Curved Spacetime Research Articles

Vanishing vacuum energy

The vacuum energy problem arises because quantum fields fluctuate even at the absolute zero of temperature. These “zero-point” (T=0) vacuum fluctuations have non-zero energy. Since in general relativity all types of energy generate the space-time curvature, vacuum energy must enter the Einstein field equation as a source term. Here I find that vacuum energy is zero if and only if the vacuum equation of state embodies relativistic invariance.

On a possible quantum manifestation of the perihelion advance in a hydrogen-like atom

In a static and spherically symmetric case, by following an analog procedure for obtaining a Reissner–Nordstrom solution, thanks to the use of both the Einstein-type equation for an electromagnetic field as well as the Maxwell equation in curved space–time, we managed to find the Schwarzschild-like solution outside a charged sphere Q in interaction with a test charged particle q at an atomic scale where the gravitational force is negligibly small compared to the electrostatic force. Then, in the context of an extension of the equivalence principle to the electromagnetic interaction, we have studied the hydrogen atom. At the atomic scale, where quantum effects can no longer be ignored and the concept of trajectory is abandoned, the corrective terms derived from the geodesic equation for the electron are used within a perturbation theory. At the first order, these radial corrections of the Hamiltonian can partially remove the degeneracy of Bohr’s levels through a Lamb-like shift of the energy levels (2s) and (2p), estimated to E(2s) – E(2p) = 2.4595087102 × 10−4 eV. To match the experimental value of the Lamb shift, 4.372 × 10−6 eV, we have postulated the existence of an electromagnetic background that would describe statistically the vacuum energy by the introduction of a “cosmological”-like constant in the Einstein-like equation for electromagnetism. We have pointed out a divergence when n → +∞ in energy corrections due to a “cosmological” constant that technically could be overcome by the use of a cutoff as well as the renormalization of the electron’s mass.

Neutron star pulse profile observations as extreme gravity probes

The x-ray emission of hot spots on the surface of neutron stars is the prime target of the Neutron star Interior Composition Explorer (NICER). These x-ray pulse profiles not only encode information of the bulk properties of these stars, which teaches us about matter at supranuclear densities, but also about the spacetime curvature around them which teaches us about relativistic gravity. We explore the possibility of performing strong-gravity tests with NICER observations using a recently developed pulse profile model beyond general relativity. Our results suggest that NICER can in principle place constraints on deviations from general relativity due to an additional scalar degree of freedom which are independent and competitive relative to constraints with binary pulsar observations.

자기장을 이용한 중력의 시공간 변형에 대한 실험적 연구

The curvature of spacetime represented by Einstein field equation has many physical implications, including gravity. As light is deflected by the curvature of spacetime, a magnetic field will also be influenced by the curved spacetime. A permanent magnet is generally known to maintain its persistent magnetic field on the ground as long as there is no external magnetic interference. However, a series of experiments find that there are noticeable changes in the magnetic fields distribution while the permanent magnet rotates. The magnetic field lines of the permanent magnet are deflected towards Earth’s centre, implying a possibility that we can use magnetic field, a more efficient tool than a satellite, to measure the curvature of spacetime. However, comparing the experimental results of this study with theoretically obtained values of the curvature of spacetime remains a vast area of research for future studies.

Teaching General Relativity with sector models: the field equations

The field equations of the general theory of relativity state the connection between spacetime curvature and matter, often summarized as “matter curves spacetime”. In this contribution we analyze the structure of the field equations from a pedagogical point of view and describe a formulation that is accessible in secondary school and undergraduate physics. This formulation of the field equations requires the concept of curvature in three dimensions and we show how this notion can be introduced using sector models. The field equations are illustrated using the black hole as an example.

The Geometrical Trinity of Gravity

The geometrical nature of gravity emerges from the universality dictated by the equivalence principle. In the usual formulation of General Relativity, the geometrisation of the gravitational interaction is performed in terms of the spacetime curvature, which is now the standard interpretation of gravity. However, this is not the only possibility. In these notes, we discuss two alternative, though equivalent, formulations of General Relativity in flat spacetimes, in which gravity is fully ascribed either to torsion or to non-metricity, thus putting forward the existence of three seemingly unrelated representations of the same underlying theory. Based on these three alternative formulations of General Relativity, we then discuss some extensions.

