Pub Date : 2024-06-06DOI: 10.1088/1361-6382/ad550c
Ö. Yeşiltaş
We have discussed the Dirac equation in the Schwarzschild spacetime via pseudo-supersymmetric quantum mechanics and obtained the partner Hamiltonain of the initial Hamiltonian operator. We have shown that partner metric tensors of the corresponding Hamiltonians can be obtained through the intertwining relations of pseudo-supersymmetric approaches. Moreover, approximate solutions of the radial part are obtained within N = 2 supersymmetry and radial potential graphs are given, then, quasinormal modes are discussed in the limit of r → ±∞.
我们通过伪超对称量子力学讨论了施瓦兹柴尔德时空中的狄拉克方程，并得到了初始哈密顿算子的伙伴哈密顿域。我们已经证明，通过伪超对称方法的交织关系，可以得到相应哈密顿的伙伴度量张量。此外，我们还在 N = 2 超对称范围内得到了径向部分的近似解，并给出了径向势图，然后讨论了 r → ±∞ 极限下的准正常模式。
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Pub Date : 2024-05-15DOI: 10.1088/1361-6382/ad4c4b
Alan Sunny, Semin Xavier, S. Shankaranarayanan
This work tests the no-hair conjecture in f(R) gravity models. No-hair conjecture asserts that all black holes in General Relativity coupled to any matter must be Kerr–Newman type. However, the conjecture fails in some cases with non-linear matter sources. Here, we address this by explicitly constructing multiple slow-rotating black hole solutions, up to second order in rotational parameter, for a class of f(R) models ( f(R) =(alpha_{0} + alpha_{1},R)^{p}, p > 1). Such an f(R) includes all higher-powers of R. We analytically show that multiple vacuum solutions satisfy the field equations up to the second order in the rotational parameter. In other words, we show that the multiple vacuum solutions depend on arbitrary constants, which depend on the coupling parameters of the model. Hence, our results indicate that the no-hair theorem for modified gravity theories merits extending to include the coupling constants. The uniqueness of our result stems from the fact that these are obtained directly from metric formalism without conformal transformation. We discuss the kinematical properties of these black hole solutions and compare them with slow-rotating Kerr. Specifically, we show that the circular orbits for the black holes in f(R) are smaller than that of Kerr. This implies that the inner-most stable circular orbit for black holes in f(R) is smaller than Kerr's; hence, the shadow radius might also be smaller. Finally, we discuss the implications of our results for future observations.
这项工作检验了f(R)引力模型中的 "无毛猜想"。无毛猜想认为，广义相对论中所有与任何物质耦合的黑洞都必须是克尔-纽曼型的。然而，该猜想在某些非线性物质源的情况下失效了。在这里，我们通过为一类f(R)模型（f(R) =(alpha_{0} + alpha_{1},R)^{p}, p > 1）明确构造多个慢速旋转黑洞解（旋转参数可达二阶）来解决这个问题。我们通过分析表明，多重真空解满足旋转参数二阶以内的场方程。换句话说，我们证明多重真空解取决于任意常数，而这些常数取决于模型的耦合参数。因此，我们的结果表明，修正引力理论的无发定理值得扩展到耦合常数。我们结果的唯一性源于它们是直接从度量形式主义中得到的，无需保角变换。我们讨论了这些黑洞解的运动学性质，并将它们与慢速旋转的克尔理论进行了比较。具体地说，我们发现 f(R) 中黑洞的圆形轨道小于克尔轨道。这意味着f(R)中黑洞的最内层稳定圆形轨道比克尔的小，因此影子半径也可能更小。最后，我们讨论了我们的结果对未来观测的影响。
{"title":"Infinitely degenerate slowly rotating solutions in f(R) gravity","authors":"Alan Sunny, Semin Xavier, S. Shankaranarayanan","doi":"10.1088/1361-6382/ad4c4b","DOIUrl":"https://doi.org/10.1088/1361-6382/ad4c4b","url":null,"abstract":"\u0000 This work tests the no-hair conjecture in f(R) gravity models. No-hair conjecture asserts that all black holes in General Relativity coupled to any matter must be Kerr–Newman type. However, the conjecture fails in some cases with non-linear matter sources. Here, we address this by explicitly constructing multiple slow-rotating black hole solutions, up to second order in rotational parameter, for a class of f(R) models ( f(R) =(alpha_{0} + alpha_{1},R)^{p}, p > 1). Such an f(R) includes all higher-powers of R. We analytically show that multiple vacuum solutions satisfy the field equations up to the second order in the rotational parameter. In other words, we show that the multiple vacuum solutions depend on arbitrary constants, which depend on the coupling parameters of the model. Hence, our results indicate that the no-hair theorem for modified gravity theories merits extending to include the coupling constants. The uniqueness of our result stems from the fact that these are obtained directly from metric formalism without conformal transformation. We discuss the kinematical