Submit to Special Issue Submit Abstract to Special Issue Review for Universe Propose a Special Issue

Journal Menu

Journal Browser

► Journal Browser

Celebrating the 110th Anniversary of General Relativity: Advances, Challenges and Perspectives

Print Special Issue Flyer
Special Issue Editors
Special Issue Information
Keywords
Benefits of Publishing in a Special Issue
Published Papers

A special issue of Universe (ISSN 2218-1997). This special issue belongs to the section "Gravitation".

Deadline for manuscript submissions: 30 June 2026 | Viewed by 15943

Share This Special Issue

Special Issue Editors

Prof. Dr. Lorenzo Iorio

E-Mail Website
Guest Editor

Ministero dell’ Istruzione e del Merito, Viale Unità di Italia 68, 70125 Bari, Italy
Interests: general relativity and gravitation; classical general relativity; post-newtonian approximation; perturbation theory; related approximations; gravitational waves; observational cosmology; mathematical and relativistic aspects of cosmology; modified theories of gravity; higher-dimensional gravity and other theories of gravity; experimental studies of gravity; experimental tests of gravitational theories; geodesy and gravity; harmonics of the gravity potential field; geopotential theory and determination; satellite orbits; orbit determination and improvement; astrometry and reference systems; ephemerides, almanacs, and calendars; lunar, planetary, and deep-space probes
Special Issues, Collections and Topics in MDPI journals

Prof. Dr. Øyvind Grøn

E-Mail Website
Guest Editor

Art and Design, Faculty of Technology, Oslo and Akershus University College of Applied Sciences, P.O. Box 4 St., Olavs Plass, NO-0130 Oslo, Norway
Interests: cosmology; early universe; inflation; general theory of relativity; electromagnetism of uniformly accelerated charges; conceptual understanding of general relativity
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The General Theory of Relativity (GTR), enunciated just 110 years ago, remains to this day the best description of gravitation, the feeblest out of the four fundamental interactions and, nonetheless, the one ruling the cosmos at the grandest scales.

Empirical evidence for this theory has recently begun to accumulate. However, fewer tests have been conducted regarding this compared to those supporting electromagnetism and the two nuclear interactions. Indeed, in most situations that are subject to direct experimental investigation, gravitation is far weaker than the other fundamental interactions. In particular, the GTR reaches its full potential only in extreme scenarios characterized by exceptionally intense gravitational fields that rapidly vary over the shortest space and temporal scales, and in speeds close to that of light. Such conditions can be found uniquely in the deepest astronomical recesses.

Its most spectacular confirmations recently came from the detection of gravitational waves emitted during the last stages of the cosmic dance of pairs of black holes and neutron stars that would inevitably lead to their merger, and from the radio waves emitted from matter in the neighbors of the supermassive black holes at the cores of our galaxy and of M87.

On the other hand, the lingering inability of effectively merging GTR with quantum mechanics still represents a key challenge. Strictly connected to this problem is that of the singularities that would likely mark the end of the validity domain of the theory. Additionally, the still unexplained nature of dark matter and dark energy poses challenges to it at galactic and cosmological scales.

This commemorative Special Issue, to which distinguished scholars from all over the world are invited to contribute, is devoted shedding more light on such themes.

Prof. Dr. Lorenzo Iorio
Prof. Dr. Øyvind Grøn
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 250 words) can be sent to the Editorial Office for assessment.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Universe is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

general relativity
110th anniversary
gravitation
cosmology
challenges in gravitational physics

Benefits of Publishing in a Special Issue

Ease of navigation: Grouping papers by topic helps scholars navigate broad scope journals more efficiently.
Greater discoverability: Special Issues support the reach and impact of scientific research. Articles in Special Issues are more discoverable and cited more frequently.
Expansion of research network: Special Issues facilitate connections among authors, fostering scientific collaborations.
External promotion: Articles in Special Issues are often promoted through the journal's social media, increasing their visibility.
Reprint: MDPI Books provides the opportunity to republish successful Special Issues in book format, both online and in print.

