Principles Of General Relativity Research Articles

Introducing LensCharm

Strong gravitational lensing, a phenomenon rooted in the principles of general relativity, grants us a unique window into the distant cosmos by offering a direct probe into dark matter and providing independent constraints on the Hubble constant. These research objectives call for the utmost precision in the estimation of the lens mass and the source brightness distributions. Recent strides in telescope technology promise to provide an abundance of yet undiscovered strong-lensing systems, presenting observations of unprecedented quality. Realizing the full potential of these advancements hinges on achieving the highest fidelity in both source and lens reconstruction. In this study, we introduce LensCharm, a novel Bayesian approach for strong-lensing signal reconstruction. Unlike more prevalent methods, LensCharm enables the nonparametric reconstruction of both the source and lens concurrently, along with their associated uncertainties. We showcase the distinctive strengths of our approach through comprehensive analyses of both real-world and simulated astronomical data, underscoring its superiority in achieving precise reconstructions. We have made LensCharm publicly accessible, envisioning its empowerment of the next generation of astronomical observation reconstructions and cosmological constraints derived from strong gravitational lensing.

Exploring the cosmic nexus: Black holes, gravitational waves, and the dance of the universe

In the vast cosmos, the enigmatic interplay of black holes and gravitational waves unfolds as a mesmerizing narrative, offering profound insights into the universes deepest mysteries. This paper delves into the intricate relationship between these cosmic phenomena, exploring their formation, properties, and their transformative implications in the realm of astrophysics. As colossal black holes merge, they generate gravitational waves that carry signatures of their masses, spins, and orientations. These waves, harnessed through advanced detectors like LIGO and Virgo, present a new dimension of cosmic exploration, unveiling the intricate dynamics of the universes most energetic events. Through the lens of gravitational wave astronomy, the author embarks on a journey to decipher gravitys elegant dance with spacetime, testing the fundamental principles of general relativity and pushing the boundaries of peoples understanding. This paper weaves an intricate tapestry from the cosmic threads of black holes and gravitational waves, inviting people to unravel the universes most profound enigmas and redefine peoples cosmic narrative.

The chaotic behavior of black holes: Investigating a topological retraction in anti-de Sitter spaces

In some topological universe models, a special type of curved space called the anti-de Sitter (AdS) of black hole space appears. Due to general relativity, this space has negative curvature. Here we present a novel variant of AdS space, known as chaotic AdS black hole space. We investigate the correlation between the folding of chaotic AdS black hole space and its chaotic deformation retract. In order to better understand how objects move in space, we can also use Lagrangian equations to determine the geodesics of the chaotic AdS space, and explore the properties and behavior of this new type of space. This would enable us to focus our attention and efforts better on black hole thermodynamics and quantum gravity. Finally, various types of chaotic quantum retractions in this space are identified, as well as the final limits on chaotic AdS spaces and their extensions to astrophysics. Exploring these ideas has consequently increased our understanding of the complex dynamics of the universe and the potential for developing a theory of quantum gravity that combines the principles of general relativity and quantum mechanics.

Timelike geodesic congruence in the simplest solutions of general relativity with quantum-improved metric tensor

A recent quantum-geometrical approach for the possible reconciliation of the principles of general relativity and quantum mechanics extends the fundamental tensor to the relativistic (quantum) scales, in which additional geometric structures and curvatures, i.e., additional sources of gravitation, are emerged. This paper introduces some characteristics of the emerged curvatures and their consequences on regulating the space and initial singularities. We analyze the timelike geodesic congruence in the simplest solutions of the Einstein field equations; the homogeneous, isotropic, and spherically symmetric Schwarzschild, de Sitter–Schwarzschild, and Friedmann–Lemaitre–Robertson–Walker (FLRW) metrics. From the expansion of the trajectory congruence that follows the change in the shape of the volume which keeps the same set of geodesics in the bundle along the flow lines which are generated by the velocity fields, we conclude that the analytical and numerical analyses give an unambiguous signature that the space and initial singularities are attenuated or even regulated, especially in the relativistic (quantum) regime. This means that the regulation of the singularity in Einstein’s general relativity (GR) would not be possible until quantum-mechanical ingredients are properly imposed on it.

