We provide a quantization of the Schwarzschild spacetime in the presence of a cosmological constant, based on midisuperspace methods developed in the spherically symmetric sector of loop quantum gravity, using in particular the 'improved dynamics' scheme. We include both the deSitter and anti-deSitter cases. We find that the quantization puts a Planckian upper limit on the possible values of a positive cosmological constant similar to the bounds obtained earlier from studies of homogeneous spacetimes with a cosmological constant. Using semiclassical physical states, we obtain the effective metric and demonstrate the causal structure for various cases. Quantum gravity modifications ensure that the singularity is replaced by a transition surface in all the cases, where the curvature invariants approach mass-independent Planckian bounds. Analysis of the effective stress-energy tensor shows that the null energy condition is violated in the vicinity of the transition surface.
{"title":"Spherically symmetric loop quantum gravity: Schwarzschild spacetimes with a cosmological constant","authors":"Esteban Mato, Javier Olmedo, Sahil Saini","doi":"arxiv-2408.04925","DOIUrl":"https://doi.org/arxiv-2408.04925","url":null,"abstract":"We provide a quantization of the Schwarzschild spacetime in the presence of a\u0000cosmological constant, based on midisuperspace methods developed in the\u0000spherically symmetric sector of loop quantum gravity, using in particular the\u0000'improved dynamics' scheme. We include both the deSitter and anti-deSitter\u0000cases. We find that the quantization puts a Planckian upper limit on the\u0000possible values of a positive cosmological constant similar to the bounds\u0000obtained earlier from studies of homogeneous spacetimes with a cosmological\u0000constant. Using semiclassical physical states, we obtain the effective metric\u0000and demonstrate the causal structure for various cases. Quantum gravity\u0000modifications ensure that the singularity is replaced by a transition surface\u0000in all the cases, where the curvature invariants approach mass-independent\u0000Planckian bounds. Analysis of the effective stress-energy tensor shows that the\u0000null energy condition is violated in the vicinity of the transition surface.","PeriodicalId":501041,"journal":{"name":"arXiv - PHYS - General Relativity and Quantum Cosmology","volume":"20 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141930021","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}
MY Zhang, F Hosseinifar, H Chen, T Sathiyaraj, H Hassanabadi
This study examines the properties of a special regular black hole. This analysis investigates the Hawking temperature, remnant radius and mass, as well as the effect of parameter $xi$ on thermodynamic quantities like entropy, heat capacity, and free energy. The emission rate, evaporation process, quasi-normal modes by calculating Rosen-Morse potential, and topological behavior of the black hole are also explored.
{"title":"A New Approach for Calculation of Quasi-Normal Modes and Topological Charges of Regular Black Holes","authors":"MY Zhang, F Hosseinifar, H Chen, T Sathiyaraj, H Hassanabadi","doi":"arxiv-2408.04704","DOIUrl":"https://doi.org/arxiv-2408.04704","url":null,"abstract":"This study examines the properties of a special regular black hole. This\u0000analysis investigates the Hawking temperature, remnant radius and mass, as well\u0000as the effect of parameter $xi$ on thermodynamic quantities like entropy, heat\u0000capacity, and free energy. The emission rate, evaporation process, quasi-normal\u0000modes by calculating Rosen-Morse potential, and topological behavior of the\u0000black hole are also explored.","PeriodicalId":501041,"journal":{"name":"arXiv - PHYS - General Relativity and Quantum Cosmology","volume":"46 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141930014","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 study the gravitational wave (GW) phase shift arising from R{o}mer delay in binary black hole (BBH) mergers formed dynamically in three-body systems, where both the inner orbit of the merging binary and the outer orbit are eccentric. We provide a semi-analytical model and several analytical approximations that allow for fast evaluation of both the temporal evolution and the maximum value of the phase shift. The highest phase shifts occur when the binary merges close to the pericentre of the outer orbit, and can in this case be orders-of-magnitude larger compared to the circular limit. At high outer orbit eccentricities, the orbital curvature leaves distinct imprints onto the phase shift if the binary passes the outer pericentre during its inspiral. By comparing with phase-shifts measured in numerical chaotic 3-body scatterings, we show that our model accurately describes the observed phase of dynamically assembled binary systems in realistic astrophysical scenarios, providing a way to directly determine their formation channel via single GW observations.