On neutralization of charged black holes

Abstract For non-spinning, charged (Reissner–Nordström) black holes, the particles with an opposite sign of charge with respect to that of the black hole will be pulled into the black hole by the extra electromagnetic force. Such a hole will be quickly neutralized so that there should not exist significantly charged, non-spinning black holes in the universe. The case of spinning, charged (Kerr–Newmann, KN) black holes is more complicated. For a given initial position and initial velocity of the particle, an oppositely charged particle does not always more easily fall into the black hole than a neutral particle. The possible existence of a magnetosphere further complicate the picture. One therefore cannot straightforwardly conclude that a charged spinning black hole will be neutralized. In this paper, we make the first step to investigate the neutralization of KN black holes without introducing a magnetosphere. We track the particle trajectories under the influence of the curved space–time and the electromagnetic field carried by the spinning, charged black hole. A statistical method is used to investigate the neutralization problem. We find a universal dependence of the falling probability into the black hole on the charge of the test particle, with the oppositely charged particles having a higher probability of falling. We therefore conclude that charged, spinning black holes without a magnetosphere should be quickly neutralized, consistent with people’s intuition. The neutralization problem of KN black holes with a corotating force-free magnetosphere is subject to further studies.

Dynamical suppression of spacetime torsion

A surprising feature of our present four dimensional universe is that its evolution appears to be governed solely by spacetime curvature without any noticeable effect of spacetime torsion. In the present paper, we give a possible explanation of this enigma through “cosmological evolution” of spacetime torsion in the backdrop of a higher dimensional braneworld scenario. Our results reveal that the torsion field may had a significant value at early phase of our universe, but gradually decreased with the expansion of the universe. This leads to a negligible footprint of torsion in our present visible universe. We also show that at an early epoch, when the amplitude of the torsion field was not suppressed, our universe underwent through an inflationary stage having a graceful exit within a finite time. To link the model with observational constraints, we also determine the spectral index for curvature perturbation (n_s) and tensor to scalar ratio (r) in the present context, which match with the results of Planck 2018 (combining with BICEP-2 Keck-Array) data (Akrami et al. in arXiv:1807.06211 [astro-ph.CO], 2019; Ade et al. in Phys Rev Lett 116:031302 https://doi.org/10.1103/PhysRevLett.116.031302, arXiv:1510.09217 [astro-ph.CO], 2016).

Spontaneous scalarization in generalized scalar-tensor theory

Spontaneous scalarization is a mechanism that endows relativistic stars and black holes with a nontrivial configuration only when their spacetime curvature exceeds some threshold. The standard way to trigger spontaneous scalarization is via a tachyonic instability at the linear level, which is eventually quenched due to the effect of non-linear terms. In this paper, we identify all of the terms in the Horndeski action that contribute to the (effective) mass term in the linearized equations and, hence, can cause or contribute to the tachyonic instability that triggers scalarization.

A Conceivable Path to Immortality in Your Present Body That Uses Physics, Electronics and 'Cloning'

The goal of this paper is to present a plausible path to immortality. The aim is therefore of a medical nature, though the means to that end is decidedly multidisciplinary – using physics, cosmology, geometry, topology and electronics besides medical concepts. Achievement of such an ambitious goal as immortality would appear to require input from many aspects of science. Those other concepts may make it unsuited to a medical journal devoted to clinical practice, but it’s publishable in a journal about hypotheses. The article starts by suggesting the entire universe could be composed, at the most fundamental level, of electronics’ binary digits. These enter a natural or artificial time-warp in the distant, far advanced future to produce the Mobius strips, figure-8 Klein bottles, adaptive Wick rotation, and “vector-tensor-scalar geometry” that make up the past and present cosmos. Then the article says the basics of mammalian cloning have been understood since Dolly the sheep’s birth in 1996. How can an adult mind be “downloaded” into a cloned brain? It’s proposed that individual cells and synapses in the original brain can be connected with their counterparts in the cloned brain via space-time warping. Since space-time and brains may be composed of binary digits, all the information in one organ could be successfully downloaded into the other – transferring each brain area’s memories, perceptual abilities, creativity, etc. Einstein's General Relativity says gravity is a push caused by the curvature of space-time (gravitation therefore is space-time). This means the space-time warping referred to a couple of sentences ago is gravity. Gravity thus establishes a permanent connection between patients and any form of treatment (including cloning). Such a permanent connection may help explain the placebo effect that occurs when no known treatment is applied. To the relief of many, the article finishes by suggesting gravity – and the surfing of gravitational waves – will make the prospect of human cloning completely unnecessary. This is because the final section, CREATION OF THE COSMOS USING BITS, PI AND IMAGINARY TIME, shows that the human mind generated by the brain has an essential role in creating the universe and, therefore, in our interactions with physical reality – leading to the repairing of every minor (even microscopic) defect in the body and brain as it occurs. Space-time (gravity) connections allowing downloading of minds will one day be extended to everyone who ever lived, resulting in resurrection of loved ones to eternal life and health.

