Pub Date : 2025-10-28DOI: 10.1007/s10714-025-03489-9
Nikolaos Dimakis, Alex Giacomini, Genly Leon, Andronikos Paliathanasis, Ekaterina Pozdeeva, Sergey Vernov
We examine the cosmological dynamics of Einstein-Gauss-Bonnet gravity models in a four-dimensional spatially flat FLRW metric. These models are described by (fleft( R,mathcal {G}right) =fleft( R+mu mathcal {G}right) ) theory of gravity. They are equivalent to models linear in the Ricci scalar R and in the Gauss-Bonnet scalar (mathcal {G}) with one nonminimally coupled scalar field without kinetic term. We analyze the stability of de Sitter solutions and construct the phase space of the field equations to investigate the cosmological evolution. We show that (fleft( R+mu mathcal {G}right) )-theory provides a double inflationary epoch, this can be used to unify the early-time and late-time acceleration phases of the universe. Moreover, we discuss the initial value problem for theory to be cosmologically viable. Finally, the effects of the cold dark matter in cosmic evolution are discussed.
{"title":"(f(R,mathcal {G}))-cosmological dynamics in the FLRW background","authors":"Nikolaos Dimakis, Alex Giacomini, Genly Leon, Andronikos Paliathanasis, Ekaterina Pozdeeva, Sergey Vernov","doi":"10.1007/s10714-025-03489-9","DOIUrl":"10.1007/s10714-025-03489-9","url":null,"abstract":"<div><p>We examine the cosmological dynamics of Einstein-Gauss-Bonnet gravity models in a four-dimensional spatially flat FLRW metric. These models are described by <span>(fleft( R,mathcal {G}right) =fleft( R+mu mathcal {G}right) )</span> theory of gravity. They are equivalent to models linear in the Ricci scalar <i>R</i> and in the Gauss-Bonnet scalar <span>(mathcal {G})</span> with one nonminimally coupled scalar field without kinetic term. We analyze the stability of de Sitter solutions and construct the phase space of the field equations to investigate the cosmological evolution. We show that <span>(fleft( R+mu mathcal {G}right) )</span>-theory provides a double inflationary epoch, this can be used to unify the early-time and late-time acceleration phases of the universe. Moreover, we discuss the initial value problem for theory to be cosmologically viable. Finally, the effects of the cold dark matter in cosmic evolution are discussed.</p></div>","PeriodicalId":578,"journal":{"name":"General Relativity and Gravitation","volume":"57 10","pages":""},"PeriodicalIF":2.8,"publicationDate":"2025-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145382401","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-10-25DOI: 10.1007/s10714-025-03479-x
Filipe Moura, João Rodrigues
We compute analytically greybody factors for asymptotically flat spherically symmetric black holes with stringy higher derivative corrections in d dimensions in the high frequency limit. Our calculations include both the eikonal limit - where the real part of the frequency of the scattered wave is much larger than the imaginary part - and the highly damped case - where the imaginary part of the frequency is much larger than the real part -, addressing the emission of gravitons and test scalar fields, and yielding full transmission and reflection scattering coefficients.
{"title":"Greybody factors of string-corrected d-dimensional black holes","authors":"Filipe Moura, João Rodrigues","doi":"10.1007/s10714-025-03479-x","DOIUrl":"10.1007/s10714-025-03479-x","url":null,"abstract":"<div><p>We compute analytically greybody factors for asymptotically flat spherically symmetric black holes with stringy higher derivative corrections in <i>d</i> dimensions in the high frequency limit. Our calculations include both the eikonal limit - where the real part of the frequency of the scattered wave is much larger than the imaginary part - and the highly damped case - where the imaginary part of the frequency is much larger than the real part -, addressing the emission of gravitons and test scalar fields, and yielding full transmission and reflection scattering coefficients.</p></div>","PeriodicalId":578,"journal":{"name":"General Relativity and Gravitation","volume":"57 10","pages":""},"PeriodicalIF":2.8,"publicationDate":"2025-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145352862","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-10-23DOI: 10.1007/s10714-025-03482-2
Gabriele Veneziano
I will summarise recent work on constructing regular bouncing string cosmologies in the framework of Hohm and Zwiebach’s classification of all order (alpha ') corrections compatible with O(d, d) symmetry.
