Spacetime Geometry Research Articles

Ricci limit flows and weak solutions

In this paper we reconcile several different approaches to Ricci flow through singularities that have been proposed over the last few years by Kleiner–Lott, Haslhofer–Naber and Bamler. Specifically, we prove that every noncollapsed limit of Ricci flows, as provided by Bamler’s precompactness theorem, as well as every singular Ricci flow of Kleiner–Lott, is a weak solution in the sense of Haslhofer–Naber. We also generalize all path-space estimates of Haslhofer–Naber to the setting of noncollapsed Ricci limit flows. The key step to establish these results is a new hitting estimate for Brownian motion. A fundamental difficulty, in stark contrast to all prior hitting estimates in the literature, is the lack of lower heat kernel bounds under Ricci flow. To overcome this, we introduce a novel approach to hitting estimates that compensates for the lack of lower heat kernel bounds by making use of the heat kernel geometry of space-time.

The accelerating universe in a noncommutative analytically continued foliated quantum gravity

Abstract Based on an analytically continued Riemannian foliated quantum gravity super-Hamiltonian, known as branch cut quantum gravity (BCQG) we propose a novel approach to investigating the effects of noncommutative geometry on a minisuperspace of variables, influencing the acceleration behavior of the Universe’s wave function and the cosmic scale factor. Noncommutativity is introduced through a deformation of the conventional Poisson algebra, enhanced with a symplectic metric. The resulting symplectic manifold provides a natural setting that enables an isomorphism between canonically conjugate dual vector spaces, spanning the BCQG cosmic scale factor and its complementary quantum counterpart. Using this formulation, we describe the dynamic evolution of the Universe’s wave function, the cosmic scale factor, and its complementary quantum image. Our results strongly suggest that the noncommutative algebra induces late-time accelerated growth of the wave function, the Universe’s scale factor, and its complementary quantum counterpart, offering a new perspective on explaining the accelerating cosmic expansion rate and the inflationary period. In contrast to the inflationary model, where inflation requires a remarkably fine-tuned set of initial conditions in a patch of the Universe, analytically continued non-commutative foliated quantum gravity captures short and long scales, driving the evolutionary dynamics of the Universe through a reconfiguration of the primordial cosmic content of matter and energy. This reconfiguration is encapsulated into a quantum field potential, which leads to the generation of relic gravitational waves, a topic for future investigation. Graphical representations and contour plots indicate a characteristic torsion (or twist) deformation of spacetime geometry. This result introduces new speculative elements regarding the reconfiguration of matter and energy as a driver of spacetime torsion deformation, generating relic gravitational waves and serving as an alternative topological mechanism for the Universe’s acceleration. However, these assumptions require further investigation.

Cosmological foundations revisited with Pantheon+

Abstract We reanalyse the Pantheon+ supernova catalogue to compare a cosmology with non-FLRW evolution, the timescape cosmology, with the standard ΛCDM cosmology. To this end, we analyse the Pantheon+ for a geometric comparison between the two models. We construct a covariance matrix to be as independent of cosmology as possible, including independence from the FLRW geometry and peculiar velocity with respect to FLRW average evolution. This framework goes far beyond most other definitions of model independence. We introduce new statistics to refine Type Ia supernova (SNe Ia) light-curve analysis. In addition to conventional galaxy correlation functions used to define the scale of statistical homogeneity we introduce empirical statistics which enables refined analysis of the distribution biases of SNe Ia light-curve parameters βc and $\alpha {x_{\lower2pt\hbox{$\scriptstyle 1$}}}$. For lower redshifts, the Bayesian analysis highlights important features attributable to the increased number of low-redshift supernovae, the artefacts of model-dependent light-curve fitting and the cosmic structure through which we observe supernovae. This indicates the need for cosmology-independent data reduction to conduct a stronger investigation of the emergence of statistical homogeneity and to compare alternative cosmologies in light of recent challenges to the standard model. Dark energy is generally invoked as a place-holder for new physics. For the first time, we find evidence that the timescape cosmology may provide a better overall fit than ΛCDM and that its phenomenology may help disentangle other astrophysical puzzles. Our from-first-principles reanalysis of Pantheon+ supports future deeper studies between the interplay of matter and nonlinear spacetime geometry in a data-driven setting.

