Curved Spacetime Research Articles

Multi-Bubble Universe Model: A Quantum-Relativistic Gravitational Theory of Space-Time

A multi-bubble model of universe is presented, in which gravity is the result of the aging of electromagnetic dipoles produced in quantum fluctuations of the action inside a condensate of a particular type of balancing gravitons. In the model, the exchange of gravitons among the dipoles and the potential of vacuum balances the energy of the fluctuation. The effect is to create bubbles of space-time that by growing they expand the local vacuum. The model suggests that the universe originates from overlapping of bubbles of space-time associated with dipoles. Matter is originated during gravitons decay. The use of the Bridge Theory demonstrates how the attractive force field that emerges in each bubble is in the first approximation in accordance with Newtonian gravity at small, medium and large distances in accordance with the theory of General Relativity by also introducing a variable cosmological term that justifies some observed cosmological anomalies. The model overcomes the current concepts of Dark Energy and Dark Mass in favor of a gravity produced by the curvature of space-time of the bubble. The existence of the balancing gravitons provides an estimate of the actual amounts of Dark Energy, Dark Matter and matter measured in the current universe. The estimated theoretical mass of the balancing gravitons is consistent with the Kaluza-Klein gravitons of 2.68 TeV observed in the ATLAS experiment during Run #1. Moreover, the use of the observational data of the rotation speeds of two samples of galaxies allows to verify the good agreement of the real universe with the model, providing a possible explanation of the variability in the measurement of the Hubble constant.

Theory of 3F4D Universe (Beyond Standard Model of Particle Physics)

In this theory, “mass is equivalent to length of imaginary straight line segment” and “direction to imaginary line segment is intrinsic property of that particle which is Equivalent to its intrinsic spin”. With this concept, all fundamental particles, fermions and bosons are described as quanta imaginary string particles with a definite direction. For e.g. unidirectional imaginary straight line with fixed length are massive spin 1/2 fermions; while unidirectional imaginary quanta curved lines are massless spin 1 bosons. Thus, it gives co-relation between massless (curved imaginary line) and spin = 1 properties of boson as proved in QED theory. All fundamental particles of standard model and beyond standard model are arranged in one simple diagram in 3 folds (bottom fold, middle upper and lower folds and top fold) and are projected in 4th Imaginary Dimension in order of decreased in Mass from TeV to approx. 0 eV. This theory is beyond standard model because it predicts new fundamental particles viz. dark matter (spin = 0 massive boson) along with gravitons (spin = 2, massless bosons); 4th pair of neutrinos, vertical massless boson (VMB) particles and tri-axis massive boson (spin = 0) particle. The discovery of these new particles will act as solid proof to this theory. With this 3F4D representation of the universe at an atomic and sub-atomic level, it solves lots of current problems of SM of particle physics like matter-antimatter asymmetry, origin of mass of hadrons like protons, origin of mass and L.H. nature for neutrinos, wave-particle duality of particles, etc. giving true insight of fundamental particles. With proving that, dark matter is not a quanta particle, rather it is a single entity and spreads/expands throughout the universe in the form of “web of spider”, it shows space-time is not empty, but it is filled with Continuous lines of Dark Matter and we, materialistic massive objects are floating/sailing w.r.t. current of this vast ocean. Correlation of its continuity with time gives new a definition to time: “Time is neither Illusion nor 4th Dimension, but, it represents Continuous Flow of Single Entity, Dark Matter”. Space-time is not Empty and is filled with massive dark matter, hence, we have to add more terms to newtonian gravitational equation to account for gravitational strength of mass of surrounding dark matter which represents curvature of space-time in terms of Increase in its mass-density w.r.t. to mass-density of flat universe. Finally, using an empirical formula (h = k*c*Q; k = boltzmann’s constant = mass in TeV range) and inverse relation of mass-density of DM with age of the universe (H2 = Constant&#8226G&#8226Mass-Density of DM); Unification of Gravity at TeV is achieved without consideration of “Gravitational Constant, G”, hence, Planck’s Scale is not required.

