We consider a class of axially symmetric solutions to Einstein’s equations incorporating a -dependent scalar field and extend these solutions by introducing electric and magnetic charges via Harrison transformations. Subsequently, we enhance the charged metrics by incorporating the NUT parameter through Ehlers transformations, yielding a novel class of charged-Taub-NUT metrics that represent exact solutions to Einstein’s equations. Finally, we investigate some of astrophysical aspects of the charged-Taub-NUT metrics, focusing on phenomena such as gravitational lensing and quasi-normal modes (QNMs).
{"title":"A class of charged-Taub-NUT-scalar metrics via Harison and Ehlers transformations","authors":"Mahnaz Tavakoli Kachi, Behrouz Mirza, Fatemeh Sadeghi","doi":"10.1016/j.aop.2025.169924","DOIUrl":"10.1016/j.aop.2025.169924","url":null,"abstract":"<div><div>We consider a class of axially symmetric solutions to Einstein’s equations incorporating a <span><math><mi>θ</mi></math></span>-dependent scalar field and extend these solutions by introducing electric and magnetic charges via Harrison transformations. Subsequently, we enhance the charged metrics by incorporating the NUT parameter through Ehlers transformations, yielding a novel class of charged-Taub-NUT metrics that represent exact solutions to Einstein’s equations. Finally, we investigate some of astrophysical aspects of the charged-Taub-NUT metrics, focusing on phenomena such as gravitational lensing and quasi-normal modes (QNMs).</div></div>","PeriodicalId":8249,"journal":{"name":"Annals of Physics","volume":"474 ","pages":"Article 169924"},"PeriodicalIF":3.0,"publicationDate":"2025-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143097019","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 : 2025-01-10DOI: 10.1016/j.aop.2025.169923
Mohammad Umar
In this study, we introduce the Cantor-structured Dirac comb potential, referred to as the Cantor Dirac comb (CDC-) potential system, and investigate non-relativistic quantum tunneling through this novel potential configuration. This system is engineered by positioning delta potentials at the boundaries of each rectangular potential segment of Cantor potential. This study is the first to investigate quantum tunneling through a fractal geometric Dirac comb potential. This potential system exemplifies a particular instance of the super periodic potential (SPP), a broader class of potentials that generalize locally periodic potentials. Utilizing the theoretical framework of SPP, we derived a closed-form expression for the transmission probability for this potential architecture. We report various transmission characteristics, including the appearance of band-like features and the scaling behavior of the reflection coefficient with wave vector , which is governed by a scaling function expressed as a finite product of the Laue function. A particularly striking feature of the system is the occurrence of sharp transmission resonances, which may prove useful in applications such as highly sharp transmission filters.
{"title":"Transmission through Cantor structured Dirac comb potential","authors":"Mohammad Umar","doi":"10.1016/j.aop.2025.169923","DOIUrl":"10.1016/j.aop.2025.169923","url":null,"abstract":"<div><div>In this study, we introduce the Cantor-structured Dirac comb potential, referred to as the Cantor Dirac comb (CDC-<span><math><msub><mrow><mi>ρ</mi></mrow><mrow><mi>N</mi></mrow></msub></math></span>) potential system, and investigate non-relativistic quantum tunneling through this novel potential configuration. This system is engineered by positioning delta potentials at the boundaries of each rectangular potential segment of Cantor potential. This study is the first to investigate quantum tunneling through a fractal geometric Dirac comb potential. This potential system exemplifies a particular instance of the super periodic potential (SPP), a broader class of potentials that generalize locally periodic potentials. Utilizing the theoretical framework of SPP, we derived a closed-form expression for the transmission probability for this potential architecture. We report various transmission characteristics, including the appearance of band-like features and the scaling behavior of the reflection coefficient with wave vector <span><math><mi>k</mi></math></span>, which is governed by a scaling function expressed as a finite product of the Laue function. A particularly striking feature of the system is the occurrence of sharp transmission resonances, which may prove useful in applications such as highly sharp transmission filters.</div></div>","PeriodicalId":8249,"journal":{"name":"Annals of Physics","volume":"474 ","pages":"Article 169923"},"PeriodicalIF":3.0,"publicationDate":"2025-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143097021","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 : 2025-01-09DOI: 10.1016/j.aop.2024.169904
Irakli Titvinidze , Julian Stobbe , Alexey N. Rubtsov , Georg Rohringer
