational theory mantle held by Newtonian Gravity for the previous 200 years. This article reviews the status of GR in terms of its self-consistency, completeness, and the evidenc...
This review examines the role of differential forms, Pfaffian systems, and hypersurfaces in general relativity. These mathematical constructions provide the essential tools for general relativity, in which the curvature of spacetime—described b...
In this paper, different aspects of the concept of spin are studied. The most well-established one is, of course, the quantum mechanical aspect: spin is a broken symmetry in the sense that the solutions of the Dirac equation tend to have directional...
This work places the invariant
We first take a closer look at the original warp drive proposal by Alcubierre, examine its kinematics in the context of a covariant 3+1 setting, and explain some drawbacks of this construction. In this model, changes in the velocity profile are suppr...
The classical uncertainty principle inequalities are imposed over the general relativity geodesic equation as a mathematical constraint. In this way, the uncertainty principle is reformulated in terms of proper space–time length element, Planck lengt...
In this paper we represent a different approach to the calculation of the perihelion shift than the one presented in common text books. We do not rely on the Schwarzschild metric and the Hamilton–Jacobi technique to obtain our results. Instead...
In this paper, we briefly present RELXILL_NK, the first and currently only readily available model of the relativistic reflection spectrum of black hole accretion disks that includes non-Kerr solutions for the black hole spacetime, thus allowing for...
The relativity experiment is part of the Mercury Orbiter Radio science Experiment (MORE) on-board the ESA/JAXA BepiColombo mission to Mercury. Thanks to very precise radio tracking from the Earth and accelerometer, it will be possible to perform an a...
In this paper, we review our current efforts to test General Relativity in the strong field regime by studying the reflection spectrum of supermassive black holes. So far we have analyzed 11 sources with observations of NuSTAR, Suzaku, Swift, and XMM...
Recently, non-standard Lagrangians have gained a growing importance in theoretical physics and in the theory of non-linear differential equations. However, their formulations and implications in general relativity are still in their infancies despite...
A new experiment in the field of gravitation, SaToR-G, is presented. The experiment aims to compare the predictions of different theories of gravitation in the limit of weak field and slow motion. The ultimate goal of the experiment is to look for po...
This paper explores the optical approach to simplifying complex concepts in general relativity (GR) and nonlinear vacuum electrodynamics. The focus is on using optical analogies to simplify the understanding of spacetime curvature and interactions in...
Following Smolin, we proceed to unification of general relativity and quantum theory by operating solely with events, i.e., without appealing to physical systems and space-time. The universe is modelled as a dendrogram (finite tree) expressing the hi...
In this paper, we investigated the capability of Yukawa gravity to explain the Schwarzschild precession of S-stars as a probe for General Relativity and to map the allowed parameter space of a potential fifth force. We simulated the S38 star orbit in...
The optical equivalence principle is analyzed according to the possibility of describing unbounded states, and the suitable approximations are calculated for highly energetic phenomena. Among these possibilities, the relevance for laser fields, inter...
During the last 15–20 years, the experimental methods for autonomous navigation and inter-satellite links have been developing rapidly in order to ensure navigation control and data processing without commands from Earth stations. Inter-satelli...
This study derives space travel pricing by Walrasian Equilibrium, which is logical reasoning from the general relativity theory (GRT), the accounting equation, and economic supply and demand functions. The Cobb–Douglas functions embed the endog...
Recent results of the LARASE research program in terms of model improvements and relativistic measurements are presented. In particular, the results regarding the development of new models for the non-gravitational perturbations that affect the orbit...
This paper proposes a theoretical study that investigates quantum effects on the gravity of black holes. This study utilizes a gravitational model that incorporates quantum mechanics derived from the classical-like quantum hydrodynamic representation...
Einstein’s theory of general relativity is often regarded as the best theory of gravity that we know. [...]
In the present work, we investigate anisotropic compact stars under the general relativistic platform. Following a novel technique, we found an exact self-bound analytical stellar solution. The obtained solution was matched on the spherical surface o...
Building on the first paper in this series (Paper I), a unified perspective on Poincaré and Galilei physics in a 5-dimensional spacetime setting is further pursued through a consideration of the kinematics of general relativity, with the gravi...
The recent detections of gravitational waves from binary systems of black holes are in remarkable agreement with the predictions of General Relativity. In this pedagogical mini-review, I go through the physics of the different phases of the evolution...
Recently, the secular pericentre precession was analytically computed to the second post-Newtonian (2PN) order by the present author with the Gauss equations in terms of the osculating Keplerian orbital elements in order to obtain closer contact with...
General Relativity (GR) holds a special place amongst all fundamental theories of physics: on one hand, it is the theory of all gravitational phenomena; on the other hand, it is also a theory of spacetime [...]
Information entropy and its extension, which are important generalizations of entropy, are currently applied to many research domains. In this paper, a novel generalized relative entropy is constructed to avoid some defects of traditional relative en...
Einstein presented the Hole Argument against General Covariance, understood as invariance with respect to a change in coordinates, as a consequence of his initial failure to obtain covariant equations that, in the weak static limit, contain Newton&rs...
The Weyl method for finding solutions in general relativity using symmetry by varying an action with respect to a reduced set of field variables is known to fail in some cases. We add to the list of failures by considering an application of the Weyl...
The existence of a photon circular orbit can tell us a lot about the nature of the underlying spacetime, since it plays a pivotal role in the understanding of the characteristic signatures of compact objects, namely the quasi-normal modes and shadow...
The motive of the current article is to study and characterize the geometrical and physical competency of the conharmonic curvature inheritance (Conh CI) symmetry in spacetime. We have established the condition for its relationship with both conforma...
We study the problem of matching interior and exterior solutions to Einstein’s equations along a particular hypersurface. We present the main aspects of the
of 515