\u03ba-Minkowski-deformation of U(1) gauge theory

We construct a noncommutative kappa-Minkowski deformation of U(1) gauge theory, following a general approach, recently proposed in JHEP 08 (2020) 041. We obtain an exact (all orders in the non-commutativity parameter) expression for both the deformed gauge transformations and the deformed field strength, which is covariant under these transformations. The corresponding Yang-Mills Lagrangian is gauge covariant and reproduces the Maxwell Lagrangian in the commutative limit. Gauge invariance of the action functional requires a non-trivial integration measure which, in the commutative limit, does not reduce to the trivial one. We discuss the physical meaning of such a nontrivial commutative limit, relating it to a nontrivial space-time curvature of the undeformed theory. Moreover, we propose a rescaled kappa-Minkowski noncommutative structure, which exhibits a standard flat commutative limit.

Quantum Field Theory on Noncommutative Curved Space-times and Noncommutative Gravity

In the noncommutative gauge-theoretical formulation of Langman and Szabo, apparently it appears that the torsion generated there is a generalized one i.e. it may containvector, axial vector and tensor components. However, when we transcribe the noncommutative gauge theory in terms of the Maxwell gauge theory using the Seiberg-Wittencorrespondence, we have noted that upto the first order in the noncommutative parameter, this effectively can be taken to induce a change in chiral anomaly and hence theassociated torsion should be an axial vector one. The noncommutative gauge symmetriesgive a very natural and explicit realizations of the mixing of space-time and internal symmetries which is a characteristic feature of the conventional gauge theory of gravity. Thegauge fields of the dimensionally reduced noncommutative Yang-Mills theory map ontoaWeitzenbӧck space time and a teleparallel theory of gravity arises as the zero curvature reduction of a Poincare gauge theory which induces an Einstein-Cartan space-timecharacterized by connections with both nonvanishing torsion and curvature. However, theteleparallelism equivalent of general relativity involves all the components of torsion. Thechiral anomaly in the Einstein-Cartan space U₄ is characterized by the topological invariants like Pontryagin density as well as the Nieh-Yan density when the latter term involvesthe length scale governed by the measure of noncommutativity of space points. It is shownthat we have discussed the equivalence of this formalism with noncommutative U(1) Yang Mills theory.

Probing High School Students’ Understanding of Einstein’s Theory of Gravity Using Thought Experiments and Analogy

In this study, we probed high school students’ understanding of Einstein’s theory of gravity by implementing an approach which mainly consists of two steps: firstly, exposing students to TEs describing the Equivalence Principle; secondly, applying the analogy of parallel lines on a curved surface with the path of two falling balls in a real gravitational field to help students deduce the idea of gravity as the spacetime curvature. A total of 12 high school students voluntarily participated in this study where data regarding their understanding were measured by means of an identical pen-and-paper test and interviews. Even though none of the students could explain what the Einstein’s version of gravity is in the pre-test, their responses in the post-test indicated that the approach we applied could help them understand the Einstein’s theory of gravity. Not only could they recall what the gravity is, most of them managed to provide related analogy they have learnt to explain their thoughts. Apart from its easily comprehensible steps, the study suggested that the approach is worth adopting to teach Einstein’s theory of gravity as it reflects the similar path ever taken by Einstein when starting to formulate his theory of gravity.

The Uniformly Accelerated Frame as a Test Bed for Analysing the Gravitational Redshift

Ever since Eddington’s analysis of the gravitational redshift a century ago, and the arguments in the relativity community that it produced, fine details of the roles of proper time and coordinate time in the redshift remain somewhat obscure. We shed light on these roles by appealing to the physics of the uniformly accelerated frame, in which coordinate time and proper time are well defined and easy to understand; and because that frame exists in flat spacetime, special relativity is sufficient to analyse it. We conclude that Eddington’s analysis was indeed correct—as was the 1980 analysis of his detractors, Earman and Glymour, who (it turns out) were following a different route. We also use the uniformly accelerated frame to pronounce invalid Schild’s old argument for spacetime curvature, which has been reproduced by many authors as a pedagogical introduction to curved spacetime. More generally, because the uniformly accelerated frame simulates a gravitational field, it can play a strong role in discussions of proper and coordinate times in advanced relativity.