We present a method to study the time evolution of the single impurity Anderson model which exploits a mean field decoupling of the interacting impurity and the non-interacting bath (in form of a chain). This is achieved by the introduction of a pair of auxiliary Majorana fermions between the impurity and the chain. After decoupling, we obtain a self-consistent set of equations for the impurity and chain. First, we study the behavior of the system in equilibrium at zero temperature. We observe a phase transition as a function of the interaction at the impurity and the coupling between the impurity and the chain between the Kondo regime, where the mean field parameters are zero and, hence, we have a well-defined spin at the impurity, to a phase where mean field parameters acquire finite values leading to a screening of the impurity spin by conduction bath electrons. In the latter case, we observe charge and spin fluctuations at the impurity site. Let us note that, while the sharp equilibrium phase transition is a feature of the mean field treatment of the problem it is likely to show itself as a crossover in an exact treatment of the problem. Starting from this equilibrium ground state at zero temperature we quench in the interaction strength at the impurity and/or the hybridization strength between the impurity and the chain and study the time evolution of the system. We find that for quenches to weak to intermediate coupling the system converges to the equilibrium state defined by the final set of parameters after the quench. We analyze the oscillation frequency and as well as the thermalization rate during this quench. A quench to a strong interaction value results in persistent oscillations and a trapping of the system in a non-thermal state. We speculate that these two regimes of different long-time behavior are separated by a dynamical phase transition. We, however, argue that, while our description of the weak to moderate correlated regimes is correct at all time scales, for large final interaction, our approximation is fully valid only at moderate time scale whereas persistent oscillations and related sharp phase transitions are likely artifacts of the mean field treatment of the problem (as in the equilibrium case).
{"title":"Mean field decoupling of single impurity Anderson model through auxiliary Majorana fermions","authors":"Irakli Titvinidze , Julian Stobbe , Alexey N. Rubtsov , Georg Rohringer","doi":"10.1016/j.aop.2024.169904","DOIUrl":"10.1016/j.aop.2024.169904","url":null,"abstract":"<div><div>We present a method to study the time evolution of the single impurity Anderson model which exploits a mean field decoupling of the interacting impurity and the non-interacting bath (in form of a chain). This is achieved by the introduction of a pair of auxiliary Majorana fermions between the impurity and the chain. After decoupling, we obtain a self-consistent set of equations for the impurity and chain. First, we study the behavior of the system in equilibrium at zero temperature. We observe a phase transition as a function of the interaction at the impurity and the coupling between the impurity and the chain between the Kondo regime, where the mean field parameters are zero and, hence, we have a well-defined spin at the impurity, to a phase where mean field parameters acquire finite values leading to a screening of the impurity spin by conduction bath electrons. In the latter case, we observe charge and spin fluctuations at the impurity site. Let us note that, while the sharp equilibrium phase transition is a feature of the mean field treatment of the problem it is likely to show itself as a crossover in an exact treatment of the problem. Starting from this equilibrium ground state at zero temperature we quench in the interaction strength at the impurity and/or the hybridization strength between the impurity and the chain and study the time evolution of the system. We find that for quenches to weak to intermediate coupling the system converges to the equilibrium state defined by the final set of parameters after the quench. We analyze the oscillation frequency and as well as the thermalization rate during this quench. A quench to a strong interaction value results in persistent oscillations and a trapping of the system in a non-thermal state. We speculate that these two regimes of different long-time behavior are separated by a dynamical phase transition. We, however, argue that, while our description of the weak to moderate correlated regimes is correct at all time scales, for large final interaction, our approximation is fully valid only at moderate time scale whereas persistent oscillations and related sharp phase transitions are likely artifacts of the mean field treatment of the problem (as in the equilibrium case).</div></div>","PeriodicalId":8249,"journal":{"name":"Annals of Physics","volume":"474 ","pages":"Article 169904"},"PeriodicalIF":3.0,"publicationDate":"2025-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143141051","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 : 2025-01-08DOI: 10.1016/j.aop.2025.169920
M. Bulakhov , A.S. Peletminskii , Yu.V. Slyusarenko
We develop a general kinetic approach to studying high-frequency collective excitations in arbitrary-spin quantum gases. To this end, we formulate a many-body Hamiltonian that includes the multipolar exchange interaction as well as the coupling of a multipolar moment with an external field. By linearizing the respective collisionless kinetic equation, we find a general dispersion equation that allows us to examine the high-frequency collective modes for arbitrary-spin atoms obeying one or another quantum statistics. We analyze some of its particular solutions describing spin waves and zero sound for Bose and Fermi gases.
