Olivier Minazzoli
It is argued that de Sitter space-times might be solutions of entangled relativity once the quantum trace anomaly from matter fields in curved space-times is taken into account. This hypothesis would be an elegant solution to the acceleration of the expansion of the universe within the rigid framework of entangled relativity.
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We discuss the generalization of Doubly Special Relativity to a curved de Sitter background. The model has three observer-independent scales, the velocity of light $c$, the radius of curvature of the geometry $α$, and the Planck energy $κ$, and can be realized in a noncommutative position space. It is possible to construct a model exhibiting a duality for the interchange of positions and momenta together with the exchange of $α$ and $κ$.
The relative geodesic motion in central charts (i.e. static and spherically symmetric) on the $(1+3)$-dimensional de Sitter spacetimes is studied in terms of conserved quantities. The Lorentzian isometries are derived, relating the coordinates of the local chart of a fixed observer with the coordinates of a mobile chart considered as the rest frame of a massive paticle freely moving on a timelike geodesic. The time dilation and Lorentz contraction are discussed pointing out some notable features of the de Sitter relativity in central charts.
In this manuscript, we show that the external Schwarzschild metric can be a good approximation of exact black hole solutions of entangled relativity. Since entangled relativity cannot be defined from vacuum, the demonstrations need to rely on the definition of matter fields. The electromagnetic field being the easiest (and perhaps the only) existing matter field with infinite range to consider, we study the case of a charged black hole -- for which the solution of entangled relativity and a dilaton theory agree -- as well as the case of a pure radiation -- for which the solution of entangled r…
On the Principle of Relativity of Inertia in both General and Entangled Relativities
本文论证纠缠相对论比广义相对论更经济，能在特定极限下恢复广义相对论与标准量子场论，且更符合爱因斯坦对满意相对论理论的原始愿景。
The relative geodesic motion on $(1+3)$-dimensional anti-de Sitter spacetimes is studied in terms of conserved quantities by adapting the Nachtmann boosting method created initially for the de Sitter spacetimes. In this approach the Lorentzian isometriy is derived, relating the coordinates of the local chart of a fixed observer with the coordinates of a mobile chart considered as the rest frame of a massive mobile object moving on a timelike anti-de Sitter geodesic. The transformation of the conserved quantities is also investigated, constructing thus a complete theory of the relative geodesic…
Between Snyder's quantized space-time model in de Sitter space of momenta and the \dS special relativity on \dS-spacetime of radius $R$ with Beltrami coordinates, there is a one-to-one dual correspondence supported by a minimum uncertainty-like argument. Together with Planck length $\ell_P$, $R\simeq (3/Λ)^{1/2}$ should be a fundamental constant. They lead to a dimensionless constant $g{\sim\ell_PR^{-1}}=(G\hbar c^{-3}Λ/3)^{1/2}\sim 10^{-61}$. These indicate that physics at these two scales should be dual to each other and there is in-between gravity of local \dS-invariance characterized by $g…
We briefly revisit the Schwarzschild-de Sitter solution in the context of five-dimensional general relativity. We obtain a class of five-dimensional solutions of Einstein vacuum field equations into which the four-dimensional Schwarzschild-de Sitter space can be locally and isometrically embedded. We show that this class of solutions is well-behaved in the limit of lambda approaching zero. Applying the same procedure to the de Sitter cosmological model in five dimensions we obtain a class of embedding spaces which are similarly well-behaved in this limit. These examples demonstrate that the pr…
A new redshift formula is obtained considering the longitudinal Doppler effect in the de Sitter expanding universe where the relative geodesic motion is governed by the Lorenzian isometries of our new de Sitter relativity [I. I. Cot\u aescu, {Eur. Phys. J. C} {\bf 77} (2017) 485]. This formula combines in a non-trivial manner the well-known cosmological contribution given by Lama\' itre's law with that of the relative motion of the source with respect to a fixed observer as in de Sitter relativity instead of special relativity. Other related quantities as the dispersion relation, the propagati…
We describe the first numerical Tolman-Oppenheimer-Volkoff solutions of compact objects in entangled relativity, which is an alternative to the framework of general relativity that does not have any additional free parameter. Assuming a simple polytropic equation of state and the conservation of the rest-mass density, we notably show that, for any given density, compact objects are always heavier (up to $\sim 8\%$) in entangled relativity than in general relativity -- for any given central density within the usual range of neutron stars' central densities, or for a given radius of the resultin…
I present two results that show that, despite its unusual non-linear form, the phenomenology of entangled relativity remains close to the one of general relativity -- without having any free parameter that can be fine tuned in order to facilitate this. In particular, I present the analytical solutions for spherically charged black-holes, and both the analytical and numerical solutions for neutron stars.