Further information on MDPI's Special Issue policies can be found here.

Published Papers (15 papers)

Download All Papers

Order results

Result details

Show export options Show export options

Select all

Export citation of selected articles as:

Research

Jump to: Review

23 pages, 805 KB

Open AccessArticle

CLASH-VLT: The Fifth Force in Chameleon Gravity from Joint Lensing and Kinematics Cluster Mass Profiles

by Lorenzo Pizzuti, Federico Rivano, Keiichi Umetsu and Andrea Biviano

Universe 2026, 12(5), 124; https://doi.org/10.3390/universe12050124 - 26 Apr 2026

Viewed by 424

Abstract

We present a high-precision joint gravitational-lensing and kinematic analysis of nine massive galaxy clusters from the CLASH and CLASH-VLT surveys to test chameleon screening gravity and its

f (R)

sub-class at Mpc scales. We investigate the dependence on the assumed parametrization [...] Read more.

We present a high-precision joint gravitational-lensing and kinematic analysis of nine massive galaxy clusters from the CLASH and CLASH-VLT surveys to test chameleon screening gravity and its

f (R)

sub-class at Mpc scales. We investigate the dependence on the assumed parametrization of the total cluster mass profile by adopting three models, namely Navarro–Frenk–White (NFW), Burkert, and Hernquist. When cuspy models (NFW or Hernquist) are assumed in the general chameleon framework, the combined constraints from the nine clusters are fully consistent with General Relativity (GR), excluding large regions of the modified-gravity parameter space (the coupling constant

Q

and the background chameleon field

ϕ_{\infty}

), providing one of the tightest bounds on general chameleon models with clusters to date. In contrast, adopting a Burkert profile—disfavored by lensing data—leads to a mild (∼2σ) departure from the GR expectation in joint analysis. When considering the

f (R)

sub-case, we obtain a bound on the background scalaron field of

| f_{R} | ≲ 2 - 5 \times 10^{- 5}

(95% C.L.) for NFW and Hernquist models, in agreement with current constraints at cosmological scales, and an apparent deviation from standard gravity of

{log}_{10} | f_{R} | = - 4.7 \pm 1.2

for the Burkert case. We investigate the impact of systematics in the kinematical analysis, showing that the tension is mitigated when clusters exhibiting clear dynamical disturbance are excluded from the sample. Our results show that galaxy clusters provide competitive tests of screened modified gravity at mega-parsec scales, while highlighting the critical role of accurate mass modeling and dynamical-state assessment. The upcoming generation of wide-field lensing surveys and spectroscopic follow-up programs will enable similar analyses on substantially larger samples, offering the prospect of tightening cluster-based constraints on gravity and the dark sector. Full article

(This article belongs to the Special Issue Celebrating the 110th Anniversary of General Relativity: Advances, Challenges and Perspectives)

► Show Figures

Figure 1

17 pages, 6467 KB

Open AccessArticle

The No-Hair Theorems at Work in the Tidal Disruption Event AT2020afhd

by Lorenzo Iorio

Universe 2026, 12(5), 120; https://doi.org/10.3390/universe12050120 - 23 Apr 2026

Viewed by 418

Abstract

Recently, the coprecession of both the accretion disk and the jet formed following the tidal disruption event associated with the optical transient AT2020afhd, driven by a supermassive black hole of almost ten million solar masses, were independently measured in both the X and radio bands, respectively, showing a periodicity of nearly 20 days over about 300 days. An analytical model of the general relativistic gravitomagnetic Lense-Thirring precession of the effective orbit of a fictitious test particle revolving about a spinning primary can explain the observed precessional features. It yields allowed regions in the system’s parameter space which, as far as the hole’s dimensionless spin parameter is concerned, are essentially in agreement with those obtained in the literature with general relativistic magnetohydrodynamic simulations. The present analytical approach can be extended to include the precession due to the hole’s quadrupole mass moment as well. It breaks the degeneracy in the allowed regions occurring for negative and positive values of the spin parameter when only the Lense-Thirring effect is considered. The best estimate for the hole’s mass yields the range 0.185–0.215 for the dimensionless spin parameter. Using the same strategy with the gravitomagnetic frequency for an extended disk of finite size with a parameterized power-law mass density yields to distinct, generally non-overlapping allowed regions for each value of the power-law index adopted. Some of the assumptions on which this work is based are critically examined. Full article