Noncommutative DKP field and pair creation in curved space–time

This study is about the application of the noncommutativity on the DKP equation up to first-order in [Formula: see text] for the process of pair creation of spin-1 particles from vacuum in [Formula: see text] curved space–time. The density of particles created in the vacuum can be calculated with the help of the Bogoliubov transformations. The noncommutative density of created particles is found to decrease as [Formula: see text], so that the rate of particle creation increases whenever a noncommutativity parameter is small and this corresponds to the spirit of quantum mechanics.

Quasinormal modes of Dirac field in Einstein–Born–Infeld dilaton black hole

The Dirac quasinormal modes of Einstein–Born–Infeld dilaton black holes are studied. We separate the Dirac equation in the curve spacetime into radial and angular parts by Newman–Penrose formalism, and we fortunately obtain the exact analytical solutions of these equations. Then we get the analytical expressions for the quasinormal modes of the black hole. Our results show that the quasinormal frequencies are purely imaginary which means the black hole is very stable. Furthermore, we find that the area spacing of the black hole is described by $$\Delta A_{min}=8\pi \hbar $$ which supports Bekenstein’s conjecture.

Novel effect induced by spacetime curvature in quantum hydrodynamics

The interplay between quantum fluctuation and spacetime curvature is shown to induce an additional quantum-curvature (QC) term in the energy-momentum tensor of fluid using the generalized framework of the stochastic variational method (SVM). The QC term is necessary to satisfy the momentum conservation but the corresponding quantum hydrodynamics is not necessarily cast into the form of the Schrödinger equation, differently from the case of the Euclidean spacetime. This seems to suggest that the existence of the Hilbert space is not a priori requirement in the quantization of curved spacetime systems. As an example, we apply the Friedmann-Robertson-Walker (FRW) metric and show that this term contributes to the cosmological acceleration although it is too small in the present non-relativistic toy model.

The regular black hole in four dimensional Born–Infeld gravity

In the context of Born–Infeld gravity theories we report the existence of a regular black hole interior representing a spherically symmetric vacuum solution of the theory. It reduces to the Schwarzschild interior metric in the weak field region. In particular, there is a new length scale which is related to the Born–Infeld parameter . This endows the spacetime with an inner (i.e. well inside the event horizon) asymptotic region which is unattainable for observers. The central curvature singularity is replaced by an infinitely long cosmic string with constant curvature invariants related to . The presence of this limiting curvature spacetime renders the black hole timelike and null geodesically complete, free from the classical Schwarzschild singularity. The transition between the usual black hole interior and this maximum curvature space is achieved without introducing any kind of matter content nor topological changes.

Determinantal invariant gravity

Einstein–Hilbert action with a determinantal invariant has been considered. The obtained field equation contains the inverse Ricci tensor, [Formula: see text]. The linearized solution of invariant has been examined, and it is concluded that the constant curvature spacetime metric solution of the field equation gives different curvature constant for each values of [Formula: see text]. The [Formula: see text] gives a trivial solution for constant curvature, [Formula: see text].

The Electrical Magnetism of Maxwell (1873) Is the “Crooked Mirror” of Physical Science

The concept of the electric magnetism Maxwell (1873) is a result of the superficial and exceptionally erroneous impression of Great Physicist from the well-known experience of Oersted. However the world scientific community adopted this erroneous impression as the ultimate truth and, following Maxwell, declared the moving electric charges to be direct sources of the magnetic field. At same time, the true sources of the magnetic field the magnetic poles (magnetic charges) which are the real structural components of atoms and substance, were “buried alive”. Such theoretical discoveries as the curvature of four-dimensional space-time, explaining the physics of gravity, the big bang, the journey through “Black holes” in space and time, and many others, are well known. All these discoveries were formed without taking into account the existence of real magnetic poles (magnetic charges) since were based on the provisions of Maxwell’s flawed electromagnetic concept. The main reason which for more than 100 years inhibits the detection and recognition of real magnetic charges, are the special conditions of their confinement in a substance that are radically in the substance different from confinement of electrons. The results the experiments of F. Ehrenhaft, the present author and others in which of real magnetic charges were observed in the structures of atoms and substance prove that the existing concept of electric magnetism is deeply erroneous, and the fundamental change in physical priorities is the most important task today. Physical science, freed from vicious EM-concept of Maxwell and the accompanying relativism will offer humanity innovations in the form of practically useful physical effects and manifestations. This article presents 11 such innovations discovered by the author when embedded into the representations of real magnetic charges including, example, the electromagnetic (vortex) nature of the gravitational field, as well as the effects of Gravitational levitation and Intra-atomic gravitational shielding (IAGS). The first effect allows, for example, a person to go out into space without the use of jet thrust. The IAGS effect largely determines the physics of such fundamental manifestations as the chemical bonding, nuclear forces, and radioactivity.