{"title":"Recent progress in classical string cosmology","authors":"Gabriele Veneziano","doi":"10.1007/s10714-025-03482-2","DOIUrl":"10.1007/s10714-025-03482-2","url":null,"abstract":"<div><p>I will summarise recent work on constructing regular bouncing string cosmologies in the framework of Hohm and Zwiebach’s classification of all order <span>(alpha ')</span> corrections compatible with <i>O</i>(<i>d</i>, <i>d</i>) symmetry.</p></div>","PeriodicalId":578,"journal":{"name":"General Relativity and Gravitation","volume":"57 10","pages":""},"PeriodicalIF":2.8,"publicationDate":"2025-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10714-025-03482-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145352816","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-10-22DOI: 10.1007/s10714-025-03487-x
M. Z. Bhatti, Kazuharu Bamba, I. Siddique, Bander Almutairi, Z. Yousaf
We explore the thermodynamics of a novel solution for the Reissner-Nordström-Anti-de Sitter (AdS) black hole, uniquely incorporating the Gauss-Bonnet term. Unlike previous studies that primarily focused on standard General Relativity or other modifications, this inclusion allows for a modified entropy formulation, facilitating the computation of key thermodynamic quantities such as Gibbs free energy, the first law of thermodynamics, the equation of state, and Hawking temperature. We identify critical points and graphically represent the relationship between temperature and Gibbs free energy as a function of the horizon radius. Ultimately, we assess the thermal stability of the Reissner-Nordström-AdS black hole within the framework of Gauss-Bonnet gravity, emphasizing the influence of the Gauss-Bonnet term unlike previous studies that primarily focused on standard General Relativity or other modifications. As a result, it is found that the Gauss-Bonnet coupling significantly alters the thermodynamic behavior and stability structure of the black hole, revealing richer phase transition phenomena.
{"title":"Gauss-Bonnet entropy and thermal dynamics of RN-AdS black holes","authors":"M. Z. Bhatti, Kazuharu Bamba, I. Siddique, Bander Almutairi, Z. Yousaf","doi":"10.1007/s10714-025-03487-x","DOIUrl":"10.1007/s10714-025-03487-x","url":null,"abstract":"<div><p>We explore the thermodynamics of a novel solution for the Reissner-Nordström-Anti-de Sitter (AdS) black hole, uniquely incorporating the Gauss-Bonnet term. Unlike previous studies that primarily focused on standard General Relativity or other modifications, this inclusion allows for a modified entropy formulation, facilitating the computation of key thermodynamic quantities such as Gibbs free energy, the first law of thermodynamics, the equation of state, and Hawking temperature. We identify critical points and graphically represent the relationship between temperature and Gibbs free energy as a function of the horizon radius. Ultimately, we assess the thermal stability of the Reissner-Nordström-AdS black hole within the framework of Gauss-Bonnet gravity, emphasizing the influence of the Gauss-Bonnet term unlike previous studies that primarily focused on standard General Relativity or other modifications. As a result, it is found that the Gauss-Bonnet coupling significantly alters the thermodynamic behavior and stability structure of the black hole, revealing richer phase transition phenomena.</p></div>","PeriodicalId":578,"journal":{"name":"General Relativity and Gravitation","volume":"57 10","pages":""},"PeriodicalIF":2.8,"publicationDate":"2025-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10714-025-03487-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145352415","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-10-22DOI: 10.1007/s10714-025-03485-z
P. H. R. S. Moraes, R. V. Lobato, Sneha Pradhan, P. K. Sahoo
Massive white dwarfs have recently been investigated in extended theories of gravity. In the present work, we construct, for the first time, the equilibrium configurations of white dwarfs in the recently proposed (f(mathcal {R,L,T})) theory of gravity, for the specific case (f(mathcal {R},mathcal {L}, mathcal {T}) = mathcal {R} + alpha mathcal {L} mathcal {T}), where (alpha ) serves as a free parameter within this gravitational theory, (mathcal {R}) is the Ricci scalar, (mathcal {L}) is the matter Lagrangian density and (mathcal {T}) is the trace of the energy-momentum tensor. We numerically solve the Tolman-Oppenheimer-Volkoff-like and mass equations from a set of boundary conditions and the Chandrasekhar equation of state. We show that it is possible to increase the maximum masses of white dwarfs depending on the value of the theory parameter. What constraints this mass increasing is the value of the central density of the white dwarf. Finally, the theory remarkably recovers general relativity and Newtonian limit for small densities.