(This article belongs to the Special Issue Celebrating the 110th Anniversary of General Relativity: Advances, Challenges and Perspectives)

► Show Figures

Figure 1

34 pages, 556 KB

Open AccessArticle

Finsler-Randers-Bianchi Type-V Cosmological Model and Modified

f (R, T)

Gravity in Lyra Geometry

by Sachin Kumar, Praduman Kumar Dwivedi, Chayan Kumar Mishra, Ioannis Ampazis and Panayiotis C. Stavrinos

Universe 2026, 12(4), 100; https://doi.org/10.3390/universe12040100 - 31 Mar 2026

Viewed by 614

Abstract

In this research paper, we investigate a Finsler-Randers spacetime in the context of a Bianchi type-V model of universe within the framework of Lyra geometry, employing a modified

f (R, T)

gravity theory that incorporates a cosmological constant

Λ

[...] Read more.

In this research paper, we investigate a Finsler-Randers spacetime in the context of a Bianchi type-V model of universe within the framework of Lyra geometry, employing a modified

f (R, T)

gravity theory that incorporates a cosmological constant

Λ

. We have derived the corresponding anisotropic Friedmann equations for the Finsler–Randers Bianchi type-V model of universe with modified

f (R, T)

gravity in Lyra geometry, including the contributions of the cosmological constant and Randers anisotropic terms

b_{0} (t)

and obtained analytical solutions. Further, we have examined the behavior of various dynamical parameters, commonly used in cosmological analysis, both geometrical and graphical interpretations have been provided. Furthermore, we have derived the Raychaudhuri equation in terms of the cosmological constant as a function of the cosmic time t. Our analysis reveals that the shear scalar

σ^{2}

and the scalar expansion

θ

decrease with cosmic time and tend to zero at late times, indicating the isotropization of the universe in the presence of the cosmological constant; however, the Hubble parameter approaches a constant value rather than vanishing, while the energy density

ρ

, pressure

P

, and the Lyra gauge function

β

remain finite and non-zero even at large cosmic times. Ultimately, we conclude that the universe described by this framework exhibits continuous acceleration, as indicated by the negative value of the deceleration parameter q. Full article

(This article belongs to the Special Issue Celebrating the 110th Anniversary of General Relativity: Advances, Challenges and Perspectives)

► Show Figures

Figure 1

36 pages, 527 KB

Open AccessArticle

The Most General Four-Derivative Unitary String Effective Action with Torsion and Stringy Running Vacuum Model Inflation: Old Ideas from a Modern Perspective

by Nick E. Mavromatos and George Panagopoulos

Universe 2026, 12(3), 90; https://doi.org/10.3390/universe12030090 - 22 Mar 2026

Viewed by 336

Abstract

The string-inspired running vacuum model (StRVM) of inflation is based on a Chern–Simons (CS) gravity effective action in which the only four-spacetime-derivative-order term is a gravitational anomalous CS–Pontryagin density coupled to an axion. In this work, we revisit curvature-squared string-inspired effective actions from the point of view of appropriate local field redefinitions, leaving the perturbative string scattering matrices invariant. We require simultaneously unitarity and torsion interpretation of the field strength of the Kalb–Ramond antisymmetric tensor, features characterizing the (3+1)-dimensional StRVM cosmology. Unlike the higher-dimensional case, the above features are possible in the context of (3+1)-dimensional spacetimes, obtained after string compactification. We demonstrate that the unitarity and torsion interpretation requirements lead to a single type of extra four-derivative terms in the effective gravitational action, not discussed in the previous literature on StRVM, which is, however, shown to be subleading by many orders of magnitude compared to the terms of the StRVM framework. Hence, its presence has no practical implications for the relevant inflationary (and, hence, postinflationary) physics of the StRVM. This demonstrates the phenomenological completeness of the StRVM cosmological scenario, which is thus fully embeddable in the UV-complete (quantum gravity-compatible) string theory framework. Full article