Entangling detectors in anti-de Sitter space

We examine in (2+1)-dimensional anti-de Sitter (AdS) space the phenomena of entanglement harvesting — the process in which a pair of detectors (two-level atoms) extract entanglement from a quantum field through local interactions with the field. We begin by reviewing the Unruh-DeWitt detector and its interaction with a real scalar field in the vacuum state, as well as the entanglement harvesting protocol in general. We then examine how the entanglement harvested by a pair of such detectors depends on their spacetime trajectory, separation, spacetime curvature, and boundary conditions satisfied by the field. The harvested entanglement is interpreted as an indicator of field entanglement between the localized regions where the detectors interact with the field, and thus this investigation allows us to probe indirectly the entanglement structure of the AdS vacuum. We find an island of separability for specific values of the detectors’ energy gap and separation at intermediate values of the AdS length for which entanglement harvesting is not possible; an analogous phenomena is observed in AdS4, to which we compare and contrast our results. In the process we examine how the transition probability of a single detector, as a proxy for local fluctuations of the field, depends on spacetime curvature, its location in AdS space, and boundary conditions satisfied by the field.

Von Neumann stability of modified loop quantum cosmologies

von Neumann stability analysis of quantum difference equations in loop quantized spacetimes has often proved useful to understand the viability of quantizations and whether a general relativistic description is recovered at small spacetime curvatures. We use this technique to analyze the infra-red behavior of the quantum Hamiltonian constraint in recently explored modifications of loop quantum cosmology: mLQC-I and mLQC-II, for the spatially flat FLRW model. We investigate the behavior for the scheme, where the minimum area of loops in the quantization procedure does not take physical metric in to account, and the scheme where quantization procedure uses a physical metric. The fate of stability of quantum difference equations is tested for massless scalar field as well as with inclusion of a positive cosmological constant. We show that for mLQC-I and mLQC-II, the difference equation fails to be von Neumann stable for the scheme if a cosmological constant is included signaling problematic behavior at large volumes. Both of the modified loop quantum cosmologies are von Neumann stable for the scheme. In contrast to standard loop quantum cosmology, properties of roots turn out to be richer and intricate. Our results demonstrate the robustness of the scheme (or ‘improved dynamics’) in loop quantization of cosmological spacetimes even when non-trivial quantization ambiguities of the Hamiltonian are considered, and show that the scheme is non-viable in this setting.

Cylindrical gravitational waves: C-energy, super-energy and associated dynamical effects

The energy content of cylindrical gravitational wave spacetimes is analyzed by considering two local descriptions of energy associated with the gravitational field, namely those based on the C-energy and the Bel–Robinson super-energy tensor. A Poynting–Robertson-like effect on the motion of massive test particles, beyond the geodesic approximation, is discussed, allowing them to interact with the background field through an external force which accounts for the exchange of energy and momentum between particles and waves. In addition, the relative strains exerted on a bunch of particles displaced orthogonally to the direction of propagation of the wave are examined, providing invariant information on spacetime curvature effects caused by the passage of the wave. The explicit examples of monochromatic waves with either a single or two polarization states as well as pulses of gravitational radiation are discussed.

Relativistic quantum motion of the scalar bosons in the background space–time around a chiral cosmic string

In this paper, a relativistic behavior of spin-zero bosons is studied in a chiral cosmic string space–time. The Duffin–Kemmer–Petiau (DKP) equation and DKP oscillator are written in this curved space–time and are solved by using an appropriate ansatz and the Nikiforov–Uvarov method, respectively. The influences of the topology of this space–time on the DKP spinor and energy levels and current density are also discussed in detail.