Einstein, Barcelona, Symmetry & Cosmology: The Birth of an Equation for the Universe

Albert Einstein visited Spain only once, precisely one hundred years ago. The circumstances, of a very different kind, of this visit will be explained here. In special, some important events happened to Einstein during that period, which, eventually, were key for converting modern cosmology into a genuine physical theory. Among them is the famous Einstein-Friedmann controversy, first, on the mathematical validity of Friedmann’s equations and, later, their possible usefulness as a reliable tool to describe the real world. A summary of the deepest ideas underlying Einstein’s contributions to the theory of relativity, which he had already completed before his visit, will precede the discussion, also supplemented with a description, in very simple terms, of the three main relativistic theories, namely Galileo’s one, and Einstein’s special and general theory. They pave the way towards a definitive theory of total relativity, so far unattainable. It will be recalled that the most general relativity principle, faithfully reflecting Ernst Mach’s far-reaching ideas, might have much to do with the symmetry-breaking paradigm, a most crucial tool in quantum field theory and high energy physics.

Equivalence principle, de-Sitter space, and cosmological twistors

In this paper, I discuss the impact of the positive cosmological constant on the interplay between the equivalence principle in general relativity, and the rules of quantum mechanics. At the nonrelativistic level, there is an ambiguity in the definition of a phase of a wave function measured by inertial and accelerating observes. This is the cosmological analogue of the Penrose effect, which can also be seen as a nonrelativistic limit of the Unruh effect. The symmetries of the associated Schrödinger equation are generated by the Newton–Hooke algebra, which arises from a nonrelativistic limit of a cosmological twistor space.

Born reciprocity and relativistic generalized uncertainty principle in Finsler structure: Fundamental tensor in discretized curved spacetime

The main findings of the generalized uncertainty principle (GUP), the phenomenological approach, for instance, the emergence of a minimal measurable length uncertainty, are obtained in various versions from theories of quantum gravity, such as string theory, loop quantum gravity, doubly special relativity and black hole physics. GUP counts for impacts of relativistic energies and finite gravitational fields on the fundamental theories of quantum mechanics (QM), the noncommutation and measurement uncertainty. Utilizing GUP in reconciling principles of general relativity (GR) and QM, thereby enables to draw convincing conclusions about quantum gravity. To resolve the shortcuts reported with the nonrelativistic three-dimensional GUP, namely, violation of Lorentz covariance, dependence on frame of reference, and violation of the linear additional law of momenta, we introduce relativistic four-dimensional generalized uncertainty principle (RGUP) to curved spacetime. To unify GR and QM, we apply the Born reciprocity principle (BRP), distance-momentum duality symmetry and RGUP to estimate the fundamental tensor in discretized curved spacetime. To this end, we generalize Riemann geometry. The Finsler geometry, which is characterized by manifold and Finsler structure, allows to directly apply RGUP to the Finsler structure of a free particle so that [Formula: see text] can be expressed as [Formula: see text], from which the metric tensor in discretized Riemann spacetime could be deduced. We conclude that [Formula: see text] is homogeneous with degree [Formula: see text] in [Formula: see text], while [Formula: see text] is [Formula: see text]-homogeneous resulting in [Formula: see text]. Despite, the astonishing similarity with the conformal transformation, know as Weyl tensor, this study suggests that principles of QMs could be unambiguously imposed on the resulting fundamental tensor. Also, we conclude that the features of Finsler geometry assumed in this study are likely the ones of the duel Hamilton geometry.

On quantum‐induced revisiting Einstein tensor in the relativistic regime

AbstractFor a rigorous approach to reconcile principles of general relativity (GR) and quantum mechanics (QM), we suggest applying the generalized relativistic noncommutative Heisenberg algebra on spacetime coordinates and momenta of a test particle on curved Riemann geometry manifold, which in turn is extended to an eight‐dimensional manifold. The natural generalization of the four‐dimensional Riemann geometry is the Finsler geometry, in which the quadratic restriction on the length measure is relaxed. With the minimum measurable length derived from the relativistic generalized four‐dimensional uncertainty principle, the quantum‐induced corrections to the fundamental tensor could be determined in the relativistic regime. Accordingly, the affine connections could be revisited. With the quantum‐induced revisiting Riemann curvature tensor and its contractions, the Ricci curvature tensor, and then the Ricci scalar, we have been able to construct a quantum‐induced revision of the Einstein tensor, in which besides quantum‐induced corrections, additional geometric structures emerge. On the surface of the 2‐sphere, we compared the quantum‐induced revisiting and non‐revisiting Einstein tensor and concluded that the difference between both versions strongly depends on the minimum measurable length and the local geodesics of the test particle through the additional curvature.