properties of these black hole solutions and compare them with slow-rotating Kerr. Specifically, we show that the circular orbits for the black holes in f(R) are smaller than that of Kerr. This implies that the inner-most stable circular orbit for black holes in f(R) is smaller than Kerr's; hence, the shadow radius might also be smaller. Finally, we discuss the implications of our results for future observations.","PeriodicalId":505126,"journal":{"name":"Classical and Quantum Gravity","volume":"70 10","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140976126","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}
General relativity (GR) is a highly successful theory that describes gravity as a geometric phenomenon. The gravitational redshift, a classic test of GR, can potentially be violated in alternative gravity theories, and experimental tests on this effect are crucial for our understanding of gravity. In this paper, considering the space-ground clock comparisons with free-space links, we discuss a high-precision Doppler cancellation-based measurement model for testing gravitational redshift. This model can effectively reduce various sources of error and noise, reducing the influences of the first-order Doppler effect, atmospheric delay, Shapiro delay, etc. China's Lunar Exploration Project (CLEP) is proposed to equip the deep-space H maser with a daily stability of $2times10^{-15}$, which provides an approach for testing gravitational redshift. Based on the simulation, we analyze the space-ground clock comparison experiments of the CLEP experiment, and simulation analysis demonstrates that under ideal condition of high-precision measurement of the onboard H-maser frequency offset and drift, the CLEP experiment may reach the uncertainty of $3.7times10^{-6}$ after a measurement session of 60 days. Our results demonstrate that if the issue of frequency offset and drift is solved, CLEP missions have a potential of testing the gravitational redshift with high accuracy.
广义相对论（GR）是一种非常成功的理论，它将引力描述为一种几何现象。引力红移是对 GR 的经典检验，在其他引力理论中有可能被违背，对这一效应的实验检验对我们理解引力至关重要。本文考虑到空地时钟与自由空间链路的比较，讨论了一种用于测试引力红移的基于多普勒抵消的高精度测量模型。该模型可以有效减少各种误差源和噪声，降低一阶多普勒效应、大气延迟、夏皮罗延迟等的影响。中国探月工程拟装备日稳定度为2times10^{-15}$的深空H maser，这为测试引力红移提供了一种方法。在模拟的基础上，我们分析了CLEP实验的空地时钟比对实验，模拟分析表明，在对星载H-maser频率偏移和漂移进行高精度测量的理想条件下，CLEP实验经过60天的测量，其不确定度可能达到3.7times10^{-6}$。我们的结果表明，如果解决了频率偏移和漂移问题，CLEP 任务就有可能高精度地测试引力红移。
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Pub Date : 2024-05-13DOI: 10.1088/1361-6382/ad4ae1
Tadashi Sasaki
We consider the bending angle of the trajectory of a photon incident from and deflected to infinity around a Reissner-Nordström black hole. We treat the bending angle as a function of the squared reciprocal of the impact parameter and the squared electric charge of the background normalized by the mass of the black hole. It is shown that the bending angle satisfies a system of two inhomogeneous linear partial differential equations with polynomial coefficients. This system can be understood as an isomonodromic deformation of the inhomogeneous Picard-Fuchs equation satisfied by the bending angle in the Schwarzschild spacetime, where the deformation parameter is identified as the background electric charge. Furthermore, the integrability condition for these equations is found to be a specific type of the Painlevé VI equation that allows an algebraic solution. We solve the differential equations both at the weak and strong deflection limits. In the weak deflection limit, the bending angle is expressed as a power series expansion in terms of the squared reciprocal of the impact parameter and we obtain the explicit full-order expression for the coefficients. In the strong deflection limit, we obtain the asymptotic form of the bending angle that consists of the divergent logarithmic term and the finite O(1) term supplemented by linear recurrence relations which enable us to straightforwardly derive higher order coefficients. In deriving these results, the isomonodromic property of the differential equations plays an important role. Lastly, we briefly discuss the applicability of our method to other types of spacetimes such as a spinning black hole.