(This article belongs to the Special Issue Celebrating the 110th Anniversary of General Relativity: Advances, Challenges and Perspectives)

11 pages, 710 KB

Open AccessCommunication

Computing the Graph-Changing Dynamics of Loop Quantum Gravity

by Thiago L. M. Guedes, Guillermo A. Mena Marugán, Francesca Vidotto and Markus Müller

Universe 2025, 11(12), 387; https://doi.org/10.3390/universe11120387 - 24 Nov 2025

Viewed by 954

Abstract

In loop quantum gravity (LQG), states of the gravitational field are represented by labeled graphs called spin networks. Their dynamics can be described by a Hamiltonian constraint, which acts on the spin network states, modifying both spins and graphs. Fixed-graph approximations of the dynamics have been extensively studied, but its full graph-changing action so far remains elusive. The latter, alongside the solutions of its constraint, are arguably the missing features in canonical LQG to access phenomenology in all its richness. Here, we discuss a recently developed numerical tool that, for the first time, implements graph-changing dynamics via the Hamiltonian constraint. We explain how it is used to find new solutions to that constraint and to show that some quantum geometric observables behave differently than in the graph-preserving truncation. We also point out that these new numerical methods can find applications in other domains. Full article

(This article belongs to the Special Issue Celebrating the 110th Anniversary of General Relativity: Advances, Challenges and Perspectives)

► Show Figures

Figure 1

10 pages, 330 KB

Open AccessArticle

Traversable Kaluza–Klein Wormholes?

by Christopher Simmonds and Matt Visser

Universe 2025, 11(10), 347; https://doi.org/10.3390/universe11100347 - 17 Oct 2025

Cited by 1 | Viewed by 1126

Abstract

Various authors have suggested that Kaluza–Klein variants of traversable wormholes might to some extent ameliorate the defocussing properties (the curvature condition violations, and implied energy condition violations) inherent in positing the existence of a traversable wormhole throat. Unfortunately such a hope is ill-founded. We shall show that in a traditional Kaluza–Klein context the price paid for completely eliminating the defocussing properties of the wormhole throat is extremely high—to completely eliminate curvature condition violations the 5th dimension has to become truly enormous (formally infinite) in the vicinity of the wormhole throat, in a manner that is fundamentally incompatible with the traditional Kaluza–Klein ansatz. At best, the extra dimensions allow one to move the curvature condition violations around, they cannot be eliminated except at prohibitive cost. While traversable Kaluza–Klein wormholes might be interesting for other reasons, it must be emphasized that adding a 5th dimension is not particularly useful in terms of ameliorating violations of the curvature conditions. Full article

(This article belongs to the Special Issue Celebrating the 110th Anniversary of General Relativity: Advances, Challenges and Perspectives)

► Show Figures

Figure 1

12 pages, 544 KB

Open AccessArticle

Ringing of Reissner–Nordström Black Holes with a Non-Abelian Hair in Gravity’s Rainbow

by Mehrab Momennia

Universe 2025, 11(10), 341; https://doi.org/10.3390/universe11100341 - 15 Oct 2025