Comparing equivalent gravities: common features and differences

We discuss equivalent representations of gravity in the framework of metric-affine geometries pointing out basic concepts from where these theories stem out. In particular, we take into account tetrads and spin connection to describe the so called Geometric Trinity of Gravity. Specifically, we consider General Relativity, constructed upon the metric tensor and based on the curvature R; Teleparallel Equivalent of General Relativity, formulated in terms of torsion T and relying on tetrads and spin connection; Symmetric Teleparallel Equivalent of General Relativity, built up on non-metricity Q, constructed from metric tensor and affine connection. General Relativity is formulated as a geometric theory of gravity based on metric, whereas teleparallel approaches configure as gauge theories, where gauge choices permit not only to simplify calculations, but also to give deep insight into the basic concepts of gravitational field. In particular, we point out how foundation principles of General Relativity (i.e. the Equivalence Principle and the General Covariance) can be seen from the teleparallel point of view. These theories are dynamically equivalent and this feature can be demonstrated under three different standards: (1) the variational method; (2) the field equations; (3) the solutions. Regarding the second point, we provide a procedure starting from the (generalised) second Bianchi identity and then deriving the field equations. Referring to the third point, we compare spherically symmetric solutions in vacuum recovering the Schwarzschild metric and the Birkhoff theorem in all the approaches. It is worth stressing that, in extending the approaches to f(R), f(T), and f(Q) gravities respectively, the dynamical equivalence is lost opening the discussion on the different number of degrees of freedom intervening in the various representations of gravitational theories.

A High-Speed Test of the Equivalence Principle

It is well known that Newton’s work on mechanics depended in a crucial way on the previous observations of Galileo. The key insight of Galileo was that one can analyze the motion of bodies using experiments and mathematical equations. One experimental observation that roughly emerges from this work in modern terms is that two objects of different mass that are simultaneously released from rest and allowed to fall under the influence of gravity through a vacuum should hit the ground at the same time (this is essentially what is called the equivalence principle in general relativity). In popular legend, it is said that Galileo tested this by dropping two balls of different masses from the Leaning Tower of Pisa and showing that they hit the ground at the same time, but the historical evidence suggests that this is unlikely as he seems to have experimented mostly with balls rolling down inclined slopes.

A modified Michelson interferometer to measure sub-milliradian changes in angle

Modern short-range gravity experiments that seek to test the Newtonian inverse-square law or weak equivalence principle of general relativity typically involve measuring the minute variations in the twist angle of a torsion pendulum. Motivated by various theoretical arguments, recent efforts largely focus on measurements with test mass separations in the sub-millimeter regime. To measure the twist, many experiments employ an optical autocollimator with a noise performance of ∼300 nrad/Hz in the 0.1–10 mHz band, enabling a measurement uncertainty of a few nanoradians in a typical integration time. We investigated an alternative method for measuring a small twist angle through the construction of a modified Michelson interferometer. The main modification is the introduction of two additional arms that allow for improved angular alignment. A series of detectors and LabView software routines were developed to determine the orientation of a mirror attached to a sinusoidally driven rotation stage that oscillated with an amplitude of 0.35 mrad and a period of 200 s. In these measurements, the resolution of the interferometer is 8.1 μrad per fringe, while its dynamic range spanned 0.962 mrad. We compare the performance of this interferometric optical system to existing autocollimator-based methods, discussing its implementation, possible advantages, and future potential, as well as disadvantages and limitations.

Some Warnings About Quantum Space Gravimetry Enhance Earth Observations Project

Abstract In this paper, we discuss in brief some basic issues of quantum space gravimetry, related to standard approach of geodesy which is based on the Newton model of gravity and Euclidean geometry. We emphasize the need to apply relativistic gravity in practical high-precision geodesy. Here we do not intend to solve the existing hard experimental and theoretical problems, being essential for the topic: development of quantum gravity, physics of dark matter and dark energy, novel physical principles of extended general relativity, in particular, a nonlinear superposition principle in general relativity and its extensions, and so on. Rather, we point out the fundamental unsolved problems, which are substantial for quantum space gravimetry and future practical high-precision geodesy. We outline the possible ways for their study and decision. Thus, to some extend, the present paper is a program for further developments, not a presentation of the fnal solutions. Our goal is to warn corresponding scientifc community about the ultimate necessity for going outside the frameworks of the formulated more than three century ago, and used up to now in geodesy, Newton gravity, together with Euclidian geometry. At present, in the emerging high-precision geodesy one must replace them with modern models of gravity and corresponding non-Euclidean geometry. Without using and further development of those issues, the interpretation of data obtained from high-precision measurements by satellites for geodetic use seems to be quite problematic, uncertain, and may be misleading for practitioners.

