We explore the characteristics of two novel regular spacetimes that exhibit a non-zero vacuum energy term, under the form of a (quasi) anti-de Sitter phase. Specifically, the first metric is spherical, while the second, derived by applying the generalized Newman-Janis algorithm to the first, is axisymmetric. We show that the equations of state of the effective fluids associated with the two metrics asymptotically tend to negative values, resembling quintessence. In addition, we study test particle motions, illustrating the main discrepancies among our models and more conventional metrics exhibiting non-vanishing anti-de Sitter phase.
{"title":"Motion of test particles in quasi anti-de Sitter regular black holes","authors":"Dario Corona, Roberto Giambò, Orlando Luongo","doi":"arxiv-2402.18997","DOIUrl":"https://doi.org/arxiv-2402.18997","url":null,"abstract":"We explore the characteristics of two novel regular spacetimes that exhibit a\u0000non-zero vacuum energy term, under the form of a (quasi) anti-de Sitter phase.\u0000Specifically, the first metric is spherical, while the second, derived by\u0000applying the generalized Newman-Janis algorithm to the first, is axisymmetric.\u0000We show that the equations of state of the effective fluids associated with the\u0000two metrics asymptotically tend to negative values, resembling quintessence. In\u0000addition, we study test particle motions, illustrating the main discrepancies\u0000among our models and more conventional metrics exhibiting non-vanishing anti-de\u0000Sitter phase.","PeriodicalId":501275,"journal":{"name":"arXiv - PHYS - Mathematical Physics","volume":"170 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140001738","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We review Wang-Yau quasi-local definitions along the line of gravitational Hamiltonian. This makes clear the connection and difference between Wang-Yau definition and Brown-York or even global ADM definition. We make a brief comment on admissibility condition in Wang-Yau quasi-lcoal mass. We extend the positivity proof for Wang-Yau quasi-local energy to allow possible presence of strictly stable apparent horizons through establishing solvability of Dirac equation in certain 3-manifolds that possess cylindrical ends, as in the case of Jang's graph blowing up at marginally outer trapped surfaces.
{"title":"Some Remarks on Wang-Yau Quasi-Local Mass","authors":"Bowen Zhao, Lars Andersson, Shing-Tung Yau","doi":"arxiv-2402.19310","DOIUrl":"https://doi.org/arxiv-2402.19310","url":null,"abstract":"We review Wang-Yau quasi-local definitions along the line of gravitational\u0000Hamiltonian. This makes clear the connection and difference between Wang-Yau\u0000definition and Brown-York or even global ADM definition. We make a brief\u0000comment on admissibility condition in Wang-Yau quasi-lcoal mass. We extend the\u0000positivity proof for Wang-Yau quasi-local energy to allow possible presence of\u0000strictly stable apparent horizons through establishing solvability of Dirac\u0000equation in certain 3-manifolds that possess cylindrical ends, as in the case\u0000of Jang's graph blowing up at marginally outer trapped surfaces.","PeriodicalId":501275,"journal":{"name":"arXiv - PHYS - Mathematical Physics","volume":"101 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140001736","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Any non-trivial scattering with massless fields in four spacetime dimensions will generically produce an out-state with memory. Scattering with any massless fields violates the standard assumption of asymptotic completeness -- that all "in" and "out" states lie in the standard (zero memory) Fock space -- and therefore leads to infrared divergences in the standard $S$-matrix amplitudes. We define an infrared finite scattering theory valid for general quantum field theories and quantum gravity. The (infrared finite) "superscattering" map $$$ is defined as a map between "in" and "out" states which does not require any a priori choice of a preferred Hilbert space. We define a "generalized asymptotic completeness" which accommodates states with memory in the space of asymptotic states. We define a complete basis of improper states on any memory Fock space (called "BMS particle" states) which are eigenstates of the energy-momentum -- or, more generally, the BMS supermomentum -- that generalize the usual $n$-particle momentum basis to account for states with memory. We then obtain infrared finite $$$-amplitudes defined as matrix elements of $$$ in the BMS particle basis. This formulation of the scattering theory is a key step towards analyzing fine-grained details of the infrared finite scattering theory. In quantum gravity, invariance of $$$ under BMS supertranslations implies factorization of $$$-amplitudes as the frequency of one of the BMS particles vanishes. This proves an infrared finite analog of the soft graviton theorem. Similarly, an infrared finite soft photon theorem in QED follows from invariance of $$$ under large gauge transformations. We comment on how one must generalize this framework to consider $$$-amplitudes for theories with collinear divergences (e.g., massless QED and Yang-Mills theories).
