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The Schrödinger Equation for a Spherically Symmetric System, Its Structure and Solutions# 球对称系统的Schrödinger方程、结构和解#
IF 1 4区 物理与天体物理
Gravitation and Cosmology Pub Date : 2025-09-04 DOI: 10.1134/S0202289325700185
R. I. Ayala Oña, T. P. Shestakova
{"title":"The Schrödinger Equation for a Spherically Symmetric System, Its Structure and Solutions#","authors":"R. I. Ayala Oña,&nbsp;T. P. Shestakova","doi":"10.1134/S0202289325700185","DOIUrl":"10.1134/S0202289325700185","url":null,"abstract":"<p>The Wheeler–DeWitt geometrodynamics, as the first attempt to develop a quantum theory of gravity, faces certain challenges, including the problem of time and interpretation of the wave function. In this paper, we present the extended phase space approach to quantization of gravity as an alternative approach to the Wheeler–DeWitt quantum geometrodynamics. For a space-time with a nontrivial topology, the Wheeler–DeWitt equation loses its sense, but we can derive the Schrödinger equation. Until now, the Schrödinger equation was derived for systems with a finite number of degrees of freedom, and we need to generalize the procedure for field models. The simplest field model is a spherically symmetric one. We derive the integro-differential Schrödinger equation for this model, examine its structure, and find its solution.</p>","PeriodicalId":583,"journal":{"name":"Gravitation and Cosmology","volume":"31 3","pages":"312 - 318"},"PeriodicalIF":1.0,"publicationDate":"2025-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144934692","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}
引用次数: 0
On the Possible Anisotropy of the Unruh Radiation. Part III: A Screened Detector 关于Unruh辐射可能的各向异性。第三部分：筛选检测器
IF 1 4区 物理与天体物理
Gravitation and Cosmology Pub Date : 2025-09-04 DOI: 10.1134/S0202289325700239
E. E. Kholupenko
{"title":"On the Possible Anisotropy of the Unruh Radiation. Part III: A Screened Detector","authors":"E. E. Kholupenko","doi":"10.1134/S0202289325700239","DOIUrl":"10.1134/S0202289325700239","url":null,"abstract":"<p>The process of detection of Unruh radiation by a screened pointlike monopole detector with a narrow directivity pattern is considered for massive and massless scalar fields in (3+1)D space-time. The corresponding stationary energy-angular dependencies of the screened detector responses to the Unruh radiation are calculated numerically for massive and massless particles and are estimated analytically for massless particles. It is shown that in all cases the response is significantly anisotropic, and its energy profile strongly depends on the shape of the screening function. The corresponding brightness temperature of the observed Unruh radiation may exceed the Unruh temperature by orders of magnitude for a directivity pattern narrow enough. These points confirm that the Unruh radiation cannot be considered as thermal (equilibrium) radiation. The generation of the Unruh radiation is a pair production process that is symmetric and implies the existence of counterpart radiation going to infinity. The spectrum of this outgoing counterpart radiation also depends on the accelerated detector properties and, in principle, can be observed by detectors at rest in an initial Minkowski frame. This may allow one to detect and identify the counterpart radiation in particle accelerators in the future. The interaction of the Unruh radiation with an accelerated screened detector should lead to the emergence of a reaction force acting on this detector.</p>","PeriodicalId":583,"journal":{"name":"Gravitation and Cosmology","volume":"31 3","pages":"353 - 365"},"PeriodicalIF":1.0,"publicationDate":"2025-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144934760","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}
引用次数: 0
Photon Spheres near Black Holes in a Model with an Anisotropic Fluid 各向异性流体模型中黑洞附近的光子球
IF 1 4区 物理与天体物理
Gravitation and Cosmology Pub Date : 2025-09-04 DOI: 10.1134/S0202289325700264
V. D. Ivashchuk, S. V. Bolokhov, F. B. Belissarova, N. Kydyrbay, A. N. Malybayev, G. S. Nurbakova, B. Zheng