{"title":"Eccentric features in the gravitational wave phase of dynamically formed black hole binaries","authors":"Kai Hendriks, Lorenz Zwick, Johan Samsing","doi":"arxiv-2408.04603","DOIUrl":"https://doi.org/arxiv-2408.04603","url":null,"abstract":"We study the gravitational wave (GW) phase shift arising from R{o}mer delay\u0000in binary black hole (BBH) mergers formed dynamically in three-body systems,\u0000where both the inner orbit of the merging binary and the outer orbit are\u0000eccentric. We provide a semi-analytical model and several analytical\u0000approximations that allow for fast evaluation of both the temporal evolution\u0000and the maximum value of the phase shift. The highest phase shifts occur when\u0000the binary merges close to the pericentre of the outer orbit, and can in this\u0000case be orders-of-magnitude larger compared to the circular limit. At high\u0000outer orbit eccentricities, the orbital curvature leaves distinct imprints onto\u0000the phase shift if the binary passes the outer pericentre during its inspiral.\u0000By comparing with phase-shifts measured in numerical chaotic 3-body\u0000scatterings, we show that our model accurately describes the observed phase of\u0000dynamically assembled binary systems in realistic astrophysical scenarios,\u0000providing a way to directly determine their formation channel via single GW\u0000observations.","PeriodicalId":501041,"journal":{"name":"arXiv - PHYS - General Relativity and Quantum Cosmology","volume":"37 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141930016","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}
M. Umair Shahzad, Nazek Alessa, Abdul Wahab, Rafda Rafique
This paper is devoted to studying the optical and thermal geometrical properties of Hot, NUT-KerrNewman-Kasuya-AdS black hole (BH). This BH is characterized by the NUT charge and a parameter Q that comprises the electric and magnetic charge. We compute the image of the BH shadow in two types: 1) at infinity, 2) at specific limit by analytical approach. We also investigate the effect of Nut, spin, inclination angle, and cosmological constant on the shape of shadow. We analyze that for type 1, the shadow in increasing for higher values of NUT charge, the cosmological constant, rotation parameters, and inclination angle, while for type 2, by increasing these parameters, the circular symmetry of the image of the BH shadow variate. Moreover, we discuss well-known thermal geometries such as Weinhold, Ruppeiner, HPEM, and Quevedo case I & II spacetime. It is found that Ruppeiner , HPEM and Quevedo (II) formulations provide physical information about the microscopic structure as compared to Weinhold and Quevedo (I) geometries of Hot NUT-Kerr-Newman-Kasuya-AdS BH. Our findings provides distinctive characteristics in the shadow and thermal geometries of this BH as compare to other BH types.
{"title":"Optical Properties and Thermal Geometries of Hot NUT-Kerr-Newman-Kasuya-AdS Spacetime","authors":"M. Umair Shahzad, Nazek Alessa, Abdul Wahab, Rafda Rafique","doi":"arxiv-2408.04365","DOIUrl":"https://doi.org/arxiv-2408.04365","url":null,"abstract":"This paper is devoted to studying the optical and thermal geometrical\u0000properties of Hot, NUT-KerrNewman-Kasuya-AdS black hole (BH). This BH is\u0000characterized by the NUT charge and a parameter Q that comprises the electric\u0000and magnetic charge. We compute the image of the BH shadow in two types: 1) at\u0000infinity, 2) at specific limit by analytical approach. We also investigate the\u0000effect of Nut, spin, inclination angle, and cosmological constant on the shape\u0000of shadow. We analyze that for type 1, the shadow in increasing for higher\u0000values of NUT charge, the cosmological constant, rotation parameters, and\u0000inclination angle, while for type 2, by increasing these parameters, the\u0000circular symmetry of the image of the BH shadow variate. Moreover, we discuss\u0000well-known thermal geometries such as Weinhold, Ruppeiner, HPEM, and Quevedo\u0000case I & II spacetime. It is found that Ruppeiner , HPEM and Quevedo (II)\u0000formulations provide physical information about the microscopic structure as\u0000compared to Weinhold and Quevedo (I) geometries of Hot\u0000NUT-Kerr-Newman-Kasuya-AdS BH. Our findings provides distinctive\u0000characteristics in the shadow and thermal geometries of this BH as compare to\u0000other BH types.","PeriodicalId":501041,"journal":{"name":"arXiv - PHYS - General Relativity and Quantum Cosmology","volume":"39 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141930019","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 analyze the long-term evolution of hierarchical triple systems in Newtonian gravity to second order in the quadrupolar perturbation parameter, and to sixth order in $epsilon = a/A$, the ratio of the semimajor axes of the inner and outer orbits. We apply the ``two-timescale'' method from applied mathematics to the Lagrange Planetary Equations for the inner and outer orbits, in which each osculating orbit element is split into an orbit averaged part that evolves on the long perturbative timescale, and an ``average-free'' part that is oscillatory in the orbital timescales. Averages