我们考虑的是一个光子从赖斯纳-诺德斯特伦黑洞入射并在其周围被去质化的轨迹的弯曲角。我们将弯曲角视为撞击参数平方倒数和背景电荷平方的函数，并以黑洞质量归一化。研究表明，弯曲角满足两个非均质线性偏二导方程的多项式系数系统。这个系统可以理解为非均质皮卡-富克斯方程的等单调变形，由施瓦兹柴尔德时空中的弯曲角满足，其中变形参数被确定为背景电荷。此外，我们还发现这些方程的可积分性条件是潘列维 VI 方程的一种特殊类型，可以用代数方法求解。我们同时求解了弱和强脱附极限下的二阶方程。在弱脱附极限，弯曲角以冲击参数平方倒数的幂级数展开表示，我们得到了系数的显式全阶表达式。在强脱附极限中，我们得到了弯曲角的渐近形式，它由发散对数项和有限 O(1)项组成，并辅以线性递推关系，使我们能够直接推导出更高阶的系数。在推导这些结果的过程中，二导方程的等单调性发挥了重要作用。最后，我们简要讨论了我们的方法在其他类型的空间（如旋转黑洞）中的适用性。
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Pub Date : 2024-05-09DOI: 10.1088/1361-6382/ad494e
Timothy Andersen
Gravitational alternatives to dark matter require additional fields or assumptions beyond general relativity while continuing to agree with tight solar system constraints. Modified Newtonian Dynamics (MOND), for example, predicts the Tully-Fisher relation for galaxies more accurately than dark matter models while limiting to Newtonian gravity in the solar system. On the other hand, MOND does a poor job predicting larger scale observations such as the Cosmic Microwave Background and Matter Power Spectra. Tensor-Vector-Scalar (TeVeS) theory is a relativistic generalization of MOND that accounts for these observations without dark matter. In this paper, I derive a generalized TeVeS from Kaluza-Klein theory in one extra dimension as a consequence of $n=0$ Kaluza-Klein modes. In the KK theory, MOND is a special case of a slicing condition in the 5D ADM formalism enforced by a reference fluid as in the Isham-Kuchav{r} method which may arise from a broken displacement symmetry. This has two benefits: first is means that TeVeS is compatible with Kaluza-Klein dark matter theory, which is a strong candidate for Weakly Interacting Massive Particles (WIMPs), the other is that it provides an elegant mechanism for the scalar and vector fields. It constrains most of the freedom in the definition of TeVeS which does not have a field theoretic motivation. This is important because the Kaluza-Klein theory predicts that spin-2 tensor modes must propagate at the speed of light, in agreement with observation, from theoretical constraints while TeVeS has to match this observation empirically. Furthermore, it removes need for the interpolating function in MOND and the Lorentz-violating condition on the vector field to be physical since they are analogous to a gauge condition and depend on state of motion.