On free fall of quantum matter

We propose an approach that allows to systematically take into account gravity in quantum particle physics. It is based on quantum field theory and the general principle of relativity. These are used to build a model for quantum particles in curved spacetime. We compute by its means a deviation from a classical geodesic in the Earth’s gravitational field. This shows that free fall depends on quantum- matter properties. Specifically, we find that the free-fall universality and the wave-packet spreading are mutually exclusive phenomena. We then estimate the Eötvös parameter for a pair of atoms freely falling near the Earth’s surface, provided that the wave-packet spreading is more fundamental than the weak equivalence principle.

Mechanical and Maxwell’s equations relative to an observer and principle of general relativity

The principle of general relativity states that every observer has the right to analyze the physical world from his point of view. However, a transcription code is necessary to compare different descriptions. It is just this code that allows to obtain a physics that is universal in the class of observers. First of all, an observer, identified with a frame of reference R, must have procedures not only to attribute coordinates to each event but also to measure any physical quantity. In the literature, formal procedures are proposed to derive physical quantities and equations relative to an observer starting from the absolute ones. In this paper, these formal approaches are shown to be equivalent to entrust the proper inertial frame [Formula: see text] at an event [Formula: see text] to carry out the measure of physical quantities. Then the observer R adopts the results obtained by [Formula: see text] without introducing his own measures. Since these adopted measures are carried out in the absence of gravitation, the obtained relative equations describe how the evolution with respect to R of proper quantities is modified by gravitation. Finally, after determining the transformation of proper quantities in going from R to another frame R’, a principle of general relativity is formulated in an appropriate class of observers.

Quantum superposition of spacetimes obeys Einstein's equivalence principle

We challenge the view that there is a basic conflict between the fundamental principles of Quantum Theory and General Relativity and, in particular, the fact that a superposition of massive bodies would lead to a violation of the Equivalence Principle. It has been argued that this violation implies that such a superposition must inevitably spontaneously collapse (like in the Diósi–Penrose model). We identify the origin of such an assertion in the impossibility of finding a local and classical reference frame in which Einstein's Equivalence Principle would hold. In contrast, we argue that the formulation of the Equivalence Principle can be generalized so that it holds for reference frames that are associated with quantum systems in a superposition of spacetimes. The core of this new formulation is the introduction of a quantum diffeomorphism to such Quantum Reference Frames. This procedure reconciles the principle of linear superposition in Quantum Theory with the principle of general covariance and the Equivalence Principle of General Relativity. Hence, it is not necessary to invoke a gravity-induced spontaneous state reduction when a massive body is prepared in a spatial superposition.

Demonstrating the first postulate of relativity in a lift

The first of the two postulates of relativity states that the laws of physics are the same in all inertial reference frames. Often it is assumed that the postulates are mainly concerned with objects moving at a significant fraction of the speed of light. However, the postulates are applicable at all speeds from a snail to a photon. To practically demonstrate the first postulate, the time for a ball to drop a known distance was measured in a stationary and moving lift. An accelerometer app on an iPhone 7 was used to measure the vertical acceleration while the lift travelled between floors and verified that the lift ascended and descended at a constant speed when the ball was dropped. The slow-motion feature of the iPhone 7 (240 fps) was used to capture videos of the falling ball. The number of frames for the ball to fall in a stationary, descending, and ascending lift was respectively A t-test revealed no significant difference between these values, confirming the validity of the first postulate. The accelerometer signal was integrated to estimate the average speed of the lift between the bottom and top floor, which was then used to estimate the height difference. An electronic balance placed on the floor of the lift was used to demonstrate the first postulate and the equivalence principle of General Relativity that states that gravitational and inertial mass are equivalent.

Testing gravity with cold atom interferometry: results and prospects

Atom interferometers have been developed in the last three decades as new powerful tools to investigate gravity. They were used for measuring the gravity acceleration, the gravity gradient, and the gravity-field curvature, for the determination of the gravitational constant, for the investigation of gravity at microscopic distances, to test the equivalence principle of general relativity and the theories of modified gravity, to probe the interplay between gravitational and quantum physics and to test quantum gravity models, to search for dark matter and dark energy, and they were proposed as new detectors for the observation of gravitational waves. Here I describe past and ongoing experiments with an outlook on what I think are the main prospects in this field and the potential to search for new physics.