{"title":"White dwarfs in (f(mathcal {R},mathcal {L}, mathcal {T})) gravity","authors":"P. H. R. S. Moraes, R. V. Lobato, Sneha Pradhan, P. K. Sahoo","doi":"10.1007/s10714-025-03485-z","DOIUrl":"10.1007/s10714-025-03485-z","url":null,"abstract":"<div><p>Massive white dwarfs have recently been investigated in extended theories of gravity. In the present work, we construct, for the first time, the equilibrium configurations of white dwarfs in the recently proposed <span>(f(mathcal {R,L,T}))</span> theory of gravity, for the specific case <span>(f(mathcal {R},mathcal {L}, mathcal {T}) = mathcal {R} + alpha mathcal {L} mathcal {T})</span>, where <span>(alpha )</span> serves as a free parameter within this gravitational theory, <span>(mathcal {R})</span> is the Ricci scalar, <span>(mathcal {L})</span> is the matter Lagrangian density and <span>(mathcal {T})</span> is the trace of the energy-momentum tensor. We numerically solve the Tolman-Oppenheimer-Volkoff-like and mass equations from a set of boundary conditions and the Chandrasekhar equation of state. We show that it is possible to increase the maximum masses of white dwarfs depending on the value of the theory parameter. What constraints this mass increasing is the value of the central density of the white dwarf. Finally, the theory remarkably recovers general relativity and Newtonian limit for small densities.</p></div>","PeriodicalId":578,"journal":{"name":"General Relativity and Gravitation","volume":"57 10","pages":""},"PeriodicalIF":2.8,"publicationDate":"2025-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145352414","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-10-21DOI: 10.1007/s10714-025-03488-w
C. I. Hernandez-Perez, A. López-Ortega
The Horowitz-Hubeny method has been used to compute the quasinormal frequencies of asymptotically anti-de Sitter backgrounds. For the dimensionally reduced BTZ black hole, in this work we propose a modification of this method and we also use a new procedure to calculate its quasinormal frequencies in a perturbative way. The proposed modification of the Horowitz-Hubeny method works for parameter values of the dimensionally reduced BTZ black hole for which the original version of the method does not converge. The proposed calculation of the quasinormal frequencies in a perturbative series takes as a basis a recently published perturbative method motivated in the improved asymptotic iteration method, and in the dimensionally reduced BTZ black hole, for small values of the inner radius, the perturbative values of the quasinormal frequencies coincide with the numerical values. Furthermore we explore numerically and analytically the quasinormal frequencies of the dimensionally reduced BTZ black hole in the near extremal limit.
{"title":"Additional results on the quasinormal frequencies of the dimensionally reduced BTZ black hole","authors":"C. I. Hernandez-Perez, A. López-Ortega","doi":"10.1007/s10714-025-03488-w","DOIUrl":"10.1007/s10714-025-03488-w","url":null,"abstract":"<div><p>The Horowitz-Hubeny method has been used to compute the quasinormal frequencies of asymptotically anti-de Sitter backgrounds. For the dimensionally reduced BTZ black hole, in this work we propose a modification of this method and we also use a new procedure to calculate its quasinormal frequencies in a perturbative way. The proposed modification of the Horowitz-Hubeny method works for parameter values of the dimensionally reduced BTZ black hole for which the original version of the method does not converge. The proposed calculation of the quasinormal frequencies in a perturbative series takes as a basis a recently published perturbative method motivated in the improved asymptotic iteration method, and in the dimensionally reduced BTZ black hole, for small values of the inner radius, the perturbative values of the quasinormal frequencies coincide with the numerical values. Furthermore we explore numerically and analytically the quasinormal frequencies of the dimensionally reduced BTZ black hole in the near extremal limit.</p></div>","PeriodicalId":578,"journal":{"name":"General Relativity and Gravitation","volume":"57 10","pages":""},"PeriodicalIF":2.8,"publicationDate":"2025-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145352695","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-10-19DOI: 10.1007/s10714-025-03474-2
Valerio Faraoni, Luca Valsan, Uri Gorman
Forces parallel to particle trajectories occur in physically meaningful situations, including relativistic cosmology and Einstein frame scalar-tensor gravity. These situations have Newtonian analogues that we discuss to provide intuition about the underlying physics.