Einstein’s spacetime curvature and gravitational waves: Elucidating the gradient flow of scalar invariants, variations in the Ricci scalar, and gravitational wave propagation

In the general theory of relativity initially rationalized by Einstein, the gravity is considered as an occurrence ensuing from the spacetime curvature, which is in turn triggered by the presence of mass. This article provides a detailed analysis of spacetime curvature and gravitational waves, enhancing our understanding of general relativity and astrophysics. Using both analytical and numerical methods, we examined the gradient flow of scalar invariants, variations in the Ricci scalar, and gravitational wave propagation. New findings include the identification of unique curvature patterns around rotating black holes, a detailed comparison of gradient flow behavior in different spacetime geometries, and the discovery of a correlation between scalar invariant fluctuations and gravitational wave amplitudes. These findings validate numerical techniques and reveal how different parameters affect gravitational wave characteristics. While simplified models are used, the present study offers a robust framework for future research. Our work aligns with previous studies but also reveals unique aspects of wave behavior, with implications for quantum gravity and cosmology.

Semiclassical transport in two-dimensional Dirac materials with spatially variable tilt

We use Boltzmann theory to study the semi-classical dynamics of electrons in a two-dimensional (2D) tilted Dirac material in which the tilt varies in space. The spatial variation of the tilt parameter induces a non-trivial spacetime geometry on the background of which the electrons roam about. As the first manifestation of graivto-electric phenomena, we find a geometric planar Hall effect according to which a current flows in a direction transverse to the chemical potential gradient and is proportional to gxy component of the emergent spacetime structure. The longitudinal conductivity contains information about the gravitational red-shift factors. Furthermore, in the absence of externally applied electric field there can be “free-fall” or zero-bias currents that can be used as detectors of terahertz radiation.

Circular motion and particle collisions in ergoregion of rotating and twisting charged black holes

The presence of clouds of strings, quintessential fields, and NUT charges has significant consequences for spacetime geometry, and their study is much more important from an observational and theoretical perspective. Hence, in this article, we aim to explore the rotating and twisting charged black holes with the cloud of strings and quintessential field through horizons, ergoregions, photon regions, circular motion, and energy efficiency. First, we derive the equation of motion and the expressions for studying the photon region. To investigate circular motion, we derive the mathematical expressions of energy and angular momentum. The cloud of stings reduces the stability of angular momentum and energy in prograde particle motions and shifts their minima from the black hole’s center to the right. Static black holes with clouds of strings have the greatest angular momentum in prograde orbital motion, while rotating ones without clouds of strings have the least. Furthermore, we examine the efficiency of energy extraction through the Penrose process. The known energy extraction efficiency of the Penrose process for an extreme Kerr black hole is about 21%, but in the presence of clouds of strings, it exceeds 100%.