Regularization of the cosmological sector of loop quantum gravity with bosonic matter and the related problems with general covariance of quantum corrections

This article concerns the problems regarding different lattice regularization techniques for the matter fields of Hamiltonian constraints defined in the framework of loop quantum gravity. The analysis is formulated in the phase space-reduced cosmological model of the hypothetical theory of canonical quantum general relativity. This article explains why a different than links-related lattice smearing of fields leads to a local violation of general covariance. This happens by assuming, for instance, the nodes-related smearing. Therefore, this problem occurs in the case of any polymerlike scalar field quantization method by breaking the background independence of the semiclassical predictions. In consequence, the diffeomorphism symmetry that depends on a links distribution is broken locally at the level of generally relativistic corrections. Moreover, by using the phase space-reduced gauge fixing technique to analyze this issue, the results are general and they concern any coupling with the links-regularized gravitational degrees of freedom in loop quantum gravity. Therefore, they lead to the following no-go conclusion. Any lattice smearing of matter, not defined by using the geometrical distribution specified by the links-fluxes duality, violates the general principle of relativity.

The Symmetries of Quantum and Classical Information. The Ressurected “Ether" of Quantum Information

The paper considers the symmetries of a bit of information corresponding to one, two or three qubits of quantum information and identifiable as the three basic symmetries of the Standard model, U(1), SU(2), and SU(3) accordingly. They refer to “empty qubits” (or the free variable of quantum information), i.e. those in which no point is chosen (recorded). The choice of a certain point violates those symmetries. It can be represented furthermore as the choice of a privileged reference frame (e.g. that of the Big Bang), which can be described exhaustively by means of 16 numbers (4 for position, 4 for velocity, and 8 for acceleration) independently of time, but in space-time continuum, and still one, 17th number is necessary for the mass of rest of the observer in it. The same 17 numbers describing exhaustively a privileged reference frame thus granted to be “zero”, respectively a certain violation of all the three symmetries of the Standard model or the “record” in a qubit in general, can be represented as 17 elementary wave functions (or classes of wave functions) after the bijection of natural and transfinite natural (ordinal) numbers in Hilbert arithmetic and further identified as those corresponding to the 17 elementary of particles of the Standard model. Two generalizations of the relevant concepts of general relativity are introduced: (1) “discrete reference frame” to the class of all arbitrarily accelerated reference frame constituting a smooth manifold; (2) a still more general principle of relativity to the general principle of relativity, and meaning the conservation of quantum information as to all discrete reference frames as to the smooth manifold of all reference frames of general relativity. Then, the bijective transition from an accelerated reference frame to the 17 elementary wave functions of the Standard model can be interpreted by the still more general principle of relativity as the equivalent redescription of a privileged reference frame: smooth into a discrete one. The conservation of quantum information related to the generalization of the concept of reference frame can be interpreted as restoring the concept of the ether, an absolutely immovable medium and reference frame in Newtonian mechanics, to which the relative motion can be interpreted as an absolute one, or logically: the relations, as properties. The new ether is to consist of qubits (or quantum information). One can track the conceptual pathway of the “ether” from Newtonian mechanics via special relativity, via general relativity, via quantum mechanics to the theory of quantum information (or “quantum mechanics and information”). The identification of entanglement and gravity can be considered also as a ‘byproduct” implied by the transition from the smooth “ether of special and general relativity’ to the “flat” ether of quantum mechanics and information. The qubit ether is out of the “temporal screen” in general and is depicted on it as both matter and energy, both dark and visible.

The dynamical approach to spin-2 gravity

This paper engages with the following closely related questions that have recently received some attention in the literature: (a) what is the status of the equivalence principle in general relativity (GR)?; (b) how does the metric field obtain its property of being able to act as a metric?; and (c) is the metric of GR derivative on the dynamics of the matter fields? The paper attempts to complement these debates by studying the spin-2 approach to (quantum) gravity. In particular, the paper argues that three lessons can be drawn from the spin-2 approach: (1) different from what is sometimes claimed in the literature, central aspects of the non-linear theory of GR are already derivable in classical spin-2 theory; in particular, ‘universal coupling’ can be considered a derived ‘theorem’ in both the classical and the quantum spin-2 approach; this provides new insights for the investigation of the equivalence principle; (2) the ‘second miracle’ that Read et al. argue characterises GR is explained in the classical as well as in the quantum version of the spin-2 approach; (3) the spin-2 approach allows for an ontological reduction of the metrical part of spacetime to the dynamics of matter fields.