In de Sitter (dS) special relativity (SR), two kinds of conserved currents are derived. The first kind is a 5-dimensional (5d) dS-covariant angular momentum (AM) current, which unites the energy-momentum (EM) and 4d AM current in an inertial-type coordinate system. The second kind is a dS-invariant AM current, which can be generalized to a conserved current for the coupling system of the matter field and gravitational field in dS gravity. Moreover, an inherent EM tensor is predicted, which comes from the spin part of the dS-covariant current. All the above results are compared to the ordinary …
The main consequences of de Sitter Special Relativity to the Standard Cosmological Model of Physical Cosmology are examined. The cosmological constant Lambda appears, in this theory, as a manifestation of the proper conformal current, which must be added to the usual energy-momentum density. As that conformal current itself vanishes in absence of sources, Lambda is ultimately dependent on the matter content, and can in principle be calculated. A present-day value very close to that given by the crossed supernova/BBR data is obtained through simple and reasonable approximations. Also a primeval…
Schwarzschild black-hole immersed in an electric or magnetic background in Entangled Relativity
本文在纠缠相对论框架下，首次提出Schwarzschild黑洞浸入电或磁场背景的精确中性解，并指出其在弱物质场密度下与广义相对论结果一致。
In this paper, we use the Killing vector method to formulate the de Sitter/Anti-de Sitter invariant special relativity (dS/AdS-SR). Through solving the Einstein equation with $Λ\neq 0$, the basic inertial metric for dS/AdS-SR is determined to be the Beltrami metric $B_{μν}(x)$. The corresponding Killing equations are system of ten simultaneous partial differential equations of first order. Their most general solutions were obtained, and all the ten independent Killing vectors were found out. These results confirm that the Beltrami metric has maximal spacetime symmetry. The ten Killing-Noether …
Slowly rotating and charged Black-holes in Entangled Relativity
本文在纠缠相对论框架下研究带电黑洞，进一步分析球对称解的性质，并首次给出缓慢旋转带电黑洞场方程的新解。
The de Sitter invariant special relativity is a natural extension of the usual Einstein special relativity. Within this framework a generalization of special relativity (SR) for the de Sitter space-time introduces a new length scale $R$, serving an origin of geometrical cosmological constant $Λ=3/R^2$. De Sitter relativity predicts the departure from the Lorentz invariance due to spacetime curvature, related to the geometrical cosmological constant. In this paper the possible impact of de Sitter special relativity effects on threshold particle processes and equivalence principle violation is c…
Recently it has been shown that despite previous claims the cosmological constant affects light bending. In the present article we study light bending and the advance of Mercury's perihelion in the context of the Newtonian limit of Schwarzschild-de Sitter spacetime employing the special relativistic equivalence of mass and energy. In both cases, up to a constant factor, we find the same results as in the full general relativistic treatment of the same phenomena. These approximate and intuitive arguments demonstrate clearly what effects should have been expected from the presence of $Λ$ in the …
Deriving Entangled Relativity
本文通过要求理论允许广义相对论解的存在，导出了纠缠相对论，并引入了具有内在解耦特性的更广泛理论类。
Radiating solutions in Entangled Relativity
本文在纠缠相对论框架下研究Mineur-Vaidya解，证明其在磁场或电场消失极限下可动态形成裸奇点。
In this manuscript, we present analytical external spherical solutions of entangled relativity, which we compare to numerical solutions obtained in a Tolman-Oppenheimer-Volkoff framework. Analytical and numerical solutions match perfectly well outside spherical compact objects, therefore validating both types of solutions at the same time. The analytical external (hairy) solutions -- which depend on two parameters only -- may be used in order to easily compute observables -- such as X-ray pusle profiles -- without having to rely on an unknown equation of state for matter inside the compact obj…
The effects of a non-vanishing value for the cosmological constant in the scenario of Lorentz symmetry breaking recently proposed by Cohen and Glashow (which they denote as Very Special Relativity) are explored and observable consequences are pointed out.