Newtonian quantum gravity and the derivation of the gravitational constant G and its fluctuations

The theory of gravity “Newtonian quantum gravity” (NQG) is an ingeniously simple theory, because it precisely predicts so-called “general relativistic phenomena,” as, for example, that observed at the binary pulsar PSR B1913 + 16, by just applying Kepler’s second law on quantized gravitational fields. It is an irony of fate that the unsuspecting relativistic physicists still have to effort with the tensor calculations of an imaginary four-dimensional space-time. Everybody can understand that a mass that moves through space must meet more “gravitational quanta” emitted by a certain mass, if it moves faster than if it moves slower or rests against a certain mass, which must cause additional gravitational effects that must be added to the results of Newton's theory of gravity. However, today's physicists cannot recognize this because they are caught in Einstein's relativistic thinking and as general relativity can coincidentally also predict these quantum effects by a mathematically defined four-dimensional curvature of space-time. Advanced NQG is also able to derive the gravitational constant G and explains why G must fluctuate. The “string theory” tries to unify quantum physics with general relativity, but as the so-called “general relativistic” phenomena are quantum physical effects, it cannot be a realistic theory. The “energy wave theory” is lead to absurdity by the author.

Black hole collapse and bounce in effective loop quantum gravity

We derive effective equations with loop quantum gravity corrections for the Lemaître–Tolman–Bondi family of space-times, and use these to study quantum gravity effects in the Oppenheimer–Snyder collapse model. For this model, after the formation of a black hole with an apparent horizon, quantum gravity effects become important in the space-time region where the energy density and space-time curvature scalars become comparable to the Planck scale. These quantum gravity effects first stop the collapse of the dust matter field when its energy density reaches the Planck scale, and then cause the dust field to begin slowly expanding. Due to this continued expansion, the matter field will eventually extend beyond the apparent horizon, at which point the horizon disappears and there is no longer a black hole. There are no singularities anywhere in this space-time. In addition, in the limit that edge effects are neglected, we show that the dynamics for the interior of the star of uniform energy density follow the loop quantum cosmology effective Friedman equation for the spatially flat Friedman–Lemaître–Robertson–Walker space-time. Finally, we estimate the lifetime of the black hole, as measured by a distant observer, to be ∼(GM)2/ℓ Pl.

A Review of Inconsistencies and Unfounded Assumptions in Physics Enables A Path Forward

It is widely recognized significant parts of leading-edge physics are at an impasse. Perhaps it is time to re-evaluate long-standing inconsistencies and assumptions that have become dogma but are erroneous and blocking progress. Newtonʼs gravitational constant GN is assumed a natural constant, having originated via Newtonʼs notion of gravity as radial force acting on mass in flat observer space. But Einstein showed gravity due to curved space time with “mass” dimensionally c2 remote from the observer energy domain. Dirac stated (elementary) particles are “no more than electromagnetic energy localized in observer space”. This suggests gravity is emergent at the particle scale by spacetime curved in three dimensions. But Newtonʼs assumed radial force is consistent only with spacetime curvature in the two dimensions orthogonal to the radial, so how can GN be fundamental? Do the different dimensionalities of Newtonʼs and Einsteinʼs theories relate to the Dark Matter issue? Describing the electron as a photon in a relativistic quantum loop localized by curved spacetime enables derivation of an expression for GN giving a value within the empirical uncertainty. The electron is posited as relativistic electromagnetic energy in dynamic equilibrium between circumferential metric tension at the Strong Force scale and radial electrostatic force, satisfying the Planck “Force Equality” premise. As historically long suspected GN contains a numerical factor of c4, derived from the cgs units, in which it was first measured, and a relativistic factor, α-4/3, which move the Planck scale into exact correspondence with the electron parameters. General Relativity is shown a fundamental femto-scale theory where the strong force in a metric curved at the particle scale is manifest in observer space reduced by the classical “Large Number” of 5.7x1044 and is evident as gravity. The expression obtained for GN is supported by deriving the MOND constant and the observed flat galactic star rotation velocity curves. Resolving identified erroneous assumptions and inconsistencies will significantly impact cosmology and particle physics and bring gravitational and electromagnetic unification closer.