{"title":"Forces parallel to particle trajectories in relativistic gravity","authors":"Valerio Faraoni, Luca Valsan, Uri Gorman","doi":"10.1007/s10714-025-03474-2","DOIUrl":"10.1007/s10714-025-03474-2","url":null,"abstract":"<div><p>Forces parallel to particle trajectories occur in physically meaningful situations, including relativistic cosmology and Einstein frame scalar-tensor gravity. These situations have Newtonian analogues that we discuss to provide intuition about the underlying physics.</p></div>","PeriodicalId":578,"journal":{"name":"General Relativity and Gravitation","volume":"57 10","pages":""},"PeriodicalIF":2.8,"publicationDate":"2025-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145316151","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-10-14DOI: 10.1007/s10714-025-03484-0
Hamid R. Bakhtiarizadeh
We perform the first study of the throttling process and heat engine efficiency of asymptotically Anti-de Sitter charged and rotating black strings in the extended phase space. For the throttling process, we calculate the Joule-Thomson coefficient and inversion temperature. We also depict the inversion and isenthalpic curves in the temperature-pressure plane, thereby identifying the corresponding cooling and heating regions. For the black string heat engine, we obtain analytical expressions for the efficiency of the Carnot and rectangular engine cycles and draw their diagrams in terms of some relevant thermodynamics variables.
{"title":"Joule-Thomson expansion and heat engine efficiency of charged rotating black strings","authors":"Hamid R. Bakhtiarizadeh","doi":"10.1007/s10714-025-03484-0","DOIUrl":"10.1007/s10714-025-03484-0","url":null,"abstract":"<div><p>We perform the first study of the throttling process and heat engine efficiency of asymptotically Anti-de Sitter charged and rotating black strings in the extended phase space. For the throttling process, we calculate the Joule-Thomson coefficient and inversion temperature. We also depict the inversion and isenthalpic curves in the temperature-pressure plane, thereby identifying the corresponding cooling and heating regions. For the black string heat engine, we obtain analytical expressions for the efficiency of the Carnot and rectangular engine cycles and draw their diagrams in terms of some relevant thermodynamics variables.</p></div>","PeriodicalId":578,"journal":{"name":"General Relativity and Gravitation","volume":"57 10","pages":""},"PeriodicalIF":2.8,"publicationDate":"2025-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145315925","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-10-13DOI: 10.1007/s10714-025-03473-3
Aavishkar Madhunlall, Chevarra Hansraj, Rituparno Goswami, Sunil D. Maharaj
In this paper we study the higher dimensional (left( N > 4right) ) homogeneous and isotropic perfect fluid spacetimes in Einstein–Gauss–Bonnet (EGB) gravity. We solve the modified field equations with higher order curvature terms to determine the evolution of the scale factor. We transparently show that this scale factor cannot become smaller than a finite minimum positive value which depends on the dimension and equation of state. This bound completely eliminates any curvature singularities in homogeneous and isotropic spacetimes, where the scale factor must tend to zero. This is a unique property of EGB gravity which, despite being ghost-free and having quasi-linear field equations like general relativity, allows for the violation of singularity theorems. This phenomenon, thus, gives a natural way to dynamically construct regular black holes via higher dimensional continual gravitational collapse.