{"title":"Photon Spheres near Black Holes in a Model with an Anisotropic Fluid","authors":"V. D. Ivashchuk,&nbsp;S. V. Bolokhov,&nbsp;F. B. Belissarova,&nbsp;N. Kydyrbay,&nbsp;A. N. Malybayev,&nbsp;G. S. Nurbakova,&nbsp;B. Zheng","doi":"10.1134/S0202289325700264","DOIUrl":"10.1134/S0202289325700264","url":null,"abstract":"<p>This semi-review paper studies null geodesics which exist for black hole solutions in a gravitational 4D model with an anisotropic fluid. The equations of state for the fluid and the solutions depends on the integer parameter <span>(q=1,2,...)</span>: <span>(p_{r}=-rho c^{2}(2q-1)^{-1},quad p_{t}=-p_{r})</span>, where <span>(rho)</span> is the mass density, <span>(c)</span> is the speed of light, <span>(p_{r})</span> and <span>(p_{t})</span> are pressures in the radial and transverse directions, respectively. Circular null geodesics are explored, and a master equation for the radius <span>(r_{*})</span> of a photon sphere is found, as well as the proposition on the existence and uniqueness of a solution to the master equation, obeying <span>(r_{*}&gt;r_{h})</span>, where <span>(r_{h})</span> is the horizon radius. Relations for the spectrum of quasinormal modes for a test massless scalar field in the eikonal approximation are overviewed and compared with the cyclic frequencies of circular null geo desics. Shadow angles are explored.</p>","PeriodicalId":583,"journal":{"name":"Gravitation and Cosmology","volume":"31 3","pages":"392 - 400"},"PeriodicalIF":1.0,"publicationDate":"2025-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144934757","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}
引用次数: 0
Conformal Invariance and Phase Transitions: Implications for Stable Black Hole Horizons? 共形不变性和相变：对稳定黑洞视界的影响？
IF 1 4区 物理与天体物理
Gravitation and Cosmology Pub Date : 2025-09-04 DOI: 10.1134/S0202289325700203
Pradosh Keshav MV, Arun Kenath
{"title":"Conformal Invariance and Phase Transitions: Implications for Stable Black Hole Horizons?","authors":"Pradosh Keshav MV,&nbsp;Arun Kenath","doi":"10.1134/S0202289325700203","DOIUrl":"10.1134/S0202289325700203","url":null,"abstract":"<p>The behavior of black hole horizons under extreme conditions—such as near collapse or phase transitions—remains less understood, particularly in the context of soft hair and Aretakis instabilities. We show that the breakdown of conformal symmetry during the balding phase induces a topological reorganization of the horizon, leading to divergent entropy corrections and emergent pressure terms. These corrections exhibit universal scaling laws, analogous to quantum phase transitions in condensed matter systems, with extremal limits functioning as quantum critical points. Interestingly, by employing quasi-equilibrium boundary conditions, one could stabilize horizon dynamics without explicitly introducing ad hoc higher-order corrections, further limiting the universal applicability of conformal invariance in black hole physics.</p>","PeriodicalId":583,"journal":{"name":"Gravitation and Cosmology","volume":"31 3","pages":"326 - 335"},"PeriodicalIF":1.0,"publicationDate":"2025-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144934696","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}
引用次数: 0
Gauge Gravitation Theory in Riemann–Cartan Space-Time and the Nonsingular Universe 黎曼-卡坦时空和非奇异宇宙中的规范引力理论
IF 1 4区 物理与天体物理
Gravitation and Cosmology Pub Date : 2025-09-04 DOI: 10.1134/S0202289325700215
A. V. Minkevich
{"title":"Gauge Gravitation Theory in Riemann–Cartan Space-Time and the Nonsingular Universe","authors":"A. V. Minkevich","doi":"10.1134/S0202289325700215","DOIUrl":"10.1134/S0202289325700215","url":null,"abstract":"<p>The gauge gravitation theory in the Riemann–Cartan space-time is investigated in order to solve the fundamental problems of the general relativity theory. The constraints on indefinite parameters of the theory, under which the solutions of isotropic cosmology describe a nonsingular accelerating Universe, are given. Numerical solutions of cosmological equations are obtained near the limiting energy density at a transition from gravitational compression to expansion, in dependence on the energy density, in the case of flat, closed and open models. Some physical and astrophysical consequences of the gauge gravitational theory in Riemann–Cartan space-time are discussed.</p>","PeriodicalId":583,"journal":{"name":"Gravitation and Cosmology","volume":"31 3","pages":"336 - 343"},"PeriodicalIF":1.0,"publicationDate":"2025-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144934693","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}