暗物质的引力替代方案需要广义相对论之外的额外场或假设，同时还要继续符合太阳系的严格约束。例如，修正牛顿动力学（MOND）比暗物质模型更准确地预测了星系的塔利-费舍尔关系，同时又限制了太阳系的牛顿引力。另一方面，MOND 在预测宇宙微波背景和物质功率谱等更大规模的观测数据方面做得很差。张量-矢量-天平（TeVeS）理论是 MOND 的相对论广义化，可以解释这些没有暗物质的观测结果。在本文中，我从卡卢扎-克莱因（Kaluza-Klein）理论推导出一个额外维度的广义 TeVeS，这是 $n=0$ 卡卢扎-克莱因模式的结果。在KK理论中，MOND是5维ADM形式主义中由参考流体（如伊萨姆-库查/v{r}方法中的参考流体）强制执行的切片条件的一个特例，它可能来自于位移对称性的破缺。这有两个好处：一是意味着TeVeS与卡卢扎-克莱因暗物质理论兼容，而卡卢扎-克莱因暗物质理论是弱相互作用大质量粒子（WIMPs）的有力候选者；二是为标量场和矢量场提供了一个优雅的机制。它限制了 TeVeS 定义中大部分没有场论动机的自由。这一点非常重要，因为卡卢扎-克莱因理论预测自旋-2张量模式必须以光速传播，这与观测结果一致，来自理论约束，而TeVeS必须从经验上与观测结果相匹配。此外，它还消除了 MOND 中的插值函数和矢量场上的洛伦兹违反条件的物理需要，因为它们类似于规规条件，取决于运动状态。
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Pub Date : 2024-05-09DOI: 10.1088/1361-6382/ad494d
Rodrigo Maier, Filipe Cattete Alves
In this paper we examine the stability of scalar perturbations in nonsingular models which emerge from an interacting vacuum component. The analysis developed in this paper relies on two phenomenological choices for the energy exchange between a nonrelativistic fluid and a vacuum component. In both scenarios it can be shown that closed models may furnish nonsingular orbits of physical interest in phase space once a decelerated past era is connected to a graceful exit to late-time acceleration. Regarding such configurations as background spacetimes we introduce scalar perturbations in order to examine the stability of these models in a high energy domain. We explicitly show that the vacuum perturbation is not an independent variable and diverges as dynamics approaches the bounce. This feature assigns a rather unstable signature to the dynamics making the choices for the energy transfer ill defined at least for nonsingular configurations at the bounce scale.
{"title":"Scalar Perturbations in Nonsingular Universes from Interacting Vacuum","authors":"Rodrigo Maier, Filipe Cattete Alves","doi":"10.1088/1361-6382/ad494d","DOIUrl":"https://doi.org/10.1088/1361-6382/ad494d","url":null,"abstract":"\u0000 In this paper we examine the stability of scalar perturbations in nonsingular models which emerge from an interacting vacuum component. The analysis developed in this paper relies on two phenomenological choices for the energy exchange between a nonrelativistic fluid and a vacuum component. In both scenarios it can be shown that closed models may furnish nonsingular orbits of physical interest in phase space once a decelerated past era is connected to a graceful exit to late-time acceleration. Regarding such configurations as background spacetimes we introduce scalar perturbations in order to examine the stability of these models in a high energy domain. We explicitly show that the vacuum perturbation is not an independent variable and diverges as dynamics approaches the bounce. This feature assigns a rather unstable signature to the dynamics making the choices for the energy transfer ill defined at least for nonsingular configurations at the bounce scale.","PeriodicalId":505126,"journal":{"name":"Classical and Quantum Gravity","volume":" 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140994700","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}
Pub Date : 2024-04-18DOI: 10.1088/1361-6382/ad407e
A. Bertocco, M. Bruno, Rosario De Rosa, L. Di Fiore, Domenico D'Urso, F. Frasconi, A. Gennai, L. Lucchesi, M. Refat, F. Pilo, D. Rozza, P. Ruggi, V. Sipala, I. Tosta e Melo, L. Trozzo
Seismic noise and local disturbances are dominant noise sources for ground-based Gravitational Waves detectors in the low frequency region (0.1 to 10 Hz) limiting their sensitivity and duty cycle. With the introduction of high-performance seismic isolation systems based on mechanical pendula, the 2nd generation laser interferometric detectors have reached the scientific goal of the first direct observation of GW signals thanks to the extension of the detection bandwidth down to 10 Hz. Now, the 3rd generation instrument era is approaching, and the Einstein Telescope giant interferometer is becoming a reality with the possibility to install the detector in an underground site where seismic noise is 100 times smaller than on surface. Moreover, new available technologies as well as the experience acquired in operating advanced detectors are key points to further extend the detection bandwidth down to 2 Hz with the possibility to suspend cryogenic payload and then mitigating Thermal Noise too. Here, we present a preliminary study devoted to improving seismic attenuation performance of the Advanced VIRGO Superattenuator in the low frequency region of about five orders of magnitude. Particular care has been carried on in analyzing the possibility to improve the vertical attenuation performance with a multi-stage pendulum chain equipped with magnetic anti-springs that is hung to a double Inverted Pendulum in nested configuration. The feedback control requirements and possible strategies to be adopted for this last element will be presented.