Cosmology in Entangled Relativity
本文指出广义相对论是纠缠相对论在无宇宙学常数时的内禀退耦极限，并据此讨论暗能量候选者，进而提出其拉格朗日量可能只是无穷微扰级数首项的新假设。
In present paper we construct the classical and minisuperspace quantum models of an extended charged particle. The modelling is based on the radiation fluid singular hypersurface filled with physical vacuum. We demonstrate that both at classical and quantum levels such a model can have equilibrium states at the radius equal to the classical radius of a charged particle. In the cosmological context the model could be considered also as the primary stationary state, having the huge internal energy being nonobservable for an external observer, from which the Universe was born by virtue of the qua…
Revisiting the Entangled Relativity gravity framework
本文重访纠缠相对论框架，将其嵌入更广理论集合，通过标量-张量重构和内禀解耦条件，提出满足条件的理想流体拉格朗日量，并指出其作为广义相对论替代方案的潜力，但需重新审视守恒律与观测数据关联。
The properties of Lorentz transformations in de Sitter relativity are studied. It is shown that, in addition to leaving invariant the velocity of light, they also leave invariant the length-scale related to the curvature of the de Sitter spacetime. The basic conclusion is that it is possible to have an invariant length parameter without breaking the Lorentz symmetry. This result may have important implications for the study of quantum kinematics, and in particular for quantum gravity.
In the presence of a cosmological constant, interpreted as a purely geometric entity, absence of matter is represented by a de Sitter spacetime. As a consequence, ordinary Poincare' special relativity is no longer valid and must be replaced by a de Sitter special relativity. By considering the kinematics of a spinless particle in a de Sitter spacetime, we study the geodesics of this spacetime, the ensuing definitions of canonical momenta, and explore possible implications for quantum mechanics.
In two previous papers we presented the LARES 2 space experiment aimed at a very accurate test of frame-dragging and at other tests of fundamental physics and measurements of space geodesy and geodynamics. We presented the error sources of the LARES 2 experiment, its error budget and Monte Carlo simulations and covariance analyses confirming an accuracy of a few parts in one thousand in the test of frame-dragging. Here we discuss the impact of the orbital perturbation known as the de Sitter effect, or geodetic precession, in the error budget of the LARES 2 frame-dragging experiment. We show th…
A special relativity based on the de Sitter group is introduced, which is the theory that might hold up in the presence of a non-vanishing cosmological constant. Like ordinary special relativity, it retains the quotient character of spacetime, and a notion of homogeneity. As a consequence, the underlying spacetime will be a de Sitter spacetime, whose associated kinematics will differ from that of ordinary special relativity. The corresponding modified notions of energy and momentum are obtained, and the exact relationship between them, which is invariant under a re-scaling of the involved quan…
Owing to the existence of an invariant length at the Planck scale, Einstein special relativity breaks down at that scale. A possible solution to this problem is arguably to replace the Poincaré invariant Einstein special relativity by a de Sitter invariant special relativity. In addition to reconciling Lorentz symmetry with the existence of an invariant length, such replacement produces concomitant changes in all relativistic theories, including general relativity, which becomes what we have called 'de Sitter modified general relativity'. In this paper, the Newtonian limit of this theory is us…
The replacement of the Poincaré-invariant Einstein special relativity by a de Sitter-invariant special relativity produces concomitant changes in all relativistic theories, including general relativity. A crucial change in the latter is that both the background de Sitter curvature and the gravitational dynamical curvature turns out to be included in a single curvature tensor. This means that the cosmological term no longer explicitly appears in Einstein equation, and is consequently not restricted to be constant. In this paper, the Newtonian limit of such theory is obtained, and the ensuing Ne…