Geometric torsion, four-form, Riemann duals and Quintessence

We revisit an emergent gravity scenario in [Formula: see text][Formula: see text][Formula: see text] dimensions underlying a propagating geometric torsion [Formula: see text] with a renewed interest. We show that a pair-symmetric [Formula: see text]th-order curvature tensor is sourced by Neveu–Schwarz (NS) two-form in a [Formula: see text] gauge theoretic formulation. Interestingly, the new spacetime curvature governs a torsion-free geometry sourced by an NS form and shares the properties of the Riemann tensor. On the other hand, a completely anti-symmetric [Formula: see text]th-order tensor in the formulation is shown to incorporate a dynamical geometric torsion and is argued to be identified with a nonperturbative correction. The four-form turns out to be [Formula: see text] gauge invariant underlying an onshell NS form. We show that an emergent gravity theory may elegantly be described with an axionic scalar presumably signifying a quintessence coupling to the Riemann-type geometries. The curvatures are appropriately worked out to obtain a [Formula: see text] emergent form theory. Investigation reveals that a pair of [Formula: see text]-brane is created across an event horizon. We show that an emergent [Formula: see text] theory in a decoupling limit identifies with the bosonic sector of [Formula: see text], Supergravity in [Formula: see text].

Properties of the spherically symmetric polymer black holes

In this paper we systematically study a five-parameters class of spherically symmetric polymer black/white hole solutions, and find that only three independent combinations are physical and uniquely determine the spacetime properties. After exploring the whole 3-dimensional (3D) phase space, we find that the model has very rich physics, and depending on the choice of these parameters, various possibilities exist, including: (i) spacetimes that have the standard black/white hole structures, that is, spacetimes that are free of spacetime curvature singularities and possess two asymptotically flat regions, which are connected by a transition surface (throat) with a finite and non-zero geometric radius. The black/white hole masses measured by observers in the two asymptotically flat regions are all positive, and the surface gravity of the black (white) hole is positive (negative). (ii) Spacetimes that have wormhole-like structures, in which the two masses are all positive, but no horizons exist.(iii) Spacetimes that still possess curvature singularities, which can be either hidden inside trapped regions or naked. However, such spacetimes correspond to only some limit cases, and the necessary (but not sufficient) condition is that at least one of the two "polymerization" parameters vanishes. In addition, even for solar mass black/white holes, quantum gravitational effects can be still very large at the black/white hole horizons, again depending on the choice of the parameters.

Modification to tunneling radiation of arbitrary spin fermions in stationary axisymmetric Sen black hole space–time

Considering the modified Lorentz dispersion relation, combined with the Dirac equation and Rarita–Schwinger equation of fermions in stationary axisymmetric Sen black hole space–time, the fermion tunneling radiation of the black hole is modified accurately, and meaningful physical quantities such as the modified fermion tunneling rate, event horizon temperature, and entropy of the black hole are obtained. The discussion of the conclusions shows that the effect of the Lorentz dispersion relation and Lorentz violation theory on particle dynamics must be considered in curved space–time during the study of quantum theory and Hawking tunneling radiation.

Classical Simulations of Quantum Field Theory in Curved Spacetime I: Fermionic Hawking-Hartle Vacua from a Staggered Lattice Scheme

We numerically compute renormalized expectation values of quadratic operators in a quantum field theory (QFT) of free Dirac fermions in curved two-dimensional (Lorentzian) spacetime. First, we use a staggered-fermion discretization to generate a sequence of lattice theories yielding the desired QFT in the continuum limit. Numerically-computed lattice correlators are then used to approximate, through extrapolation, those in the continuum. Finally, we use so-called point-splitting regularization and Hadamard renormalization to remove divergences, and thus obtain finite, renormalized expectation values of quadratic operators in the continuum. As illustrative applications, we show how to recover the Unruh effect in flat spacetime and how to compute renormalized expectation values in the Hawking-Hartle vacuum of a Schwarzschild black hole and in the Bunch-Davies vacuum of an expanding universe described by de Sitter spacetime. Although here we address a non-interacting QFT using free fermion techniques, the framework described in this paper lays the groundwork for a series of subsequent studies involving simulation of interacting QFTs in curved spacetime by tensor network techniques.