{"title":"New generation of Superattenuator for Einstein Telescope: preliminary studies","authors":"A. Bertocco, M. Bruno, Rosario De Rosa, L. Di Fiore, Domenico D'Urso, F. Frasconi, A. Gennai, L. Lucchesi, M. Refat, F. Pilo, D. Rozza, P. Ruggi, V. Sipala, I. Tosta e Melo, L. Trozzo","doi":"10.1088/1361-6382/ad407e","DOIUrl":"https://doi.org/10.1088/1361-6382/ad407e","url":null,"abstract":"\u0000 Seismic noise and local disturbances are dominant noise sources for ground-based Gravitational Waves detectors in the low frequency region (0.1 to 10 Hz) limiting their sensitivity and duty cycle. With the introduction of high-performance seismic isolation systems based on mechanical pendula, the 2nd generation laser interferometric detectors have reached the scientific goal of the first direct observation of GW signals thanks to the extension of the detection bandwidth down to 10 Hz. Now, the 3rd generation instrument era is approaching, and the Einstein Telescope giant interferometer is becoming a reality with the possibility to install the detector in an underground site where seismic noise is 100 times smaller than on surface. Moreover, new available technologies as well as the experience acquired in operating advanced detectors are key points to further extend the detection bandwidth down to 2 Hz with the possibility to suspend cryogenic payload and then mitigating Thermal Noise too. Here, we present a preliminary study devoted to improving seismic attenuation performance of the Advanced VIRGO Superattenuator in the low frequency region of about five orders of magnitude. Particular care has been carried on in analyzing the possibility to improve the vertical attenuation performance with a multi-stage pendulum chain equipped with magnetic anti-springs that is hung to a double Inverted Pendulum in nested configuration. The feedback control requirements and possible strategies to be adopted for this last element will be presented.","PeriodicalId":505126,"journal":{"name":"Classical and Quantum Gravity","volume":" 36","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140688124","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}
Pub Date : 2024-04-17DOI: 10.1088/1361-6382/ad3ffb
É. Lalande, Aaron Davenport, Lory Marchand, Ashot Markosyan, Daniel Martinez, A. Paolone, M. Rezac, M. Bazzan, M. Chicoine, Julien Colaux, Matthieu Coulon, M. Fejer, A. Lussier, E. Majorana, Ludvik Martinu, Carmen Menoni, Christophe Michel, Fulvio Ricci, F. Schiettekatte, Nikita Shcheblanov, Joshua R Smith, J. Teillon, G. Terwagne, G. Vajente
Blistering is a phenomenon sometimes observed in sputtered-deposited thin films but seldom investigated in detail. Here, we consider the case of titania-doped germania (TGO)/silica multi-layers deposited by ion beam sputtering. TGO is a candidate as high refractive index material in the Bragg mirrors for the next iteration of gravitational waves detectors. It needs to be annealed at 600°C for 100h in order to reach the desired relaxation state. However under some growth conditions, in 52-layer TGO/silica stacks, blistering occurs upon annealing at a temperature near 500°C, which corresponds to the temperature where Ar desorbs from TGO. In order to better understand the blistering phenomenon, we measure the Ar transport in single layers of TGO and silica. In the case of <1 μm-thick TGO layers, the Ar desorption is mainly limited by detrapping. The transport model also correctly predicts the evolution of the total amount of Ar in a 8.5 μm stack of TGO and silica layers annealed at 450°C, but in that case, the process is mainly limited by diffusion. Since Ar diffusion is an order of magnitude slower in TGO compared to silica, we observe a correspondingly strong accumulation of Ar in TGO. The Ar transport model is used to explain some regimes of the blisters growth, and we find indications that Ar accumulation is a driver for their growth in general, but the blisters nucleation remains a complex phenomenon influenced by several other factors including stress, substrate roughness, and impurities.