Viewed by 669

Abstract

In this paper, we consider massless scalar perturbations minimally coupled to gravity in the background spacetime of charged black holes in Yang–Mills theory with gravity’s rainbow modification. We calculate the corresponding quasinormal frequencies by employing the sixth-order Wentzel—Kramers—Brillouin (WKB) approximation for both asymptotically flat and de Sitter (dS) spacetimes. We show that the Yang–Mills modification of the Reissner–Nordström black holes leads to an increase in the real and imaginary parts of frequencies. Furthermore, we find that the perturbations in asymptotically flat spacetime decay faster with more oscillations compared to dS spacetime, and we study the effects of the rainbow functions on the oscillations. Interestingly, we reveal a novel feature of this black hole case study and show that, unlike typical black hole solutions such as Schwarzschild, RN, and Kerr, the higher multipole numbers live longer than the lower ones in both asymptotically flat and dS spacetimes. Furthermore, the reflection and transmission coefficients are explored for Einstein–Maxwell–Yang–Mills black holes, and the results are compared for flat and dS asymptotes. Full article

(This article belongs to the Special Issue Celebrating the 110th Anniversary of General Relativity: Advances, Challenges and Perspectives)

► Show Figures

Figure 1

11 pages, 407 KB

Open AccessCommunication

On Restrictions of Current Warp Drive Spacetimes and Immediate Possibilities of Improvement

by Hamed Barzegar and Thomas Buchert

Universe 2025, 11(9), 293; https://doi.org/10.3390/universe11090293 - 1 Sep 2025

Cited by 2 | Viewed by 2897

Abstract

Looking at current proposals of so-called ‘warp drive spacetimes’, they appear to employ General Relativity only at an elementary level. A number of strong restrictions are imposed such as flow-orthogonality of the spacetime foliation, vanishing spatial Ricci tensor, and dimensionally reduced and coordinate-dependent velocity fields, to mention the main restrictions. We here provide a brief summary of our proposal of a general and covariant description of spatial motions within General Relativity, then discuss the restrictions that are employed in the majority of the current literature. That current warp drive models are discussed to be unphysical may not be surprising; they lack important ingredients such as covariantly non-vanishing spatial velocity, acceleration, vorticity together with curved space, and a warp mechanism. Full article

(This article belongs to the Special Issue Celebrating the 110th Anniversary of General Relativity: Advances, Challenges and Perspectives)

► Show Figures

Figure 1

17 pages, 1588 KB

Open AccessArticle

The Evolution of Radiating Stars Is Affected by Dimension

by Sunil D. Maharaj, Byron P. Brassel, Megandhren Govender and Keshlan S. Govinder

Universe 2025, 11(8), 263; https://doi.org/10.3390/universe11080263 - 9 Aug 2025

Cited by 1 | Viewed by 814

Abstract

The dynamics of a radiating star in general relativity are studied in higher dimensions for a specified shear-free metric. The temporal evolution of the radiating star depends on the spacetime dimension. In particular, we show explicitly that the gravitational potential changes with increasing spacetime dimension. A detailed analysis of the boundary condition is undertaken. We find new exact solutions and first integrals for the boundary condition equation. Known results in four dimensions are regained as special cases. A phase plane analysis indicates that the model asymptotically approaches a static end state or continues to radiate. The physical features are affected by dimension, and we indicate how the luminosity changes with increasing dimension. Full article

(This article belongs to the Special Issue Celebrating the 110th Anniversary of General Relativity: Advances, Challenges and Perspectives)

► Show Figures

Figure 1

12 pages, 5751 KB

Open AccessArticle

Chaos of Charged Particles in Quadrupole Magnetic Fields Under Schwarzschild Backgrounds

by Qihan Zhang and Xin Wu

Universe 2025, 11(7), 234; https://doi.org/10.3390/universe11070234 - 16 Jul 2025

Cited by 2 | Viewed by 755

Abstract

A four-vector potential of an external test electromagnetic field in a Schwarzschild background is described in terms of a combination of dipole and quadrupole magnetic fields. This combination is an interior solution of the source-free Maxwell equations. Such external test magnetic fields cause the dynamics of charged particles around the black hole to be nonintegrable, and are mainly responsible for chaotic dynamics of charged particles. In addition to the external magnetic fields, some circumstances should be required for the onset of chaos. The effect of the magnetic fields on chaos is shown clearly through an explicit symplectic integrator and a fast Lyapunov indicator. The inclusion of the quadrupole magnetic fields easily induces chaos, compared with that of the dipole magnetic fields. This result is because the Lorentz forces from the quadrupole magnetic fields are larger than those from the dipole magnetic fields. In addition, the Lorentz forces act as attractive forces, which are helpful for bringing the occurrence of chaos in the nonintegrable case. Full article