Study of anisotropic quark stars with interacting quark matter in f(R,T) gravity

We explore the structural properties of quark stars (QSs) in a modified gravity theory known as f(R,T) gravity, which introduces a coupling between matter and spacetime geometry, through a basic linear functional form f(R,T)=R+2βT. Our study focuses on QSs made of interacting quark matter (IQM) as an equation of state. We first derive the modified Tolman-Oppenheimer-Volkoff (TOV) equations for anisotropic matter in a spherically symmetric context and solve them numerically to obtain the structural properties of QSs. Stability is analyzed through static stability analysis, critical adiabatic indices, and sound speed profiles. Using astrophysical constraints from the “black widow” pulsar PSR J0952-0607 and the GW190814 event, we calibrate our model parameters. Our results indicate that with higher λ¯, both the maximum mass and radius of QSs increase, achieving a maximum mass of over 2M⊙, peaking at 3.15M⊙ for a radius of 14.90km at λ¯=0.9. The maximum compactness also rises to M/R=0.313 while adhering to the Buchdahl limit. Additionally, varying β in the range [−0.2,0.2] with fixed parameters shows that lower β values enhance the maximum mass of QSs, reaching 2.65M⊙ at β=−0.2, with the compactness remaining around M/R≈0.3. Furthermore, changes in μ from [−1.0,1.0] significantly affect maximum mass; at μ=1.0, the mass peaks at 3.15M⊙ and decrease to 2.68M⊙ at μ=0. The compactness increases with μ, indicating that anisotropic pressure influences the M−R relations. In summary, our findings reveal that the parameters λ¯, β, and μ play crucial roles in shaping the physical properties of QSs in the f(R,T) gravity framework, consistent with astrophysical observations from pulsars and gravitational wave events.

Parity nonconservation induced by spacetime geometry

Parity nonconservation induced by spacetime geometry

Maxwell–Dirac system in cosmology

Within the scope of a Bianchi type-I (BI) cosmological model, we study the interacting system of spinor and electromagnetic fields and its role in the evolution of the Universe. In some earlier studies, it was found that in the case of a pure spinor field, the presence of nontrivial nondiagonal components of energy–momentum tensor (EMT) leads to some severe restrictions both on the space–time geometry and/or spinor field itself, whereas in the case of electromagnetic field with induced nonlinearity, such components impose severe restrictions on metric functions and the components of the vector potential. It is shown that in the case of interacting spinor and electromagnetic fields, the restrictions are not as severe as in the other cases and in this case, a nonlinear and massive spinor field with different components of vector potential can survive in a general Bianchi type-I space–time.

Self-gravitating matter in stationary and axisymmetric black hole spacetimes

Abstract All black holes (BHs) in nature are expected to be described by the Kerr vacuum solution of general relativity. However, the Kerr BH interior contains several problematic features such as a Cauchy horizon, a curvature singularity, and a causality-violating region. Non-Kerr BH models, which are used to examine the genericity of these features, typically contain nontrivial matter content. When such self-gravitating matter is minimally-coupled to Einstein–Hilbert gravity, the Einstein equations can be directly used to investigate its physical properties. We examine here the properties of matter in a broad class of stationary and axisymmetric, geodesically-integrable BH spacetimes, and how they are linked to various features of the spacetime geometry. In these spacetimes, we find the matter to typically flow along timelike Killing orbits in the BH exterior, usually exhibiting differential rotation but sometimes additionally also non-rigid rotation. At a horizon, the matter rest-frame energy density, ε, and principal normal pressure, pn , are shown to necessarily satisfy p n = − ϵ , implying that only specific types of matter can thread stationary event horizons (e.g. electromagnetic fields but not massless real scalar fields). Furthermore, we introduce Boyer–Lindquist-like coordinates for the nonstationary regions in the BH interior, which show the matter to be comoving with the interior cosmology. We also obtain simple expressions for the expansions of the ingoing and outgoing zero angular momentum null congruences and comment on the light-focussing behavior of the cosmology. Finally, we verify above results explicitly by working with a representative set of well-known BH spacetimes which contain various types of matter—scalar fields, electromagnetic fields, anisotropic fluids. Some spacetimes have singularities while others have regular interiors. In the exterior, the matter satisfies the weak energy condition. The framework developed here can be extended to cover more general spacetimes.