{"title":"Ar transport and blister growth kinetics in titania-doped germania-based optical coatings","authors":"É. Lalande, Aaron Davenport, Lory Marchand, Ashot Markosyan, Daniel Martinez, A. Paolone, M. Rezac, M. Bazzan, M. Chicoine, Julien Colaux, Matthieu Coulon, M. Fejer, A. Lussier, E. Majorana, Ludvik Martinu, Carmen Menoni, Christophe Michel, Fulvio Ricci, F. Schiettekatte, Nikita Shcheblanov, Joshua R Smith, J. Teillon, G. Terwagne, G. Vajente","doi":"10.1088/1361-6382/ad3ffb","DOIUrl":"https://doi.org/10.1088/1361-6382/ad3ffb","url":null,"abstract":"\u0000 Blistering is a phenomenon sometimes observed in sputtered-deposited thin films but seldom investigated in detail. Here, we consider the case of titania-doped germania (TGO)/silica multi-layers deposited by ion beam sputtering. TGO is a candidate as high refractive index material in the Bragg mirrors for the next iteration of gravitational waves detectors. It needs to be annealed at 600°C for 100h in order to reach the desired relaxation state. However under some growth conditions, in 52-layer TGO/silica stacks, blistering occurs upon annealing at a temperature near 500°C, which corresponds to the temperature where Ar desorbs from TGO. In order to better understand the blistering phenomenon, we measure the Ar transport in single layers of TGO and silica. In the case of <1 μm-thick TGO layers, the Ar desorption is mainly limited by detrapping. The transport model also correctly predicts the evolution of the total amount of Ar in a 8.5 μm stack of TGO and silica layers annealed at 450°C, but in that case, the process is mainly limited by diffusion. Since Ar diffusion is an order of magnitude slower in TGO compared to silica, we observe a correspondingly strong accumulation of Ar in TGO. The Ar transport model is used to explain some regimes of the blisters growth, and we find indications that Ar accumulation is a driver for their growth in general, but the blisters nucleation remains a complex phenomenon influenced by several other factors including stress, substrate roughness, and impurities.","PeriodicalId":505126,"journal":{"name":"Classical and Quantum Gravity","volume":" 10","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140692405","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}
Pub Date : 2024-04-17DOI: 10.1088/1361-6382/ad3ffd
M. Papajčı́k, J. Podolský
We present a convenient method of algebraic classification of 2+1 spacetimes into the types I, II, D, III, N and O, without using any field equations. It is based on the 2+1 analogue of the Newman-Penrose curvature scalars Psi_A of distinct boost weights, which are specific projections of the Cotton tensor onto a suitable null triad. The algebraic types are then simply determined by the gradual vanishing of such Cotton scalars, starting with those of the highest boost weight. This classification is directly related to the specific multiplicity of the Cotton-aligned null directions (CANDs) and to the corresponding Bel-Debever criteria. Using a bivector (that is 2-form) decomposition, we demonstrate that our method is fully equivalent to the usual Petrov-type classification of 2+1 spacetimes based on the eigenvalue problem and determining the respective canonical Jordan form of the Cotton-York tensor. We also derive a simple synoptic algorithm of algebraic classification based on the key polynomial curvature invariants. To show the practical usefulness of our approach, we perform the classification of several explicit examples, namely the general class of Robinson-Trautman spacetimes with an aligned electromagnetic field and a cosmological constant, and other metrics of various algebraic types.