Octonions, trace dynamics and noncommutative geometry—A case for unification in spontaneous quantum gravity

Abstract We have recently proposed a new matrix dynamics at the Planck scale, building on the theory of trace dynamics and Connes noncommutative geometry program. This is a Lagrangian dynamics in which the matrix degrees of freedom are made from Grassmann numbers, and the Lagrangian is trace of a matrix polynomial. Matrices made from even grade elements of the Grassmann algebra are called bosonic, and those made from odd grade elements are called fermionic—together they describe an ‘aikyon’. The Lagrangian of the theory is invariant under global unitary transformations and describes gravity and Yang–Mills fields coupled to fermions. In the present article, we provide a basic definition of spin angular momentum in this matrix dynamics and introduce a bosonic(fermionic) configuration variable conjugate to the spin of a boson(fermion). We then show that at energies below Planck scale, where the matrix dynamics reduces to quantum theory, fermions have half-integer spin (in multiples of Planck’s constant), and bosons have integral spin. We also show that this definition of spin agrees with the conventional understanding of spin in relativistic quantum mechanics. Consequently, we obtain an elementary proof for the spin-statistics connection. We then motivate why an octonionic space is the natural space in which an aikyon evolves. The group of automorphisms in this space is the exceptional Lie group G 2 which has 14 generators [could they stand for the 12 vector bosons and two degrees of freedom of the graviton?]. The aikyon also resembles a closed string, and it has been suggested in the literature that 10-D string theory can be represented as a 2-D string in the 8-D octonionic space. From the work of Cohl Furey and others it is known that the Dixon algebra made from the four division algebras [real numbers, complex numbers, quaternions and octonions] can possibly describe the symmetries of the standard model. In the present paper we outline how in our work the Dixon algebra arises naturally and could lead to a unification of gravity with the standard model. From this matrix dynamics, local quantum field theory arises as a low energy limit of this Planck scale dynamics of aikyons, and classical general relativity arises as a consequence of spontaneous localisation of a large number of entangled aikyons. We propose that classical curved space–time and Yang–Mills fields arise from an effective gauging which results from the collection of symmetry groups of the spontaneously localised fermions. Our work suggests that we live in an eight-dimensional octonionic universe, four of these dimensions constitute space–time and the other four constitute the octonionic internal directions on which the standard model forces live.

Hawking radiation of Reissner–Nordström–de Sitter black hole with a global monopole derived from modified Hamilton–Jacobi equation

The tunneling characteristics at the cosmological and event horizons of Reissner–Nordström–de Sitter black hole with a global monopole are studied by using the modified Lorentz violation scalar field equation in curved space–time. Firstly, we get the modified Hamilton–Jacobi equation using the semi-classical approximation, then the Hawking radiation and thermodynamical properties of Reissner–Nordström–de Sitter black hole with a global monopole are computed based on the modified Hamilton–Jacobi equation. Our results show that Lorentz violation can lead to lower Hawking temperature and higher entropy of the black hole at the same time. This work improves the understanding of the physical nature of Lorentz violation in curved space–time.

The Metric of Space-Time Curvature in a Weak Gravitational Field and it’s Consequence in Newtonian Approximation

In Newtonian mechanics, space and time are separate but in General, Relativity is unified. It is considered that the space in the weak-field approximation is quasi-static and it arises from a perfect field whose particles have very small velocity in comparison to light velocity in this coordinate system and the metric is a gravitational potential tensor of rank two which implies the field of empty space. If each point of an area in N-dimensional space there existed a corresponding definite tensor, where the components of the tensor are the function of space and space acts as the strong or weak gravitational field.