over the two orbital timescales are performed using the well-known secular approximation. We also incorporate perturbative corrections to the relation between time and the orbital phases. We place no restrictions on the masses, on the relative orbit inclinations or on the eccentricities, beyond the requirement that the quadrupolar parameter and $epsilon$ both be small. The result is a complete set of long-timescale evolution equations for the averaged elements of the inner and outer orbits. At first order in perturbation theory, we obtain the dotriacontapole contributions explicitly at order $epsilon^6$. At second order in perturbation theory, i.e. quadratic in the quadrupole perturbation amplitude, we find contributions that scale as $epsilon^{9/2}$ (found in earlier work), $epsilon^{5}$, $epsilon^{11/2}$, and $epsilon^{6}$. At first perturbative order and dotriacontapole order, the two averaged semimajor axes are constant in time (and we prove that this holds to arbitrary multipole orders); but at second perturbative order, beginning at $O( epsilon^{5})$, they are no longer constant. Nevertheless we verify that the total averaged energy of the system is conserved, and we argue that this behavior is not incompatible with classical theorems on secular evolution of the semimajor axes.
{"title":"Higher-order effects in the dynamics of hierarchical triple systems. II. Second-order and dotriacontapole-order effects","authors":"Landen Conway, Clifford M. Will","doi":"arxiv-2408.04411","DOIUrl":"https://doi.org/arxiv-2408.04411","url":null,"abstract":"We analyze the long-term evolution of hierarchical triple systems in\u0000Newtonian gravity to second order in the quadrupolar perturbation parameter,\u0000and to sixth order in $epsilon = a/A$, the ratio of the semimajor axes of the\u0000inner and outer orbits. We apply the ``two-timescale'' method from applied\u0000mathematics to the Lagrange Planetary Equations for the inner and outer orbits,\u0000in which each osculating orbit element is split into an orbit averaged part\u0000that evolves on the long perturbative timescale, and an ``average-free'' part\u0000that is oscillatory in the orbital timescales. Averages over the two orbital\u0000timescales are performed using the well-known secular approximation. We also\u0000incorporate perturbative corrections to the relation between time and the\u0000orbital phases. We place no restrictions on the masses, on the relative orbit\u0000inclinations or on the eccentricities, beyond the requirement that the\u0000quadrupolar parameter and $epsilon$ both be small. The result is a complete\u0000set of long-timescale evolution equations for the averaged elements of the\u0000inner and outer orbits. At first order in perturbation theory, we obtain the\u0000dotriacontapole contributions explicitly at order $epsilon^6$. At second order\u0000in perturbation theory, i.e. quadratic in the quadrupole perturbation\u0000amplitude, we find contributions that scale as $epsilon^{9/2}$ (found in\u0000earlier work), $epsilon^{5}$, $epsilon^{11/2}$, and $epsilon^{6}$. At first\u0000perturbative order and dotriacontapole order, the two averaged semimajor axes\u0000are constant in time (and we prove that this holds to arbitrary multipole\u0000orders); but at second perturbative order, beginning at $O( epsilon^{5})$,\u0000they are no longer constant. Nevertheless we verify that the total averaged\u0000energy of the system is conserved, and we argue that this behavior is not\u0000incompatible with classical theorems on secular evolution of the semimajor\u0000axes.","PeriodicalId":501041,"journal":{"name":"arXiv - PHYS - General Relativity and Quantum Cosmology","volume":"191 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141930023","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}
Basheer Kalbouneh, Jessica Santiago, Christian Marinoni, Roy Maartens, Chris Clarkson, Maharshi Sarma
Studies show that the model-independent, fully non-perturbative covariant cosmographic approach is suitable for analyzing the local Universe $(zlesssim 0.1)$. However, accurately characterizing large and inhomogeneous mass distributions requires the fourth-order term in the redshift expansion of the covariant luminosity distance $d_L(z,boldsymbol{n})$. We calculate the covariant snap parameter $mathbb{S}$ and its spherical harmonic multipole moments using the matter expansion tensor and the evolution equations for lightray bundles. The fourth-order term adds 36 degrees of freedom, since the highest independent multipole of the snap is the 32-pole (dotriacontapole) $(ell=5)$. Including this term helps to de-bias estimations of the covariant deceleration parameter. Given that observations suggest axially symmetric anisotropies in the Hubble diagram for $z lesssim 0.1$ and theory shows that only a subset of multipoles contributes to the signal, we demonstrate that only 12 degrees of freedom are needed for a model-independent description of the local universe. We use an analytical axisymmetric model of the local Universe, with data that matches the Zwicky Transient Facility survey, in order to provide a numerical example of the amplitude of the snap multipoles and to forecast precision.