{"title":"Algebraic classification of 2+1 geometries: a new approach","authors":"M. Papajčı́k, J. Podolský","doi":"10.1088/1361-6382/ad3ffd","DOIUrl":"https://doi.org/10.1088/1361-6382/ad3ffd","url":null,"abstract":"\u0000 We present a convenient method of algebraic classification of 2+1 spacetimes into the types I, II, D, III, N and O, without using any field equations. It is based on the 2+1 analogue of the Newman-Penrose curvature scalars Psi_A of distinct boost weights, which are specific projections of the Cotton tensor onto a suitable null triad. The algebraic types are then simply determined by the gradual vanishing of such Cotton scalars, starting with those of the highest boost weight. This classification is directly related to the specific multiplicity of the Cotton-aligned null directions (CANDs) and to the corresponding Bel-Debever criteria. Using a bivector (that is 2-form) decomposition, we demonstrate that our method is fully equivalent to the usual Petrov-type classification of 2+1 spacetimes based on the eigenvalue problem and determining the respective canonical Jordan form of the Cotton-York tensor. We also derive a simple synoptic algorithm of algebraic classification based on the key polynomial curvature invariants. To show the practical usefulness of our approach, we perform the classification of several explicit examples, namely the general class of Robinson-Trautman spacetimes with an aligned electromagnetic field and a cosmological constant, and other metrics of various algebraic types.","PeriodicalId":505126,"journal":{"name":"Classical and Quantum Gravity","volume":" 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140690394","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}
Pub Date : 2024-04-09DOI: 10.1088/1361-6382/ad3c8c
Diksha Diksha, Alex Amato, V. Spagnuolo, Graeme McGhee, M. Chicoine, Caspar Clark, Stuart Hill, J. Hough, Ross Johnston, Remy Keil, Nena Mavridi, S. Reid, Sheila Rowan, Timon Schapals, F. Schiettekatte, Simon Tait, Iain W Martin, J. Steinlechner
One of the main noise sources in current gravitational wave detectors is the thermal noise of the high-reflectivity coatings on the main interferometer optics. Coating thermal noise is dominated by the mechanical loss of the high-refractive index material within the coating stacks, Ta2O5 mixed with TiO2. For upgrades to room-temperature detectors, a mixture of GeO2 and TiO2 is an interesting alternative candidate coating material. While the rather low refractive index of GeO2 increases with increasing TiO2 content, a higher TiO2 content results in a lower threshold temperature before heat treatment leads to crystallisation, and potentially to a degradation of optical properties. For future cryogenic detectors, on the other hand, a higher TiO2 content is beneficial as the TiO2 suppresses the low-temperature mechanical loss peak of GeO2. In this paper, we present the optical properties of coatings -- produced by plasma-assisted ion-beam evaporation -- with high TiO2 content at 1550nm, a laser wavelength considered for cryogenic gravitational-wave detectors, as a function of heat-treatment temperature. For comparison, the absorption was also measured of pure GeO2. Furthermore, results at the currently-used wavelength of 1064nm are presented.
{"title":"Optical properties of germania and titania at 1064 nm and at 1550 nm","authors":"Diksha Diksha, Alex Amato, V. Spagnuolo, Graeme McGhee, M. Chicoine, Caspar Clark, Stuart Hill, J. Hough, Ross Johnston, Remy Keil, Nena Mavridi, S. Reid, Sheila Rowan, Timon Schapals, F. Schiettekatte, Simon Tait, Iain W Martin, J. Steinlechner","doi":"10.1088/1361-6382/ad3c8c","DOIUrl":"https://doi.org/10.1088/1361-6382/ad3c8c","url":null,"abstract":"\u0000 One of the main noise sources in current gravitational wave detectors is the thermal noise of the high-reflectivity coatings on the main interferometer optics. Coating thermal noise is dominated by the mechanical loss of the high-refractive index material within the coating stacks, Ta2O5 mixed with TiO2. For upgrades to room-temperature detectors, a mixture of GeO2 and TiO2 is an interesting alternative candidate coating material. While the rather low refractive index of GeO2 increases with increasing TiO2 content, a higher TiO2 content results in a lower threshold temperature before heat treatment leads to crystallisation, and potentially to a degradation of optical properties. For future cryogenic detectors, on the other hand, a higher TiO2 content is beneficial as the TiO2 suppresses the low-temperature mechanical loss peak of GeO2. In this paper, we present the optical properties of coatings -- produced by plasma-assisted ion-beam evaporation -- with high TiO2 content at 1550nm, a laser wavelength considered for cryogenic gravitational-wave detectors, as a function of heat-treatment temperature. For comparison, the absorption was also measured of pure GeO2. Furthermore, results at the currently-used wavelength of 1064nm are presented.","PeriodicalId":505126,"journal":{"name":"Classical and Quantum Gravity","volume":"137 24","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140725535","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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