本文研究了Einstein-Gauss-Bonnet (EGB)引力下的高维(left( N > 4right) )均匀各向同性完美流体时空。通过求解具有高阶曲率项的修正场方程来确定尺度因子的演化。我们清楚地表明,这个比例因子不能小于一个有限的最小正值,这取决于维数和状态方程。这个边界完全消除了齐次和各向同性时空中的任何曲率奇点,其中比例因子必须趋于零。这是EGB引力的一个独特性质,尽管它是无鬼的,并且具有像广义相对论那样的拟线性场方程,但它允许违反奇点定理。因此,这种现象提供了一种通过高维连续引力坍缩动态构建规则黑洞的自然方法。
{"title":"Absence of curvature singularities in symmetric perfect fluid spacetimes in Einstein–Gauss–Bonnet Gravity","authors":"Aavishkar Madhunlall, Chevarra Hansraj, Rituparno Goswami, Sunil D. Maharaj","doi":"10.1007/s10714-025-03473-3","DOIUrl":"10.1007/s10714-025-03473-3","url":null,"abstract":"<div><p>In this paper we study the higher dimensional <span>(left( N > 4right) )</span> homogeneous and isotropic perfect fluid spacetimes in Einstein–Gauss–Bonnet (EGB) gravity. We solve the modified field equations with higher order curvature terms to determine the evolution of the scale factor. We transparently show that this scale factor cannot become smaller than a finite minimum positive value which depends on the dimension and equation of state. This bound completely eliminates any curvature singularities in homogeneous and isotropic spacetimes, where the scale factor must tend to zero. This is a unique property of EGB gravity which, despite being ghost-free and having quasi-linear field equations like general relativity, allows for the violation of singularity theorems. This phenomenon, thus, gives a natural way to dynamically construct regular black holes via higher dimensional continual gravitational collapse.\u0000</p></div>","PeriodicalId":578,"journal":{"name":"General Relativity and Gravitation","volume":"57 10","pages":""},"PeriodicalIF":2.8,"publicationDate":"2025-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10714-025-03473-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145315727","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-10-13DOI: 10.1007/s10714-025-03483-1
Tina A. Harriott, J.G. Williams
The null-surface formulation (NSF) of general relativity differs from the usual approach by treating the spacetime metric as a derivable quantity instead of regarding it as fundamental. The NSF has two mathematically equivalent interpretations: (a) Light rays leave a spacetime point and intersect null-infinity to form a ‘light-cone cut,’ which encodes the properties of the spacetime; (b) At null-infinity, angular coordinates (Bondi coordinates) label past light cones. Being null surfaces, these past light cones will satisfy the NSF field equations, the solution of which will provide a description of spacetime. In an earlier work, the present authors gave an exact solution for the NSF field equations in 2+1 dimensions, showing how the solution directly linked the two NSF interpretations. The present paper expands on that work by constructing the corresponding (3+1)-dimensional solution and then, as in 2+1 dimensions, linking the two interpretations so as to illustrate their equivalence. The functions relevant to the 3+1 NSF are calculated, and the field equations are shown to be satisfied. This is the first time that a nontrivial (3+1)-dimensional NSF solution has been found and its properties examined.
{"title":"Solution for the 3+1 null-surface formulation with a power-law spacetime","authors":"Tina A. Harriott, J.G. Williams","doi":"10.1007/s10714-025-03483-1","DOIUrl":"10.1007/s10714-025-03483-1","url":null,"abstract":"<div><p>The null-surface formulation (NSF) of general relativity differs from the usual approach by treating the spacetime metric as a derivable quantity instead of regarding it as fundamental. The NSF has two mathematically equivalent interpretations: (a) Light rays leave a spacetime point and intersect null-infinity to form a ‘light-cone cut,’ which encodes the properties of the spacetime; (b) At null-infinity, angular coordinates (Bondi coordinates) label past light cones. Being null surfaces, these past light cones will satisfy the NSF field equations, the solution of which will provide a description of spacetime. In an earlier work, the present authors gave an exact solution for the NSF field equations in 2+1 dimensions, showing how the solution directly linked the two NSF interpretations. The present paper expands on that work by constructing the corresponding (3+1)-dimensional solution and then, as in 2+1 dimensions, linking the two interpretations so as to illustrate their equivalence. The functions relevant to the 3+1 NSF are calculated, and the field equations are shown to be satisfied. This is the first time that a nontrivial (3+1)-dimensional NSF solution has been found and its properties examined.</p></div>","PeriodicalId":578,"journal":{"name":"General Relativity and Gravitation","volume":"57 10","pages":""},"PeriodicalIF":2.8,"publicationDate":"2025-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145315663","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}