{"title":"Expanding covariant cosmography of the local Universe: incorporating the snap and axial symmetry","authors":"Basheer Kalbouneh, Jessica Santiago, Christian Marinoni, Roy Maartens, Chris Clarkson, Maharshi Sarma","doi":"arxiv-2408.04333","DOIUrl":"https://doi.org/arxiv-2408.04333","url":null,"abstract":"Studies show that the model-independent, fully non-perturbative covariant\u0000cosmographic approach is suitable for analyzing the local Universe $(zlesssim\u00000.1)$. However, accurately characterizing large and inhomogeneous mass\u0000distributions requires the fourth-order term in the redshift expansion of the\u0000covariant luminosity distance $d_L(z,boldsymbol{n})$. We calculate the\u0000covariant snap parameter $mathbb{S}$ and its spherical harmonic multipole\u0000moments using the matter expansion tensor and the evolution equations for\u0000lightray bundles. The fourth-order term adds 36 degrees of freedom, since the\u0000highest independent multipole of the snap is the 32-pole (dotriacontapole)\u0000$(ell=5)$. Including this term helps to de-bias estimations of the covariant\u0000deceleration parameter. Given that observations suggest axially symmetric\u0000anisotropies in the Hubble diagram for $z lesssim 0.1$ and theory shows that\u0000only a subset of multipoles contributes to the signal, we demonstrate that only\u000012 degrees of freedom are needed for a model-independent description of the\u0000local universe. We use an analytical axisymmetric model of the local Universe,\u0000with data that matches the Zwicky Transient Facility survey, in order to\u0000provide a numerical example of the amplitude of the snap multipoles and to\u0000forecast precision.","PeriodicalId":501041,"journal":{"name":"arXiv - PHYS - General Relativity and Quantum Cosmology","volume":"12 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141949353","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 study the possibility of accommodating both early and late-time tensions using a novel reinforcement learning technique. By applying this technique, we aim to optimize the evolution of the Hubble parameter from recombination to the present epoch, addressing both tensions simultaneously. To maximize the goodness of fit, our learning technique achieves a fit that surpasses even the $Lambda$CDM model. Our results demonstrate a tendency to weaken both early and late time tensions in a completely model-independent manner.
{"title":"Reconciling Early and Late Time Tensions with Reinforcement Learning","authors":"Mohit K. Sharma, M. Sami","doi":"arxiv-2408.04204","DOIUrl":"https://doi.org/arxiv-2408.04204","url":null,"abstract":"We study the possibility of accommodating both early and late-time tensions\u0000using a novel reinforcement learning technique. By applying this technique, we\u0000aim to optimize the evolution of the Hubble parameter from recombination to the\u0000present epoch, addressing both tensions simultaneously. To maximize the\u0000goodness of fit, our learning technique achieves a fit that surpasses even the\u0000$Lambda$CDM model. Our results demonstrate a tendency to weaken both early and\u0000late time tensions in a completely model-independent manner.","PeriodicalId":501041,"journal":{"name":"arXiv - PHYS - General Relativity and Quantum Cosmology","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141930026","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}
In this work, we introduce a novel set of asymptotically flat wormhole solutions within the framework of $f(R,T)$ theory of gravity. Considering a linear $f(R,T)=R+ 2lambda T$ form, we show that a wide variety of wormhole solutions with asymptotically linear equation of state exist. Our solutions satisfy all the energy conditions, namely the null, weak, strong and dominant energy conditions. The relationship between free parameters in the shape function and boundary conditions is analyzed.