{"title":"General collisionless kinetic approach to studying excitations in arbitrary-spin quantum atomic gases","authors":"M. Bulakhov , A.S. Peletminskii , Yu.V. Slyusarenko","doi":"10.1016/j.aop.2025.169920","DOIUrl":"10.1016/j.aop.2025.169920","url":null,"abstract":"<div><div>We develop a general kinetic approach to studying high-frequency collective excitations in arbitrary-spin quantum gases. To this end, we formulate a many-body Hamiltonian that includes the multipolar exchange interaction as well as the coupling of a multipolar moment with an external field. By linearizing the respective collisionless kinetic equation, we find a general dispersion equation that allows us to examine the high-frequency collective modes for arbitrary-spin atoms obeying one or another quantum statistics. We analyze some of its particular solutions describing spin waves and zero sound for Bose and Fermi gases.</div></div>","PeriodicalId":8249,"journal":{"name":"Annals of Physics","volume":"474 ","pages":"Article 169920"},"PeriodicalIF":3.0,"publicationDate":"2025-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143097020","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 : 2025-01-07DOI: 10.1016/j.aop.2025.169921
Z. Yousaf , S. Khan , Mansour Shrahili , A. Malik , M.Z. Bhatti
This article introduces a simplified model of static, spherical stellar systems interacting with anisotropic dark energy, using the Buchdahl model as the background metric potential. The notion of cosmic dark energy may serve as a potential mechanism to counteract the relativistic gravitational collapse of stellar distributions into singularities. Dark energy plays a vital role in shaping the cosmos on the largest scales, as it is the driving force behind the observed accelerated expansion. Therefore, it is reasonable to think that dark energy influences the kinematics of gravitationally bound stellar structures (Sakti and Sulaksono, 2021) [65]. Motivated by this, we introduce a self-gravitating stellar system model under the influence of dark energy, which incorporates both dark and ordinary matter. The model assumes a direct proportionality between the dark energy density and the perfect fluid density. We will then analyze the astrophysical features, including the regularity of the metric variables, density, pressure, mass–radius relationship, stability, dark energy parameters, and equilibrium conditions associated with the model. The model is promising due to its adherence to energy conditions and lack of a central singularity. By examining a mass–radius diagram, we have found the maximum mass limit for this type of star. Our results show that our suggested model corresponds to a feasible and physically realistic star structure that satisfies all stability criteria.
{"title":"Modeling anisotropic dark energy self-gravitating stars satisfying the Karmarkar condition","authors":"Z. Yousaf , S. Khan , Mansour Shrahili , A. Malik , M.Z. Bhatti","doi":"10.1016/j.aop.2025.169921","DOIUrl":"10.1016/j.aop.2025.169921","url":null,"abstract":"<div><div>This article introduces a simplified model of static, spherical stellar systems interacting with anisotropic dark energy, using the Buchdahl model as the background metric potential. The notion of cosmic dark energy may serve as a potential mechanism to counteract the relativistic gravitational collapse of stellar distributions into singularities. Dark energy plays a vital role in shaping the cosmos on the largest scales, as it is the driving force behind the observed accelerated expansion. Therefore, it is reasonable to think that dark energy influences the kinematics of gravitationally bound stellar structures (Sakti and Sulaksono, 2021) [65]. Motivated by this, we introduce a self-gravitating stellar system model under the influence of dark energy, which incorporates both dark and ordinary matter. The model assumes a direct proportionality between the dark energy density and the perfect fluid density. We will then analyze the astrophysical features, including the regularity of the metric variables, density, pressure, mass–radius relationship, stability, dark energy parameters, and equilibrium conditions associated with the model. The model is promising due to its adherence to energy conditions and lack of a central singularity. By examining a mass–radius diagram, we have found the maximum mass limit for this type of star. Our results show that our suggested model corresponds to a feasible and physically realistic star structure that satisfies all stability criteria.</div></div>","PeriodicalId":8249,"journal":{"name":"Annals of Physics","volume":"474 ","pages":"Article 169921"},"PeriodicalIF":3.0,"publicationDate":"2025-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143097022","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 : 2025-01-04DOI: 10.1016/j.aop.2024.169917
A. Francisco Neto , B.M. Villegas-Martínez
A novel, basis- and integral-free perturbative method for the Dyson series describing Schrödinger dynamics in general is introduced. The trapped ions in the high-intensity regime are addressed under this new approach. The approach is based on the Omega Matrix Calculus (OMC) which is rooted in the theory of partitions of natural numbers due to MacMahon. A key ingredient in our formalism comprises a new OMC representation to compute multiple integrals involving the matrix exponential, allowing for a simpler treatment using Omega calculus elimination rules and enhancing previous representations, such as the one by Francisco Neto (2020). This approach not only implies previous perturbative approaches based on divided-differences in Kalev and Hen (2021) and the matrix method in Villegas-Martínez et al. (2022), but also simplifies the derivation process and provides a closed-form expression for the th term in the perturbative expansion solving previously open questions highlighted in prior works, including Villegas-Martínez et al. aforementioned work. Additionally, it reveals that the th term in perturbation theory is governed by a generalized exponential function based on divided differences, which simplifies to the ordinary exponential for . In specific cases, where , , and the interaction term is time-independent, the results are consistent with those obtained by Villegas-Martínez et al.