Across-horizon propagation and infinite time-dilation: An independent approach to Hawking radiation

The conformal scalar propagator as an explicit function of the Schwarzschild black-hole space-time has been established in the preceding three projects. The present project examines the precise relation which that propagator has to the amplitude the Schwarzschild black hole emit a scalar particle in a particular mode of positive energy. It is thereby established that the effect of infinite time-dilation on the event horizon results in both, the thermal radiation in the background of a static exterior space-time geometry and the detraction from thermality if energy-conservation is properly imposed as a constraint on scalar propagation. The derivation of the latter signifies an equivalent approach to the result of Parikh and Wilczek from the semi-classical perspective of the distant observer. From that perspective for that matter, Hawking radiation emerges in both contexts as the exclusive consequence of infinite time-dilation on the event horizon. These results are consistent with Hawking radiation as the exclusive consequence of the causal structure of the Schwarzschild black-hole space-time both, in a static exterior geometry and in such dynamical exterior geometry as energy-conservation signifies. The extension of the thermal case to other spin-fields and black-hole geometries is discussed.

Asymptotic bound on slow-roll parameter in stringy quintessence model

We study the late time behavior of the scalar part of the volume modulus and the dilaton in stringy quintessence model, focusing on their contributions to the Hubble slow-roll parameter ϵ which directly measures the deviation of the spacetime geometry from de Sitter space. When only one of the moduli is allowed to move, ϵ converges to the stable fixed point at late time. The fixed point value is larger than 1, thus the slow-roll cannot be realized. Moreover, if the decay rate of the quintessence potential is larger than some critical value, the positivity of the potential imposes that the stable fixed point value is just given by 3, independent of the details of the moduli dynamics. Otherwise, the fixed point value coincides with the potential slow-roll parameter. When both the volume modulus and the dilaton roll down the potential simultaneously, we can find the relation between the contributions of two moduli to ϵ satisfied at the fixed point. In this case, the fixed point value is not in general the simple sum of fixed point values in the single field case and cannot be larger than 3.

The harmonic background paradigm, or why gravity is attractive

In a work by Visser, Bassett and Liberati (VBL) (Nucl Phys B Proc Suppl 88:267, 2000) a relation was suggested between a null energy condition and the censorship of superluminal behaviour. Their result was soon challenged by Gao and Wald (Class Quantum Grav 17:4999, 2000) who argued that this relation is gauge dependent and therefore not appropriate to find such connections. In this paper, we clear up this controversy by showing that both papers are correct but need to be interpreted in distinct paradigms. In this context, we introduce a new paradigm to interpret gravitational phenomena, which we call the Harmonic Background Paradigm. This harmonic background paradigm starts from the idea that there exists a more fundamental background causality provided by a flat spacetime geometry. One of the consequences of this paradigm is that the VBL relation can provide an explanation of why gravity is attractive in all standard weak-field situations.

Anisotropic model for dark matter halo with Hernquist density profile

Using the observed flat galactic rotation curve feature and taking into account the presence of anisotropic dark matter with a Hernquist density profile, the space-time geometry of the halo region in galaxies is derived. The gravitational field inside the halo is attractive in nature, and the resultant space-time is flat. We find that our solution affirms the existence of stable circular orbits in the dark halo region. The expression for the equation of state parameter indicates that the matter within the dark halo is non-exotic in nature. An analysis is also conducted on several other aspects of the solution.

Explanation for the Absence of Secondary Peaks in Black Hole Light Curve Autocorrelations.

The observed radiation from hot gas accreting onto a black hole depends on both the details of the flow and the spacetime geometry. The lensing behavior of a black hole produces a distinctive pattern of autocorrelations within its photon ring that encodes its mass, spin, and inclination. In particular, the time autocorrelation of the light curve is expected to display a series of peaks produced by light echoes of the source, with each peak delayed by the characteristic time lapse τ between light echoes. However, such peaks are absent from the light curves of observed black holes. Here, we develop an analytical model for such light curves that demonstrates how, even though light echoes always exist in the signal, they do not produce autocorrelation peaks if the characteristic correlation timescale λ_{0} of the source is greater than τ. We validate our model against simulated light curves of a stochastic accretion model ray traced with a general-relativistic code, and then fit the model to an observed light curve for Sgr A^{*}. We infer that λ_{0}>τ, providing an explanation for the absence of light echoes in the time autocorrelations of Sgr A^{*} light curves. Our results highlight the importance for black hole parameter inference of spatially resolving the photon ring via future space-based interferometry.