{"title":"Wormholes in $f(R,T)$ gravity with variable equation of state","authors":"Sara Rastgoo, Foad Parsaei","doi":"arxiv-2408.04402","DOIUrl":"https://doi.org/arxiv-2408.04402","url":null,"abstract":"In this work, we introduce a novel set of asymptotically flat wormhole\u0000solutions within the framework of $f(R,T)$ theory of gravity. Considering a\u0000linear $f(R,T)=R+ 2lambda T$ form, we show that a wide variety of wormhole\u0000solutions with asymptotically linear equation of state exist. Our solutions\u0000satisfy all the energy conditions, namely the null, weak, strong and dominant\u0000energy conditions. The relationship between free parameters in the shape\u0000function and boundary conditions is analyzed.","PeriodicalId":501041,"journal":{"name":"arXiv - PHYS - General Relativity and Quantum Cosmology","volume":"56 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141930018","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 explored in Chan et al. 2024 how the ion-electron temperature ratio affects certain numerical models of Sagittarius A* (Sgr A*). Specifically, we studied these effects in magnetic-dominated regions in magnetic-arrested disk (MAD), focusing on the $3$-hour variability at $230$ GHz -- $M_{Delta T}$. In this study, we investigate how variations in electron temperature prescription parameter, $R_{rm Low}$, influence $M_{Delta T}$ by analyzing a series of general-relativistic raytracing (GRRT) snapshots. In certain black hole models with a spin $a > 0$, we discover that increasing $R_{rm Low}$ renders the photon ring more optically thick, obscuring the varying accretion flows that contribute to the variability. However, as $R_{rm Low}$ increases further, MAD flux eruptions become more pronounced, compensating for the decrease in $M_{Delta T}$. For models with a spin $a < 0$, although a higher $R_{rm Low}$ also increases the optical thickness of the fluid, voids within the optically thick gas fail to cover the entire photon ring. Similarly, flux eruptions are more prominent as $R_{rm Low}$ increases further, contributing to the observed rise in $M_{Delta T}$ against $R_{rm Low}$. For black holes with $a approx 0$, although the effect of increasing optical depth is still present, their $230$ GHz light curves and hence $M_{Delta T}$ are insensitive to the changes in $R_{rm Low}$. Furthermore, we find that the variability of the $230$ GHz light curves at $R_{rm Low} = 1$ correlates with fluctuations in the internal energy of the gas near the black hole, indicating that unusual gas heating may be the source of significant $M_{Delta T}$ seen in simulations. Our findings highlight potential approaches for refining $M_{Delta T}$ to better align with observations when modelling Sgr A* or other low-luminosity active galactic nuclei.