The dispersion relation of de Sitter special relativity is obtained in a simple and compact form, which is formally similar to the dispersion relation of ordinary special relativity. It is manifestly invariant under change of scale of mass, energy and momentum, and can thus be applied at any energy scale. When applied to the universe as a whole, the de Sitter special relativity is found to provide a natural scenario for the existence of an evolving cosmological term, and agrees in particular with the present-day observed value. It is furthermore consistent with a conformal cyclic view of the u…
It is known that the space of momenta of DSR can be identified with de Sitter space. In this paper, we discuss the relation of the noncanonical phase space of the Magueijo-Smolin model of DSR with the canonical 5-dimensional phase space in which the de Sitter space of momenta is embedded. We suggest that in analogy with the momentum variables, also the position variables should be constrained to lie on a null hypersurface of the five-dimensional space
A new prescription to calculate the total energies and angular momenta of asymptotically $(d+1)$-dimensional anti-de Sitter spacetimes is proposed. The method is based on an extension of the field theoretical approach to General Relativity to the case where there is an effective cosmological constant. A $(d-1)$-form $Ω$ is exhibited which, when integrated on asymptotic $(d-1)$-dimensional boundary surfaces, yields the values of those conserved quantities. The calculations are gauge independent once asymptotic conditions are not violated . Total energies and angular momenta of some known soluti…
Casimir-Polder interaction arises from the vacuum fluctuations of quantum field that depend on spacetime curvature and thus is spacetime-dependent. Here we show how to use the resonance Casimir-Polder interaction (RCPI) between two entangled atoms to detect spacetime curvature. We find that the RCPI of two static entangled atoms in the de Sitter-invariant vacuum depends on the de Sitter spacetime curvature relevant to the temperature felt by the static observer. It is characterized by a $1/L^2$ power law decay when beyond a characteristic length scale associated to the breakdown of a local ine…
The Poincare' group generalizes the Galilei group for high-velocity kinematics. The de Sitter group is assumed to go one step further, generalizing Poincare' as the group governing high-energy kinematics. In other words, ordinary special relativity is here replaced by de Sitter relativity. In this theory, the cosmological constant is no longer a free parameter, and can be determined in terms of other quantities. When applied to the whole universe, it is able to predict the value of the cosmological constant and to explain the cosmic coincidence. When applied to the propagation of ultra-high en…
We address the question of existence of regular spherically symmetric electrically charged solutions in Nonlinear Electrodynamics coupled to General Relativity. Stress-energy tensor of the electromagnetic field has the algebraic structure $T_0^0=T_1^1$. In this case the Weak Energy Condition leads to the de Sitter asymptotic at approaching a regular center. In de Sitter center of an electrically charged NED structure, electric field, geometry and stress-energy tensor are regular without Maxwell limit which is replaced by de Sitter limit: energy density of a field is maximal and gives an effect…
We show that the generalization of Doubly Special Relativity to a curved de Sitter background can be obtained starting from a six-dimensional spacetime on which quadratic constraints on position and momentum coordinates are imposed.
Standard quantum field theory from entangled relativity
本文指出纠缠相对论在特定极限下可同时退化为广义相对论与标准量子场论，表明现有基础物理理论可能只是该理论的近似。
Numerical evaluation of the exact post-Newtonian parameters in Brans-Dicke and entangled relativity theories
本文提出两种新方法计算布拉恩-狄克和纠缠相对论中的精确后牛顿参数，并发现其与标准参数差异可能超过80%。
We review the toroidal, cylindrical and planar black hole solutions in anti-de Sitter spacetimes and present their properties.