Violating Lorentz Invariance Minimally by the Emergence of Nonmetricity? A Perspective

AbstractLorentz invariance belongs to the fundamental symmetries of nature. It is basic for the successful Standard Model of Particle Physics. Nevertheless, within the last decades, Lorentz invariance has been repeatedly questioned. In fact, there exist different research programs addressing this problem. It is argued that a most adequate understanding of a possible violation of Lorentz invariance is achieved in the framework of the gauge‐theoretic approach to gravity: a non‐vanishing nonmetricity of a metric‐affine geometry of spacetime heralds the violation of the Lorentz symmetry.

Quantum geometry in condensed matter

Abstract One of the most celebrated accomplishments of modern physics is the description of fundamental principles of nature in the language of geometry. As the motion of celestial bodies is governed by the geometry of spacetime, the motion of electrons in condensed matter can be characterized by the geometry of the Hilbert space of their wave functions. Such quantum geometry, comprising of Berry curvature and quantum metric, can thus exert profound influences on various properties of materials. The dipoles of both Berry curvature and quantum metric produce nonlinear transport. The quantum metric plays an important role in flat-band superconductors by enhancing the transition temperature. The uniformly distributed momentum-space quantum geometry stabilizes the fractional Chern insulators and results in the fractional quantum anomalous Hall effect. We here review in detail quantum geometry in condensed matter, paying close attention to its effects on nonlinear transport, superconductivity, and topological properties. Possible future research directions in this field are also envisaged.

Dynamics of spin-0 (particles-antiparticles) in Bonnor-Melvin cosmological space-time using the Generalized Feshbach-Villars transformation

In this paper, we employ the Generalized Feshbach-Villars transformation (GFVT) to investigate the relativistic quantum dynamics of spin-0 scalar particles within the backdrop of a magnetic universe characterized by the Bonnor-Melvin cosmological space-time, which exhibits a geometrical topology resulting in an angular deficit. We derive the radial equation of the Klein-Gordon equation using this FV representation and obtain analytical solutions utilizing special functions. Our analysis demonstrates that various parameters associated with the space-time geometry exert significant influence on the eigenvalue solutions within this novel representation.

A study on existence of wormhole in Lemaitre–Tolman–Bondi model

An investigation has been done for possible existence of evolving wormhole (WH) solution in the background of inhomogeneous Lemaitre–Tolman–Bondi (LTB) space-time geometry. Using separable product form of the geometric (or area) radius, the shape function can be evaluated in terms of the functional part of the radial coordinate in the area radius. The conditions for a viable WH configuration have been examined.

How the non-metricity of the connection arises naturally in the classical theory of gravity

Spacetime geometry is described by two–a priori independent–geometric structures: the symmetric connection Γ and the metric tensor g. Metricity condition of Γ (i.e. ∇g = 0) is implied by the Palatini variational principle, but only when the matter fields belong to an exceptional class. In case of a generic matter field, Palatini implies non-metricity of Γ. Traditionally, instead of the (first order) Palatini principle, we use in this case the (second order) Hilbert principle, assuming metricity condition a priori. Unfortunately, the resulting right-hand side of the Einstein equations does not coincide with the matter energy-momentum tensor. We propose to treat seriously the Palatini-implied non-metric connection. The conventional Einstein’s theory, rewritten in terms of this object, acquires a much simpler and universal structure. This approach opens a room for the description of the large scale effects in General Relativity (dark matter?, dark energy?), without resorting to purely phenomenological terms in the Lagrangian of gravitational field. All theories discussed in this paper belong to the standard General Relativity Theory, the only non-standard element being their (much simpler) mathematical formulation. As a mathematical bonus, we propose a new formalism in the calculus of variations, because in case of hyperbolic field theories the standard approach leads to nonsense conclusions.