{"title":"Infrared finite scattering theory: Amplitudes and soft theorems","authors":"Kartik Prabhu, Gautam Satishchandran","doi":"arxiv-2402.18637","DOIUrl":"https://doi.org/arxiv-2402.18637","url":null,"abstract":"Any non-trivial scattering with massless fields in four spacetime dimensions\u0000will generically produce an out-state with memory. Scattering with any massless\u0000fields violates the standard assumption of asymptotic completeness -- that all\u0000\"in\" and \"out\" states lie in the standard (zero memory) Fock space -- and\u0000therefore leads to infrared divergences in the standard $S$-matrix amplitudes.\u0000We define an infrared finite scattering theory valid for general quantum field\u0000theories and quantum gravity. The (infrared finite) \"superscattering\" map $$$\u0000is defined as a map between \"in\" and \"out\" states which does not require any a\u0000priori choice of a preferred Hilbert space. We define a \"generalized asymptotic\u0000completeness\" which accommodates states with memory in the space of asymptotic\u0000states. We define a complete basis of improper states on any memory Fock space\u0000(called \"BMS particle\" states) which are eigenstates of the energy-momentum --\u0000or, more generally, the BMS supermomentum -- that generalize the usual\u0000$n$-particle momentum basis to account for states with memory. We then obtain\u0000infrared finite $$$-amplitudes defined as matrix elements of $$$ in the BMS\u0000particle basis. This formulation of the scattering theory is a key step towards\u0000analyzing fine-grained details of the infrared finite scattering theory. In\u0000quantum gravity, invariance of $$$ under BMS supertranslations implies\u0000factorization of $$$-amplitudes as the frequency of one of the BMS particles\u0000vanishes. This proves an infrared finite analog of the soft graviton theorem.\u0000Similarly, an infrared finite soft photon theorem in QED follows from\u0000invariance of $$$ under large gauge transformations. We comment on how one\u0000must generalize this framework to consider $$$-amplitudes for theories with\u0000collinear divergences (e.g., massless QED and Yang-Mills theories).","PeriodicalId":501275,"journal":{"name":"arXiv - PHYS - Mathematical Physics","volume":"100 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140001653","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
LSZ-type reduction formulae are derived for gauge fields and fermions in curved spacetime. The formulae are derived using a conserved current method applicable also to flat spacetimes. The method generalizes to more general quantum field theories. The formulae are then applied to a few problems to illustrate their use.
{"title":"Practical Derivations of Fermion and Gauge Boson Reduction Formulae in Curved Spacetimes","authors":"Jesse Huhtala, Iiro Vilja","doi":"arxiv-2402.18230","DOIUrl":"https://doi.org/arxiv-2402.18230","url":null,"abstract":"LSZ-type reduction formulae are derived for gauge fields and fermions in\u0000curved spacetime. The formulae are derived using a conserved current method\u0000applicable also to flat spacetimes. The method generalizes to more general\u0000quantum field theories. The formulae are then applied to a few problems to\u0000illustrate their use.","PeriodicalId":501275,"journal":{"name":"arXiv - PHYS - Mathematical Physics","volume":"5 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140001733","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Stefano Boccelli, Fabien Giroux, James G. McDonald
This work explores the different shapes that can be realized by the one-particle velocity distribution functions (VDFs) associated with the fourth-order maximum-entropy moment method. These distributions take the form of an exponential of a polynomial of the particle velocity, with terms up to the fourth-order. The 14- and 21-moment approximations are investigated. Various non-equilibrium gas states are probed throughout moment space. The resulting maximum-entropy distributions deviate strongly from the equilibrium VDF, and show a number of lobes and branches. The Maxwellian and the anisotropic Gaussian distributions are recovered as special cases. The eigenvalues associated with the maximum-entropy system of transport equations are also illustrated for some selected gas states. Anisotropic and/or asymmetric non-equilibrium states are seen to be associated with a non-uniform spacial propagation of perturbations.