引用次数: 0
Integrability of Truncated Hořava–Lifshitz Mixmaster Model in Rosenhain Functions 截断Hořava-Lifshitz Mixmaster模型在Rosenhain函数中的可积性
IF 1 4区 物理与天体物理
Gravitation and Cosmology Pub Date : 2025-09-04 DOI: 10.1134/S0202289325700197
A. E. Pavlov, S. M. Gaidar
{"title":"Integrability of Truncated Hořava–Lifshitz Mixmaster Model in Rosenhain Functions","authors":"A. E. Pavlov,&nbsp;S. M. Gaidar","doi":"10.1134/S0202289325700197","DOIUrl":"10.1134/S0202289325700197","url":null,"abstract":"<p>The mixmaster Hořava–Lifshitz model belongs to generalized Euclidean Toda chains with 28 vectors. The longest three vectors of the spectrum play a dominant role in studying its dynamics. The truncated cosmological model is presented as a periodic three-particle Toda chain. It is associated with an affine Kac–Moody Lie algebra <span>(A_{2}^{+})</span>. According to the Adler–van Moerbeke criterion, the truncated Hamiltonian system is algebraically completely integrable. The phase curves wrap a torus of genus 2. The Jacobi problem of inversion of ultraelliptic integrals is solved by using theta-functions of two variables. The solutions of the dynamical problem are expressed in rational functions of Rosenhain theta-functions. They are four-periodic functions.</p>","PeriodicalId":583,"journal":{"name":"Gravitation and Cosmology","volume":"31 3","pages":"319 - 325"},"PeriodicalIF":1.0,"publicationDate":"2025-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144934756","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}
引用次数: 0
Comparison of Newton, Einstein and Brans–Dicke Gravitational Effects Associated with Earth and Other Planets Shape Determination 牛顿、爱因斯坦和布兰斯-迪克引力效应与地球和其他行星形状测定的比较
IF 1 4区 物理与天体物理
Gravitation and Cosmology Pub Date : 2025-09-04 DOI: 10.1134/S0202289325700252
Sabrina Y. Fazzito, Claudio M. Simeone
{"title":"Comparison of Newton, Einstein and Brans–Dicke Gravitational Effects Associated with Earth and Other Planets Shape Determination","authors":"Sabrina Y. Fazzito,&nbsp;Claudio M. Simeone","doi":"10.1134/S0202289325700252","DOIUrl":"10.1134/S0202289325700252","url":null,"abstract":"<p>A comparison between classical, relativistic and Brans–Dicke gravitational effects related to planetary shape characterization is presented. The periastron shifts for orbits around the Earth and the giant planets which can be used as tools for determinations of their shape and density distribution, are the main object of our analysis. The conditions on the parameters improving the possibility to resolve mixed effects are studied. Differing from the approach in a previous work, we now include the observational errors for the classical expansion parameters <span>(J_{n})</span>—which are of particular relevance for the ice giants Uranus and Neptune—as well as the corrections to gravitomagnetic effects resulting from a slight inclination of the satellite orbits. Also, some non-orbital considerations are carried out for the coefficient <span>(J_{3})</span> associated to the South-North asymmetry of the mass distribution of the other two giant planets and the Earth.</p>","PeriodicalId":583,"journal":{"name":"Gravitation and Cosmology","volume":"31 3","pages":"375 - 391"},"PeriodicalIF":1.0,"publicationDate":"2025-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144934671","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}
引用次数: 0
General-Relativistic Corrections on the Optical Measurement of the Earth-Fixed Rotating Observer in the Schwarzschild Background 史瓦西背景下固定地球旋转观测仪光学测量的广义相对论修正
IF 1 4区 物理与天体物理
Gravitation and Cosmology Pub Date : 2025-09-04 DOI: 10.1134/S020228932570029X
H. Ramezani-Aval