{"title":"A new basis- and integral-free approach to perturbation theory: The Schrödinger dynamics of N trapped ions in the high-intensity regime","authors":"A. Francisco Neto , B.M. Villegas-Martínez","doi":"10.1016/j.aop.2024.169917","DOIUrl":"10.1016/j.aop.2024.169917","url":null,"abstract":"<div><div>A novel, basis- and integral-free perturbative method for the Dyson series describing Schrödinger dynamics in general is introduced. The <span><math><mi>N</mi></math></span> trapped ions in the high-intensity regime are addressed under this new approach. The approach is based on the Omega Matrix Calculus (OMC) which is rooted in the theory of partitions of natural numbers due to MacMahon. A key ingredient in our formalism comprises a new OMC representation to compute multiple integrals involving the matrix exponential, allowing for a simpler treatment using Omega calculus elimination rules and enhancing previous representations, such as the one by Francisco Neto (2020). This approach not only implies previous perturbative approaches based on divided-differences in Kalev and Hen (2021) and the matrix method in Villegas-Martínez et al. (2022), but also simplifies the derivation process and provides a closed-form expression for the <span><math><mi>n</mi></math></span>th term in the perturbative expansion solving previously open questions highlighted in prior works, including Villegas-Martínez et al. aforementioned work. Additionally, it reveals that the <span><math><mi>n</mi></math></span>th term in perturbation theory is governed by a generalized exponential function based on divided differences, which simplifies to the ordinary exponential for <span><math><mrow><mi>n</mi><mo>=</mo><mn>0</mn></mrow></math></span>. In specific cases, where <span><math><mrow><mi>N</mi><mo>=</mo><mn>1</mn></mrow></math></span>, <span><math><mrow><mi>n</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn></mrow></math></span>, and the interaction term is time-independent, the results are consistent with those obtained by Villegas-Martínez et al.</div></div>","PeriodicalId":8249,"journal":{"name":"Annals of Physics","volume":"474 ","pages":"Article 169917"},"PeriodicalIF":3.0,"publicationDate":"2025-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143097486","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 : 2025-01-04DOI: 10.1016/j.aop.2024.169918
M.D. de Oliveira, Alexandre G.M. Schmidt
This work investigates a method to map systems with gravitational fields into non-relativistic flat spacetime ones. Considering a line element of the form , we constructed an external potential in terms of the functions and . We found that the non-relativistic wave function is written in terms of the relativistic wave function. As applications, we constructed non-relativistic analogous models, introducing external potentials for two types of static and non-rotating black holes: Schwarzschild, anti-de Sitter, and de Sitter. Finally, we analyzed the physics at the event horizon region for the black holes and cosmological horizon for the de Sitter spacetime, and the values coincide with those obtained for the case with a gravitational field in the relativistic regime.