{"title":"A gallery of maximum-entropy distributions: 14 and 21 moments","authors":"Stefano Boccelli, Fabien Giroux, James G. McDonald","doi":"arxiv-2402.18453","DOIUrl":"https://doi.org/arxiv-2402.18453","url":null,"abstract":"This work explores the different shapes that can be realized by the\u0000one-particle velocity distribution functions (VDFs) associated with the\u0000fourth-order maximum-entropy moment method. These distributions take the form\u0000of an exponential of a polynomial of the particle velocity, with terms up to\u0000the fourth-order. The 14- and 21-moment approximations are investigated.\u0000Various non-equilibrium gas states are probed throughout moment space. The\u0000resulting maximum-entropy distributions deviate strongly from the equilibrium\u0000VDF, and show a number of lobes and branches. The Maxwellian and the\u0000anisotropic Gaussian distributions are recovered as special cases. The\u0000eigenvalues associated with the maximum-entropy system of transport equations\u0000are also illustrated for some selected gas states. Anisotropic and/or\u0000asymmetric non-equilibrium states are seen to be associated with a non-uniform\u0000spacial propagation of perturbations.","PeriodicalId":501275,"journal":{"name":"arXiv - PHYS - Mathematical Physics","volume":"10 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140001496","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Null infinity (Scri) arises as a boundary of the Penrose conformal completion of an asymptotically flat physical space-time. We first note that Scri is a weakly isolated horizon (WIH), and then show that its familiar properties can be derived from the general WIH framework. This seems quite surprising because physics associated with black hole (and cosmological) WIHs is very different from that extracted at Scri. We show that these differences can be directly traced back to the fact that Scri is a WIH in the conformal completion rather than the physical space-time. In particular, the BMS group at Scri stems from the symmetry group of WIHs. We also introduce a unified procedure to arrive at fluxes and charges associated with the BMS symmetries at Scri and those associated with black hole (and cosmological) horizons. This procedure differs from those commonly used in the literature and its novel elements seem interesting in their own right. The fact that is there is a single mathematical framework underlying black hole (and cosmological) horizons and Scri paves the way to explore the relation between horizon dynamics in the strong field region and waveforms at infinity. It should also be useful in the analysis of black hole evaporation in quantum gravity.
{"title":"Null Infinity as a Weakly Isolated Horizon","authors":"Abhay Ashtekar, Simone Speziale","doi":"arxiv-2402.17977","DOIUrl":"https://doi.org/arxiv-2402.17977","url":null,"abstract":"Null infinity (Scri) arises as a boundary of the Penrose conformal completion\u0000of an asymptotically flat physical space-time. We first note that Scri is a\u0000weakly isolated horizon (WIH), and then show that its familiar properties can\u0000be derived from the general WIH framework. This seems quite surprising because\u0000physics associated with black hole (and cosmological) WIHs is very different\u0000from that extracted at Scri. We show that these differences can be directly\u0000traced back to the fact that Scri is a WIH in the conformal completion rather\u0000than the physical space-time. In particular, the BMS group at Scri stems from\u0000the symmetry group of WIHs. We also introduce a unified procedure to arrive at\u0000fluxes and charges associated with the BMS symmetries at Scri and those\u0000associated with black hole (and cosmological) horizons. This procedure differs\u0000from those commonly used in the literature and its novel elements seem\u0000interesting in their own right. The fact that is there is a single mathematical\u0000framework underlying black hole (and cosmological) horizons and Scri paves the\u0000way to explore the relation between horizon dynamics in the strong field region\u0000and waveforms at infinity. It should also be useful in the analysis of black\u0000hole evaporation in quantum gravity.","PeriodicalId":501275,"journal":{"name":"arXiv - PHYS - Mathematical Physics","volume":"100 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140001846","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
For almost 75 years, the general solution for the Schr"odinger equation was assumed to be generated by a time-ordered exponential known as the Dyson series. We discuss under which conditions the unitarity of this solution is broken, and additional singular dynamics emerges. Then, we provide an alternative construction that is manifestly unitary, regardless of the choice of the Hamiltonian, and study various aspects of the implications. The new construction involves an additional self-adjoint operator that might evolve in a non-gradual way. Its corresponding dynamics for gauge theories exhibit the behavior of a collective object governed by a singular Liouville's equation that performs transitions at a measure $0$ set. Our considerations show that Schr"odinger's and Liouville's equations are, in fact, two sides of the same coin, and together they become the unified description of quantum systems.