(This article belongs to the Special Issue Celebrating the 110th Anniversary of General Relativity: Advances, Challenges and Perspectives)

► Show Figures

Figure 1

18 pages, 1269 KB

Open AccessArticle

Many Phases in a Hairy Box in Three Dimensions

by Shoichiro Miyashita

Universe 2025, 11(7), 208; https://doi.org/10.3390/universe11070208 - 25 Jun 2025

Viewed by 662

Abstract

In this paper, I investigate gravitational thermodynamics of the Einstein–Maxwell–scalar system in three dimensions without a cosmological constant. In a previous work by Krishnan, Shekhar, and Bala Subramanian, it was argued that this system has no BH saddles, but has only empty (flat space) saddles and boson star saddles. It was then concluded that the structure of the thermodynamic phase space is much simpler than in the higher-dimensional cases. I will show that, in addition to the known boson star and empty saddles, three more types of saddles exist in this system: the BG saddle, its hairy generalization, and a novel configuration called the boson star-PL saddle. As a result, the structure is richer than one might naively expect and is very similar to the higher-dimensional ones. Full article

(This article belongs to the Special Issue Celebrating the 110th Anniversary of General Relativity: Advances, Challenges and Perspectives)

► Show Figures

Figure 1

21 pages, 2916 KB

Open AccessArticle

Reissner–Nordström and Kerr-like Solutions in Finsler–Randers Gravity

by Georgios Miliaresis, Konstantinos Topaloglou, Ioannis Ampazis, Nefeli Androulaki, Emmanuel Kapsabelis, Emmanuel N. Saridakis, Panayiotis C. Stavrinos and Alkiviadis Triantafyllopoulos

Universe 2025, 11(7), 201; https://doi.org/10.3390/universe11070201 - 20 Jun 2025

Cited by 2 | Viewed by 1276

Abstract

In a previous study we investigated the spherically symmetric Schwarzschild and Schwarzschild–de Sitter solutions within a Finsler–Randers-type geometry. In this work, we extend our analysis to charged and rotating solutions, focusing on the Reissner–Nordström and Kerr-like metrics in the Finsler–Randers gravitational framework. In particular, we extract the modified gravitational field equations and we examine the geodesic equations, analyzing particle trajectories and quantifying the deviations from their standard counterparts. Moreover, we compare the results with the predictions of general relativity, and we discuss how potential deviations from Riemannian geometry could be reached observationally. Full article

(This article belongs to the Special Issue Celebrating the 110th Anniversary of General Relativity: Advances, Challenges and Perspectives)

► Show Figures

Figure 1

15 pages, 1152 KB

Open AccessArticle

A Novel Logarithmic Approach to General Relativistic Hydrodynamics in Dynamical Spacetimes

by Mario Imbrogno, Rita Megale, Luca Del Zanna and Sergio Servidio

Universe 2025, 11(6), 194; https://doi.org/10.3390/universe11060194 - 18 Jun 2025

Viewed by 639

Abstract

We introduce a novel logarithmic approach within the Baumgarte–Shapiro–Shibata–Nakamura (BSSN) formalism for self-consistently solving the equations of general relativistic hydrodynamics (GRHD) in evolving curved spacetimes. This method employs a “3 + 1” decomposition of spacetime, complemented by the “1 + log” slicing condition and Gamma-driver shift conditions, which have been shown to improve numerical stability in spacetime evolution. A key innovation of our work is the logarithmic transformation applied to critical variables such as rest-mass density, energy density, and pressure, thus preserving physical positivity and mitigating numerical issues associated with extreme variations. Our formulation is fully compatible with advanced numerical techniques, including spectral methods and Fourier-based algorithms, and it is particularly suited for simulating highly nonlinear regimes in which gravitational fields play a significant role. This approach aims to provide a solid foundation for future numerical implementations and investigations of relativistic hydrodynamics, offering promising new perspectives for modeling complex astrophysical phenomena in strong gravitational fields, including matter evolution around compact objects like neutron stars and black holes, turbulent flows in the early universe, and the nonlinear evolution of cosmic structures. Full article