{"title":"Mapping Schwarzschild, de Sitter and anti-de Sitter spacetimes into flat spacetime systems with Kratzer potentials","authors":"M.D. de Oliveira, Alexandre G.M. Schmidt","doi":"10.1016/j.aop.2024.169918","DOIUrl":"10.1016/j.aop.2024.169918","url":null,"abstract":"<div><div>This work investigates a method to map systems with gravitational fields into non-relativistic flat spacetime ones. Considering a line element of the form <span><math><mrow><mi>d</mi><msup><mrow><mi>s</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>=</mo><msup><mrow><mi>e</mi></mrow><mrow><mn>2</mn><mi>f</mi><mrow><mo>(</mo><mi>r</mi><mo>)</mo></mrow></mrow></msup><mi>d</mi><msup><mrow><mi>t</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>−</mo><msup><mrow><mi>e</mi></mrow><mrow><mn>2</mn><mi>g</mi><mrow><mo>(</mo><mi>r</mi><mo>)</mo></mrow></mrow></msup><mi>d</mi><msup><mrow><mi>r</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>−</mo><msup><mrow><mi>r</mi></mrow><mrow><mn>2</mn></mrow></msup><mi>d</mi><msup><mrow><mi>θ</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>−</mo><msup><mrow><mi>r</mi></mrow><mrow><mn>2</mn></mrow></msup><msup><mrow><mo>sin</mo></mrow><mrow><mn>2</mn></mrow></msup><mi>θ</mi><mi>d</mi><msup><mrow><mi>ϕ</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></math></span>, we constructed an external potential <span><math><mrow><mi>V</mi><mrow><mo>(</mo><mi>r</mi><mo>)</mo></mrow></mrow></math></span> in terms of the functions <span><math><mrow><mi>f</mi><mrow><mo>(</mo><mi>r</mi><mo>)</mo></mrow></mrow></math></span> and <span><math><mrow><mi>g</mi><mrow><mo>(</mo><mi>r</mi><mo>)</mo></mrow></mrow></math></span>. We found that the non-relativistic wave function is written in terms of the relativistic wave function. As applications, we constructed non-relativistic analogous models, introducing external potentials for two types of static and non-rotating black holes: Schwarzschild, anti-de Sitter, and de Sitter. Finally, we analyzed the physics at the event horizon region for the black holes and cosmological horizon for the de Sitter spacetime, and the values coincide with those obtained for the case with a gravitational field in the relativistic regime.</div></div>","PeriodicalId":8249,"journal":{"name":"Annals of Physics","volume":"474 ","pages":"Article 169918"},"PeriodicalIF":3.0,"publicationDate":"2025-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143097023","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 : 2025-01-04DOI: 10.1016/j.aop.2024.169919
Michael R.R. Good , Yen Chin Ong
The Hawking temperature of a Schwarzschild black hole can be heuristically derived by identifying the temperature with the inverse radius of the horizon up to a multiplicative constant. This does not work for more general black holes such as the Kerr and Reissner–Nordström solutions. Expounding on the details of how it fails to work nevertheless uncovers some connections with the “spring constant” of black holes and with black hole thermodynamics.
{"title":"Hawking temperature and the inverse-radius scale of the horizon","authors":"Michael R.R. Good , Yen Chin Ong","doi":"10.1016/j.aop.2024.169919","DOIUrl":"10.1016/j.aop.2024.169919","url":null,"abstract":"<div><div>The Hawking temperature of a Schwarzschild black hole can be heuristically derived by identifying the temperature with the inverse radius of the horizon up to a multiplicative constant. This does not work for more general black holes such as the Kerr and Reissner–Nordström solutions. Expounding on the details of how it fails to work nevertheless uncovers some connections with the “spring constant” of black holes and with black hole thermodynamics.</div></div>","PeriodicalId":8249,"journal":{"name":"Annals of Physics","volume":"474 ","pages":"Article 169919"},"PeriodicalIF":3.0,"publicationDate":"2025-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143097488","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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}
We classify the Ricci flat Lorentzian -manifolds satisfying three particular conditions, encoding and combining some crucial features of the Kerr metrics and the Robinson-Trautman optical structures. We prove that: (a) If , there is no Lorentzian manifold satisfying the considered Kerr type conditions, in unexpected contrast with what occurs for the metrics satisfying (very similar) Taub-NUT type conditions; (b) If there are two large classes of such Kerr type manifolds. Each class consists of manifolds fibering over open Riemann surfaces, equipped with a metric of constant Gaussian curvature or . The first class includes a three parameter family of metrics admitting real analytic extensions to and a large class of other metrics not admitting this kind of extensions. The metrics of this first class admitting such extensions are all isometric to the well known Kerr metrics, with the three parameters corresponding to the three space-like components of the angular momentum of the gravitational field. The second class contains a subclass of metrics defined on , where is the Lobachevsky Poincaré disc. This subclass is in bijection with the holomorphic functions on satisfying an appropriate open condition. These and other results are consequences of a very simple way to construct totally explicit examples of Ricci flat Lorentzian manifolds.