{"title":"On the exact solution for the Schrödinger equation","authors":"Yair Mulian","doi":"arxiv-2402.18499","DOIUrl":"https://doi.org/arxiv-2402.18499","url":null,"abstract":"For almost 75 years, the general solution for the Schr\"odinger equation was\u0000assumed to be generated by a time-ordered exponential known as the Dyson\u0000series. We discuss under which conditions the unitarity of this solution is\u0000broken, and additional singular dynamics emerges. Then, we provide an\u0000alternative construction that is manifestly unitary, regardless of the choice\u0000of the Hamiltonian, and study various aspects of the implications. The new\u0000construction involves an additional self-adjoint operator that might evolve in\u0000a non-gradual way. Its corresponding dynamics for gauge theories exhibit the\u0000behavior of a collective object governed by a singular Liouville's equation\u0000that performs transitions at a measure $0$ set. Our considerations show that\u0000Schr\"odinger's and Liouville's equations are, in fact, two sides of the same\u0000coin, and together they become the unified description of quantum systems.","PeriodicalId":501275,"journal":{"name":"arXiv - PHYS - Mathematical Physics","volume":"10 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140001739","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The newly established Seiberg-Witten (SW)/Quasinormal Modes (QNM) correspondence offers an efficient analytical approach to calculate the QNM frequencies, which was only available numerically before. This is based on the fact that both sides are characterized by Heun-type equations. We find that a similar duality exists between Seiberg-Witten theory and black hole superradiance, since the latter can also be linked to confluent Heun equation after proper transformation. Then a dictionary is constructed, with the superradiance frequencies written in terms of gauge parameters. Further by instanton counting, and taking care of the boundary conditions through connection formula, the relating frequencies are obtained analytically, which show consistency with known numerical results.
{"title":"Duality between Seiberg-Witten Theory and Black Hole Superradiance","authors":"Xian-Hui Ge, Masataka Matsumoto, Kilar Zhang","doi":"arxiv-2402.17441","DOIUrl":"https://doi.org/arxiv-2402.17441","url":null,"abstract":"The newly established Seiberg-Witten (SW)/Quasinormal Modes (QNM)\u0000correspondence offers an efficient analytical approach to calculate the QNM\u0000frequencies, which was only available numerically before. This is based on the\u0000fact that both sides are characterized by Heun-type equations. We find that a\u0000similar duality exists between Seiberg-Witten theory and black hole\u0000superradiance, since the latter can also be linked to confluent Heun equation\u0000after proper transformation. Then a dictionary is constructed, with the\u0000superradiance frequencies written in terms of gauge parameters. Further by\u0000instanton counting, and taking care of the boundary conditions through\u0000connection formula, the relating frequencies are obtained analytically, which\u0000show consistency with known numerical results.","PeriodicalId":501275,"journal":{"name":"arXiv - PHYS - Mathematical Physics","volume":"32 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139987866","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The quantum mechanically admissible definitions of the factor $expbig[(i/hbar)S(gamma)big]$ in the Feynman integral are put in bijection with the prequantisations of Kostant and Souriau. The different allowed expressions of this factor -- the inequivalent prequantisations -- are classified. The theory is illustrated by the Aharonov-Bohm experiment and by identical particles.
{"title":"Prequantisation from the path integral viewpoint","authors":"P A Horvathy","doi":"arxiv-2402.17629","DOIUrl":"https://doi.org/arxiv-2402.17629","url":null,"abstract":"The quantum mechanically admissible definitions of the factor\u0000$expbig[(i/hbar)S(gamma)big]$ in the Feynman integral are put in bijection\u0000with the prequantisations of Kostant and Souriau. The different allowed\u0000expressions of this factor -- the inequivalent prequantisations -- are\u0000classified. The theory is illustrated by the Aharonov-Bohm experiment and by\u0000identical particles.","PeriodicalId":501275,"journal":{"name":"arXiv - PHYS - Mathematical Physics","volume":"9 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140001350","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
On two different subspaces of Bruhat-Tits tree, the exact effective actions and two-point functions of deformed CFTs are calculated according to the p-adic version of AdS/CFT. These subspaces are specially chosen such that in the case of $pequiv3pmod4$, they can be viewed as a circle and a hyperbola over p-adic numbers when taken to infinities. It is found that two-point functions of CFTs depend on chordal distances of the circle and the hyperbola.
{"title":"P-adic AdS/CFT on subspaces of the Bruhat-Tits tree","authors":"Feng Qu","doi":"arxiv-2402.03730","DOIUrl":"https://doi.org/arxiv-2402.03730","url":null,"abstract":"On two different subspaces of Bruhat-Tits tree, the exact effective actions\u0000and two-point functions of deformed CFTs are calculated according to the p-adic\u0000version of AdS/CFT. These subspaces are specially chosen such that in the case\u0000of $pequiv3pmod4$, they can be viewed as a circle and a hyperbola over p-adic\u0000numbers when taken to infinities. It is found that two-point functions of CFTs\u0000depend on chordal distances of the circle and the hyperbola.","PeriodicalId":501275,"journal":{"name":"arXiv - PHYS - Mathematical Physics","volume":"17 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139768950","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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