We obtain spacetimes generated by static and spinning magnetic string sources in Einstein Relativity with negative cosmological constant. Since the spacetime is asymptotically a cylindrical anti-de Sitter spacetime, we will be able to calculate the mass, momentum, and electric charge of the solutions. We find two families of solutions, one with longitudinal magnetic field and the other with angular magnetic field. The source for the longitudinal magnetic field can be interpreted as composed by a system of two symmetric and superposed electrically charged lines with one of the electrically char…
A First-Order Gauge Approach to de Sitter General Relativity
该研究提出德西特相对论的一阶规范表述，将伪半径l(x)提升为时空场致SO(4,1)局部破缺。通过伊诺努 - 维格纳收缩等方法得出相关向量、能量 - 动量流等，证明场方程等价性，表明Λ(x)是时空挠率源，重述宇宙学常数问题。
De Sitter-invariant approach to cosmology
本文提出德西特不变狭义相对论以解决普朗克长度与洛伦兹不变性的冲突，并推导出德西特不变广义相对论下的弗里德曼方程，探讨其对宇宙学的影响。
The exact (closed form) solutions of the equations of motion in the theory of general relativity that describe motion of test particle and photon in Kerr and Kerr-(anti) de Sitter spacetimes all involve the multivariable hypergeometric function of Lauricella $F_D$: Kraniotis [Class. Quantum Grav. {\bf 21} 2004, 4743; Class. Quantum Grav. {\bf 22} 2005, 4391; Class. Quantum Grav. {\bf 24} 2007, 1775]. The domain of variables ${\cal D}_n$ of the corresponding function depends on the first integrals of motion associated with the isometries of the Kerr-(anti) de Sitter metric and Carter's constant…
It has been proposed that on (anti)-de Sitter background, the Heisenberg uncertainty principle should be modified by the introduction of a term proportional to the cosmological constant. We show that this modification of the uncertainty principle can be derived straightforwardly from the geometric properties of (anti)-de Sitter spacetime. We also discuss the connection between the so-called extended generalized uncertainty principle and triply special relativity.
In this report, a general method to extract thermodynamic quantities from solutions of the Einstein equation is developed. In 1994, Wald established that the entropy of a black hole could be identified as a Noether charge associated with a Killing vector of a global space-time (pseudo-Riemann) manifold. We reconstruct Wald's method using geometrical language, e.g$.$, via differential forms defined on the local space-time (Minkowski) manifold. Concurrently, the abstract thermodynamics are also reconstructed using geometrical terminology, which is parallel to general relativity. The corresponden…
In 5D relativity, the usual 4D cosmological constant is determined by the extra dimension. If the extra dimension is spacelike, one can get a positive cosmological constant $Λ$ and a 4D de Sitter (dS) space. In this paper we present that, if the extra dimension is timelike oppositely, the negative $Λ$ will be emerged and the induced 4D space will be an asymptotic Anti-de Sitter (AdS). Under the minimum assumption, we solve the Kaluza-Klein equation $R_{AB} = 0$ in a canonical system and obtain the AdS solution in a general case. The result shows that an AdS space is induced naturally from a Ka…
We describe connected timelike codim-2 extremal surfaces stretching between the future and the past boundaries in the static patch coordinatization of de Sitter space. These are analogous to rotated versions of certain surfaces in the $AdS$ black hole. The existence of these surfaces via the $dS/CFT$ framework suggests the speculation that $dS_4$ is dual to two copies of ghost-like CFTs in a thermofield-double-type entangled state. In studies of entanglement in ghost systems and "ghost-spin" chains, we show that similar entangled states in two copies of ghost-spin ensembles always have positiv…
The "twin paradox" of special relativity offers the possibility to make interstellar flights within a lifetime. For very long journeys with velocities close to the speed of light, however, we have to take into account the expansion of the universe. Inspired by the work of Rindler on hyperbolic motion in curved spacetime, we study the worldline of a uniformly accelerated observer in de Sitter spacetime and the communication between the traveling observer and an observer at rest.
General relativity can be unambiguously formulated with Lorentz, de Sitter and anti-de Sitter tangent groups, which determine the fermionic representations. We show that besides of the Lorentz group only anti-de Sitter tangent group is consistent with all physical requirements.