{"title":"Einstein manifolds with optical geometries of Kerr type","authors":"Masoud Ganji , Cristina Giannotti , Gerd Schmalz , Andrea Spiro","doi":"10.1016/j.aop.2024.169908","DOIUrl":"10.1016/j.aop.2024.169908","url":null,"abstract":"<div><div>We classify the Ricci flat Lorentzian <span><math><mi>n</mi></math></span>-manifolds satisfying three particular conditions, encoding and combining some crucial features of the Kerr metrics and the Robinson-Trautman optical structures. We prove that: (a) If <span><math><mrow><mi>n</mi><mo>></mo><mn>4</mn></mrow></math></span>, there is no Lorentzian manifold satisfying the considered Kerr type conditions, in unexpected contrast with what occurs for the metrics satisfying (very similar) Taub-NUT type conditions; (b) If <span><math><mrow><mi>n</mi><mo>=</mo><mn>4</mn></mrow></math></span> there are two large classes of such Kerr type manifolds. Each class consists of manifolds fibering over open Riemann surfaces, equipped with a metric of constant Gaussian curvature <span><math><mrow><mi>κ</mi><mo>=</mo><mn>1</mn></mrow></math></span> or <span><math><mrow><mi>κ</mi><mo>=</mo><mo>−</mo><mn>1</mn></mrow></math></span>. The first class includes a three parameter family of metrics admitting real analytic extensions to <span><math><mrow><mrow><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>∖</mo><mrow><mo>{</mo><mn>0</mn><mo>}</mo></mrow><mo>)</mo></mrow><mo>×</mo><mi>R</mi><mo>=</mo><mrow><mo>(</mo><msup><mrow><mi>S</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>×</mo><msub><mrow><mi>R</mi></mrow><mrow><mo>+</mo></mrow></msub><mo>)</mo></mrow><mo>×</mo><mi>R</mi></mrow></math></span> and a large class of other metrics not admitting this kind of extensions. The metrics of this first class admitting such extensions are all isometric to the well known Kerr metrics, with the three parameters corresponding to the three space-like components of the angular momentum of the gravitational field. The second class contains a subclass of metrics defined on <span><math><mrow><mrow><mo>(</mo><mi>D</mi><mo>×</mo><msub><mrow><mi>R</mi></mrow><mrow><mo>+</mo></mrow></msub><mo>)</mo></mrow><mo>×</mo><mi>R</mi></mrow></math></span>, where <span><math><mi>D</mi></math></span> is the Lobachevsky Poincaré disc. This subclass is in bijection with the holomorphic functions on <span><math><mi>D</mi></math></span> satisfying an appropriate open condition. These and other results are consequences of a very simple way to construct totally explicit examples of Ricci flat Lorentzian manifolds.</div></div>","PeriodicalId":8249,"journal":{"name":"Annals of Physics","volume":"474 ","pages":"Article 169908"},"PeriodicalIF":3.0,"publicationDate":"2025-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143097491","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 : 2025-01-03DOI: 10.1016/j.aop.2024.169914
Hengxin Lü , Sofia Di Gennaro , Yen Chin Ong
When the Bekenstein–Hawking entropy is modified, ambiguity often arises concerning whether the Hawking temperature or the thermodynamic mass should be modified. The common practice, however, is to keep the black hole solution the same as that in general relativity. On the other hand, if Jacobson’s method of deriving Einstein equations from thermodynamic is valid in the general settings, then given a generalized entropy one should first derive the corresponding modified gravity, and then look for the compatible black hole solution before investigating its thermodynamics. We comment on some properties and subtleties in this approach. In particular, we point out that generically generalized entropy would lead to a varying effective gravitational “constant” theory, in which depends on the horizon area. We discuss in what ways such theories are discernible from general relativity despite its seemingly jarring differences, and how to make sense of area-dependent field equations. As a consequence we show that in the Jacobson’s approach, the standard quantum gravitational logarithmic correction to Bekenstein–Hawking entropy is equivalent to a running gravitational “constant”. A horizon area dependent could also lead to a coupling between black hole masses and cosmological expansion, a scenario that has been studied recently in the literature, but so far lacks strong theoretical motivation. In the Tsallis case, we show that the thermodynamic mass for a Schwarzschild black hole is just a constant multiple of its ADM mass, which is considerably simpler than the approach not utilizing the Jacobson’s method.
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