(This article belongs to the Special Issue Celebrating the 110th Anniversary of General Relativity: Advances, Challenges and Perspectives)

► Show Figures

Figure 1

20 pages, 1555 KB

Open AccessArticle

Nethotrons: Exploring the Possibility of Measuring Relativistic Spin Precessions, from Earth’s Satellites to the Galactic Centre

by Lorenzo Iorio

Universe 2025, 11(6), 189; https://doi.org/10.3390/universe11060189 - 11 Jun 2025

Viewed by 1308

Abstract

By “nethotron”, from the ancient Greek verb for “to spin”, it is meant here a natural or artificial rotating object, like a pulsar or an artificial satellite, whose rotational axis is cumulatively displaced by the post-Newtonian static (gravitoelectric) and stationary (gravitomagnetic) components of the gravitational field of some massive body around which it freely moves. Until now, both relativistic effects have been measured only by the dedicated space-based mission Gravity Probe B in the terrestrial environment. It detected the gravitoelectric de Sitter and gravitomagnetic Pugh–Schiff spin precessions of four superconducting gyroscopes accumulated within a year after about 50 years from conception to completion of data analysis at a cost of 750 million US dollars to

0.3

and 19 percent accuracy, respectively. The perspectives to measure them with Earth’s long-lived laser-ranged geodetic satellites, like those of the LAGEOS family or possibly one or more of them to be built specifically from scratch, and pulsars orbiting the supermassive black hole in the Galactic Centre, yet to be discovered, are preliminarily investigated. The double pulsar PSR J0737-3039A/B is examined as well. Full article

(This article belongs to the Special Issue Celebrating the 110th Anniversary of General Relativity: Advances, Challenges and Perspectives)

► Show Figures

Figure 1

Review

Jump to: Research

44 pages, 683 KB

Open AccessReview

Structural Stability and General Relativity

by Spiros Cotsakis

Universe 2025, 11(7), 209; https://doi.org/10.3390/universe11070209 - 26 Jun 2025

Cited by 2 | Viewed by 1542

Abstract

We review recent developments in structural stability as applied to key topics in general relativity. For a nonlinear dynamical system arising from the Einstein equations by a symmetry reduction, bifurcation theory fully characterizes the set of all stable perturbations of the system, known as the ‘versal unfolding’. This construction yields a comprehensive classification of qualitatively distinct solutions and their metamorphoses into new topological forms, parametrized by the codimension of the bifurcation in each case. We illustrate these ideas through bifurcations in the simplest Friedmann models, the Oppenheimer-Snyder black hole, the evolution of causal geodesic congruences in cosmology and black hole spacetimes, crease flow on event horizons, and the Friedmann–Lemaître equations. Finally, we list open problems and briefly discuss emerging aspects such as partial differential equation stability of versal families, the general relativity landscape, and potential connections between gravitational versal unfoldings and those of the Maxwell, Dirac, and Schrödinger equations. Full article

(This article belongs to the Special Issue Celebrating the 110th Anniversary of General Relativity: Advances, Challenges and Perspectives)

► Show Figures

Journal Menu

Journal Browser

Celebrating the 110th Anniversary of General Relativity: Advances, Challenges and Perspectives

Share This Special Issue

Special Issue Editors

Special Issue Information

Keywords

Benefits of Publishing in a Special Issue

Published Papers (15 papers)

Research

Review

Further Information

Guidelines

MDPI Initiatives

Follow MDPI