Unruh-deWitt detectors in quantum superpositions of trajectories

Unruh-deWitt detectors have been utilised widely as probes for quantum particles, entanglement and spacetime curvature. Here, we extend the standard treatment of an Unruh-deWitt detector interacting with a massless, scalar field to include the detector travelling in a quantum superposition of classical trajectories. We derive perturbative expressions for the final state of the detector, and show that it depends on field correlation functions evaluated locally along the individual trajectories, as well as non-locally between the superposed trajectories. By applying our general approach to a detector travelling in a superposition of two uniformly accelerated trajectories, including those with equal and differing proper accelerations, we discover novel interference effects in the emission and absorption spectra. These effects can be traced to causal relations between the superposed trajectories. Finally, we show that in general, such a detector does not thermalise even if the superposed paths would individually yield the same thermal state.

Perfect fluid filled universe in odd dimensional pure Lovelock gravity

It is well known that d = 2 N + 1 dimensional pure Lovelock metrics do not describe bounded distributions neither do they admit nontrivial vacuum solutions. On this basis it has been variously claimed that matter fields should be nondynamical. However, from earlier work it has long been demonstrated fairly generally that 2 N + 1 pure Lovelock solutions are not kinematic. In this work we find perfect fluid filled universes with d = 2 N + 1 that exhibit curvature of spacetime. New classes of exact solutions for pure Gauss–Bonnet gravity ( N = 2 ) are generated by integrating the pressure isotropy condition with suitable metric potential choices for the critical spacetime dimension 5. Amongst the physically important cases we study are the Vaidya–Tikekar superdense star ansatz, the Finch–Skea model as well as isothermal fluids. The physical properties are analysed with the aid of graphical plots and the model is found to be causal and stable in the sense of Chandrasekhar and satisfies the energy conditions. Finally we examine the most general Lovelock polynomials for all N and d = 2 N + 1 . In particular the special case N = 3 , d = 7 has not been considered previously in the literature and we discover a number of classes of exact solutions for this case.

Higher derivative scalar-tensor theory and spatially covariant gravity: The correspondence

We investigate the correspondence between generally covariant higher derivative scalar-tensor theory and spatially covariant gravity theory. The building blocks are the scalar field and spacetime curvature tensor together with their generally covariant derivatives for the former, and the spatially covariant geometric quantities together with their spatially covariant derivatives for the later. In the case of a single scalar degree of freedom, they are transformed to each other by gauge fixing and recovering procedures, of which we give the explicit expressions. We make a systematic classification of all the scalar monomials in the spatially covariant gravity according to the total number of derivatives up to $d=4$, and their correspondence to the scalar-tensor monomials. We discusse the possibility of using spatially covariant monomials to generate ghostfree higher derivative scalar-tensor theories. We also derive the covariant 3+1 decomposition without fixing any specific coordinate, which will be useful when performing a covariant Hamiltonian analysis.

Vortex generation in the early Universe

Context. Accretion disks formed near primordial black holes can be sources of seed magnetic fields in the early Universe. In particular, the Biermann battery mechanism has been shown to generate primordial magnetic fields in an unmagnetized and turbulence-free accretion disk, but this depends on a delicate misalignment of density and pressure gradients in plasmas. Aims. We aim to reformulate the question of magnetogenesis in the context of plasma generalized vorticity and to search for a more robust mechanism of vorticity generation in the early Universe. Methods. We utilize the electro-vortical formalism in curved spacetime, which treats the plasma flow and electromagnetic field on an equal footing, and apply it to a thin accretion disk model near a rotating black hole. Results. We present a spacetime curvature-driven mechanism that persists even in the absence of the Biermann battery. We explore the vorticity and enstrophy generation rate dependencies on black hole masses and spin rates. Conclusions. Analysis indicates that the accretion disks around lower-mass, faster rotating black holes contribute the greatest amount to the enstrophy and vorticity generation rates from the spacetime curvature drive. The shorter turning radii at which the sign of the vorticity changes – corresponding with this region of phase space – may favor these length scales in vortical structure formation and subsequent evolution.