{"title":"The 230 GHz Variability of Numerical Models of Sagittarius A* II. The Physical Origins of the Variability","authors":"Ho-Sang Chan, Chi-kwan Chan","doi":"arxiv-2408.04132","DOIUrl":"https://doi.org/arxiv-2408.04132","url":null,"abstract":"We explored in Chan et al. 2024 how the ion-electron temperature ratio\u0000affects certain numerical models of Sagittarius A* (Sgr A*). Specifically, we\u0000studied these effects in magnetic-dominated regions in magnetic-arrested disk\u0000(MAD), focusing on the $3$-hour variability at $230$ GHz -- $M_{Delta T}$. In\u0000this study, we investigate how variations in electron temperature prescription\u0000parameter, $R_{rm Low}$, influence $M_{Delta T}$ by analyzing a series of\u0000general-relativistic raytracing (GRRT) snapshots. In certain black hole models\u0000with a spin $a > 0$, we discover that increasing $R_{rm Low}$ renders the\u0000photon ring more optically thick, obscuring the varying accretion flows that\u0000contribute to the variability. However, as $R_{rm Low}$ increases further, MAD\u0000flux eruptions become more pronounced, compensating for the decrease in\u0000$M_{Delta T}$. For models with a spin $a < 0$, although a higher $R_{rm Low}$\u0000also increases the optical thickness of the fluid, voids within the optically\u0000thick gas fail to cover the entire photon ring. Similarly, flux eruptions are\u0000more prominent as $R_{rm Low}$ increases further, contributing to the observed\u0000rise in $M_{Delta T}$ against $R_{rm Low}$. For black holes with $a approx\u00000$, although the effect of increasing optical depth is still present, their\u0000$230$ GHz light curves and hence $M_{Delta T}$ are insensitive to the changes\u0000in $R_{rm Low}$. Furthermore, we find that the variability of the $230$ GHz\u0000light curves at $R_{rm Low} = 1$ correlates with fluctuations in the internal\u0000energy of the gas near the black hole, indicating that unusual gas heating may\u0000be the source of significant $M_{Delta T}$ seen in simulations. Our findings\u0000highlight potential approaches for refining $M_{Delta T}$ to better align with\u0000observations when modelling Sgr A* or other low-luminosity active galactic\u0000nuclei.","PeriodicalId":501041,"journal":{"name":"arXiv - PHYS - General Relativity and Quantum Cosmology","volume":"15 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141949438","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 investigate the behavior of the Ricci scalar in the Jordan (JF) and Einstein (EF) frames, in the context of f(R) gravitation. We discuss the physical equivalence of these two representations of the theory, which are mathematically equivalent and whose metrics are connected by a conformal transformation. We find that it is possible for this quantity to be singular in the JF but finite in the EF, if the conformal transformation that connects the frames is singular at the same point as the JF Ricci scalar. The absence of this physical singularity in the EF could be used as an argument against the physical equivalence of the frames. A plot of the EF potential as a function of the associated conformal field shows that the absence of the singularity allows the field to assume values associated to arbitrarily large values of the Ricci curvature. A conjecture is then proposed: the dynamics of the conformal field can be interpreted as a mechanism that can prevent the creation of singularities in the JF.
我们以 f(R) 引力为背景，研究了里奇标量在乔丹（JF）和爱因斯坦（EF）框架中的行为。我们讨论了这两种理论表征的物理等价性，它们在数学上是等价的，其度量是通过保角变换连接起来的。我们发现，如果连接这两个框架的保角变换与 JF 里奇标量在同一点上是奇异的，那么这个量在 JF 中可能是奇异的，而在 EF 中却是有限的。如果在 EF 中不存在这种物理奇异性，就可以作为反对帧物理等价性的论据。绘制的 EF 势与相关共形场的函数关系图显示，由于不存在奇点，共形场可以假设与任意大的里奇曲率值相关的值。因此，我们提出了一个猜想：共形场的动力学可以被解释为一种机制，可以防止在 JF 中产生奇点。
{"title":"f(R) Gravitation: Equivalence of Frames Upon a Conformal Transformation","authors":"João Pedro Bravo","doi":"arxiv-2408.04672","DOIUrl":"https://doi.org/arxiv-2408.04672","url":null,"abstract":"We investigate the behavior of the Ricci scalar in the Jordan (JF) and\u0000Einstein (EF) frames, in the context of f(R) gravitation. We discuss the\u0000physical equivalence of these two representations of the theory, which are\u0000mathematically equivalent and whose metrics are connected by a conformal\u0000transformation. We find that it is possible for this quantity to be singular in\u0000the JF but finite in the EF, if the conformal transformation that connects the\u0000frames is singular at the same point as the JF Ricci scalar. The absence of\u0000this physical singularity in the EF could be used as an argument against the\u0000physical equivalence of the frames. A plot of the EF potential as a function of\u0000the associated conformal field shows that the absence of the singularity allows\u0000the field to assume values associated to arbitrarily large values of the Ricci\u0000curvature. A conjecture is then proposed: the dynamics of the conformal field\u0000can be interpreted as a mechanism that can prevent the creation of\u0000singularities in the JF.","PeriodicalId":501041,"journal":{"name":"arXiv - PHYS - General Relativity and Quantum Cosmology","volume":"106 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141930017","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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