In recent years, Planck-scale modifications to particles' dispersion relation have been deeply studied for the possibility to formulate some phenomenology of Planckian effects in astrophysical and cosmological frameworks. There are some indications [arXiv:gr-qc/0611024] that Finsler geometry can provide some generalization of Riemannian geometry which may allow to account for non-trivial (Planckian) structure of relativistic particles' configuration space. We investigate the possibility to formalize Planck-scale deformations to relativistic models in curved spacetime, within the framework of F…
We investigate static and spherically symmetric solutions in the Minimal Theory of Bigravity (MTBG). First, we show that a pair of Schwarzschild-de Sitter spacetimes with different cosmological constants and black hole masses written in the spatially-flat Gullstrand-Painlevé (GP) coordinates is a solution in the self-accelerating branch of MTBG, while it cannot be a solution in the normal branch. We then illustrate how Schwarzschild-de Sitter solutions can become compatible with the normal branch when using different coordinates. We also confirm that the self-accelerating branch of MTBG admits…
We give a possible splitting method to a Hamiltonian for the description of charged particles moving around the Reissner-Nordstrom-(anti)-de Sitter black hole with an external magnetic field. This Hamiltonian can be separated into six analytical solvable pieces, whose solutions are explicit functions of proper time. In this case, second- and fourth-order explicit symplectic integrators are easily available. They exhibit excellent long-term behavior in maintaining the boundness of Hamiltonian errors regardless of ordered or chaotic orbits if appropriate step-sizes are chosen. Under some circums…
Five dimensional Chern-Simons theory with (anti-)de Sitter SO(1,5) or SO(2,4) gauge invariance presents an alternative to General Relativity with cosmological constant. We consider the zero-modes of its Kaluza-Klein compactification to four dimensions. Solutions with vanishing torsion are obtained in the cases of a spherically symmetric 3-space and of a homogeneous and isotropic 3-space, which reproduce the Schwarzshild-de Sitter and $Λ$CDM cosmological solutions of General Relativity. We also check that vanishing torsion is a stable feature of the solutions.
Quantum of action in entangled relativity
本文证明“纠缠相对论”比广义相对论更经济，其唯一参数为能量平方量子，对应约化普朗克能量，并推导出普朗克作用量子与牛顿常数成正比变化，建立了量子与引力领域的联系，且对太阳系和中子星中的变化进行了预测。
Compact objects with scalar charge embedded in a magnetic or electric field in Einstein-Maxwell-dilaton theories
本文将施瓦西-梅尔文解推广到爱因斯坦-麦克斯韦-伸缩子理论中含非零标量荷的情形，并通过共形变换得到纠缠相对论中的解，验证了此前用于描述中子星的解析解在背景场趋于零时是精确解的良好近似。
Temporal and spatial variation of fine-structure constant $α\equiv e^2/\hbar c$ in cosmology has been reported in analysis of combination Keck and VLT data. This paper studies this variation based on consideration of basic spacetime symmetry in physics. Both laboratory $α_0$ and distant $α_z$ are deduced from relativistic spectrum equations of atoms (e.g.,hydrogen atom) defined in inertial reference system. When Einstein's $Λ\neq 0$, the metric of local inertial reference systems in SM of cosmology is Beltrami metric instead of Minkowski, and the basic spacetime symmetry has to be de Sitter (d…
Spinning Black Binaries in de Sitter space
本文在正宇宙学常数广义相对论中构造同向与反向自旋的稳态旋转黑洞双星，揭示无物质理论的连续非唯一性，并为双星并合提供初始数据。
Within the framework of Geodesic Brane Gravity, the deviation from General Relativity is parameterized by the conserved bulk energy. The corresponding geodesic evolution/nucleation of a de-Sitter brane is shown to be exclusively driven by a double-well Higgs potential, rather than by a plain cosmological constant. The (hairy) horizon serves then as the locus of unbroken $Z_{2}$ symmetry. The quartic structure of the scalar potential, singled out on finiteness grounds of the total (including the dark component) energy density, chooses the Hartle-Hawking no-boundary proposal.
Parity Isospectrality of the Kerr--Newman--de Sitter Black Hole
本研究证明亚极端Kerr--Newman--de Sitter黑洞的引力电磁扰动具有宇称等谱性，通过辐射规范下的主变量直接重构，无需慢旋转或小电荷近似。
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