{"title":"General-Relativistic Corrections on the Optical Measurement of the Earth-Fixed Rotating Observer in the Schwarzschild Background","authors":"H. Ramezani-Aval","doi":"10.1134/S020228932570029X","DOIUrl":"10.1134/S020228932570029X","url":null,"abstract":"<p>We investigate the behavior of light rays in a rotating observer’s frame in the Schwarzschild background. We derive the null geodesic equations and effective potential for photons in this space-time and then use them to investigate the radial and circular motion of light and its coordinate velocity. Then, we investigate some phenomena related to the motion of light in this space-time, including the Sagnac effect, the radar echo experiment, the gravitational redshift, and the gravitational analog of the space-time index of refraction. In all cases, for the Earth-fixed rotating observer, we calculate the corrections due to the Earth’s rotation (which appear through the rotational coordinate transformation), and the general-relativistic corrections that are obtained by assuming the Schwarzschild background.</p>","PeriodicalId":583,"journal":{"name":"Gravitation and Cosmology","volume":"31 3","pages":"415 - 421"},"PeriodicalIF":1.0,"publicationDate":"2025-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144934792","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}
引用次数: 0
A Study of a Riemann Soliton in a Perfect Fluid Space-Time and (boldsymbol{f(r,T)})-Gravity 完美流体时空和(boldsymbol{f(r,T)}) -重力中黎曼孤子的研究
IF 1 4区 物理与天体物理
Gravitation and Cosmology Pub Date : 2025-09-04 DOI: 10.1134/S0202289325700240
Sampa Pahan, Souvik Dutta
{"title":"A Study of a Riemann Soliton in a Perfect Fluid Space-Time and (boldsymbol{f(r,T)})-Gravity","authors":"Sampa Pahan,&nbsp;Souvik Dutta","doi":"10.1134/S0202289325700240","DOIUrl":"10.1134/S0202289325700240","url":null,"abstract":"<p>We carry out geometric attribution of perfect fluid space-time in terms of a Riemann soliton with a torse forming vector field. It is shown that a perfect fluid space-time becomes a dark fluid space-time when we represent the timelike velocity vector field to be a torse-forming vector field. Next, we have investigated the nature of a Riemann soliton in perfect fluid space-time under certain curvature conditions in terms of the cosmological constant, the gravitational constant, energy density and isotropic pressure. We have also constructed an example of Riemann soliton in perfect fluid space-time. Finally, we have classified the Riemann soliton in a perfect fluid space-time obeying <span>(f(r,T))</span>-gravity in terms of energy density and isotropic pressure.</p>","PeriodicalId":583,"journal":{"name":"Gravitation and Cosmology","volume":"31 3","pages":"366 - 374"},"PeriodicalIF":1.0,"publicationDate":"2025-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144934755","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}
引用次数: 0
Generalized Robertson–Walker Space-Times Admitting (boldsymbol{eta})-Ricci–Yamabe Solitons 广义Robertson-Walker时空承认(boldsymbol{eta}) -Ricci-Yamabe孤子
IF 1 4区 物理与天体物理
Gravitation and Cosmology Pub Date : 2025-09-04 DOI: 10.1134/S0202289325700288
Ansari Rakesh Baidya, Uday Chand De, Abul Kalam Mondal
{"title":"Generalized Robertson–Walker Space-Times Admitting (boldsymbol{eta})-Ricci–Yamabe Solitons","authors":"Ansari Rakesh Baidya,&nbsp;Uday Chand De,&nbsp;Abul Kalam Mondal","doi":"10.1134/S0202289325700288","DOIUrl":"10.1134/S0202289325700288","url":null,"abstract":"<p>We study <span>(eta)</span>-Ricci–Yamabe solitons and gradient <span>(eta)</span>-Ricci–Yamabe solitons in generalized Robertson–Walker space-times . At first, we provide an example of an <span>(eta)</span>-Ricci–Yamabe soliton. Next, we prove that if a generalized Robertson–Walker space-time admits an <span>(eta)</span>-Ricci–Yamabe soliton or a gradient <span>(eta)</span>-Ricci–Yamabe soliton, then it becomes a perfect fluid space-time. As a consequence, we obtain several interesting corollaries.</p>","PeriodicalId":583,"journal":{"name":"Gravitation and Cosmology","volume":"31 3","pages":"408 - 414"},"PeriodicalIF":1.0,"publicationDate":"2025-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144934759","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}
引用次数: 0
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