In this work, we obtain all spatially homogeneous space-time models related to the intersection of the set of Stäckel spaces of type (2.1) and the set of conformally Stäckel spaces of type (3.1). These models allow a complete separation of variables both in the Hamilton-Jacobi equation for massive test particles and in the eikonal equation for radiation. The models obtained in this work relate to wave-like space-time models. For the found models, solutions of the Einstein equations with the cosmological constant and radiation are obtained. For the obtained solutions, the eikonal equation and the equations of motion of massive test particles in the Hamilton-Jacobi form are integrated.
We investigate the future asymptotics of spatially homogeneous space-times with a positive cosmological constant by using and further developing geometric conformal methods in General Relativity. For a large class of source fields, including fluids with anisotropic stress, we prove that the space-times are future asymptotically simple and geometrically conformally regular. We use that result in order to show the global conformal regularity of the Einstein-Maxwell system as well as the Einstein-radiation, Einstein-dust, massless Einstein-Vlasov and particular Einstein-scalar field systems for B…
The $f(R)$ gravity models formulated in Einstein conformal frame are equivalent to Einstein gravity together with a minimally coupled scalar field. The scalar field couples with the matter sector and the coupling term is given by the conformal factor. We apply the holographic principle to such an interacting model in spatially flat and curved universes. We show that the model leads to a constant ratio of energy densities of dark matter to dark energy in a spatially flat universe. In a spatially curved universe, the ratio is not a constant and the evolution seems to be model-dependent. However,…
"Diagonal" spatially inhomogeneous (SI) models are introduced under the assumption of the existence of (proper) intrinsic symmetries and can be seen, in some sense, complementary to the Szekeres models. The structure of this class of spacetimes can be regarded as a generalization of the (twist-free) Locally Rotationally Symmetric (LRS) geometries without any global isometry containing, however, these models as special cases. We consider geometries where a six-dimensional algebra $\mathcal{IC}$ of Intrinsic Conformal Vector Fields (ICVFs) exists acting on a $2-$dimensional (pseudo)-Riemannian m…
The new manifestation of conformal invariance for a massless scalar particle in a Riemannian spacetime of general relativity is found. Conformal transformations conserve the Hamiltonian and wave function in the Foldy-Wouthuysen representation. Similarity of manifestations of conformal invariance for massless scalar and Dirac particles is proved. New exact Foldy-Wouthuysen Hamiltonians are derived for both massive and massless scalar particles in a general static spacetime and in a frame rotating in the Kerr field approximated by a spatially isotropic metric. The latter case covers an observer …
Certain local thermal observables are considered in well-known examples of spatially open FRW spaces: Milne, open de Sitter and anti de Sitter as well as Einstein static universes. Another value for fixing the ambiguity in defining the Wick square and, hence, the local temperature is motivated in the last example. Physical consequences of that choice are discussed for static and conformal vacua in those spaces.
In this paper we investigate conformal symmetries in Locally Rotationally Symmetric (LRS) spacetimes using a semitetrad covariant formalism. We demonstrate that a general LRS spacetime which rotates and spatially twists simultaneously has an inherent homothetic symmetry in the plane spanned by the fluid flow lines and the preferred spatial direction. We discuss the nature and consequence of this homothetic symmetry showing that a null Killing horizon arises when the heat flux has an extremal value. We also consider the special case of a perfect fluid and the restriction on the conformal geomet…
For a conformally-coupled scalar field we obtain the conformally-related Einstein-Langevin equations, using appropriate transformations for all the quantities in the equations between two conformally-related spacetimes. In particular, we analyze the transformations of the influence action, the stress energy tensor, the noise kernel and the dissipation kernel. In due course the fluctuation-dissipation relation is also discussed. The analysis in this paper thereby facilitates a general solution to the Einstein-Langevin equation once the solution of the equation in a simpler, conformally-related …
Standard textbooks will state that hydrodynamics requires near-equilibrium to be applicable. Recently, however, out-of-equilibrium attractor solutions for hydrodynamics have been found in kinetic theory and holography in systems with a high degree of symmetry, suggesting the possibility of a genuine out-of-equilibrium formulation of hydrodynamics. This work demonstrates that attractor solutions also occur in non-conformal kinetic theory and spatially non-homogeneous systems, potentially having important implications for the interpretation of experimental data in heavy-ion and proton-proton col…
This paper provides an analytical treatment of accelerated and geodesic motion within the framework of the Friedmann -Lemaitre-Robertson-Walker (FLRW) spacetime. By employing conformal time transformations we manage to convert second order differential equations of motion in FLRW spacetime to first order equations in the conformally transformed spacetime. This allows us to derive a general analytical solution in closed-form for accelerated motion in spatially curved FLRW spacetime. We provide few examples of this general solution for the spatially flat cases. The last part of our work focuses …
We present a new numerical code to compute non-axisymmetric eigenmodes of rapidly rotating relativistic stars by adopting spatially conformally flat approximation of general relativity. The approximation suppresses the radiative degree of freedom of relativistic gravity and the field equations are cast into a set of elliptic equations. The code is tested against the low-order f- and p-modes of slowly rotating stars for which a good agreement is observed in frequencies computed by our new code and those computed by the full theory. Entire sequences of the low order counter-rotating f-modes are …
This work investigates the possibility of achieving a conformally flat slicing of the Kerr spacetime. We consider a hypersurface of the form $t = F(r,θ,a)$, where $(t,r,θ,ϕ)$ are the Boyer-Lindquist coordinates, solve for a vanishing Cotton-York tensor of the induced metric order by order in the spin parameter $a$, and show that the procedure fails at the fifth order. We also prove that no coordinate change can induce a spatially flat recasting of the Kerr(-de Sitter) metric, beyond linear order in $a$, adopting a more general ansatz depending on $ϕ$.
We show that in a generic scalar-tensor theory of gravity, the ``referenced'' quasilocal mass of a spatially bounded region in a classical solution is invariant under conformal transformations of the spacetime metric. We first extend the Brown-York quasilocal formalism to such theories to obtain the ``unreferenced'' quasilocal mass and prove it to be conformally invariant. The appropriate reference term in this case is defined by generalizing the Hawking-Horowitz prescription, which was originally proposed for general relativity. For such a choice of reference term, the referenced quasilocal m…
In the context of theories of Kaluza-Klein type, with a large extra dimension, we study self-similar cosmological models in 5D that are homogeneous, anisotropic and spatially flat. The "ladder" to go between the physics in 5D and 4D is provided by Campbell-Maagard's embedding theorems. We show that the 5-dimensional field equations $R_{AB} = 0$ determine the form of the similarity variable. There are three different possibilities: homothetic, conformal and "wave-like" solutions in 5D. We derive the most general homothetic and conformal solutions to the 5D field equations. They require the extr…
We consider multidimensional cosmologies in even-dimensional space-times (D=2n) containg perfect fluid and a multidimensional generalization of the Maxwell field, preserving its conformal invariance (the F field, an n-form). Among models with an isotropic physical 3-space some integrable cases are found: vacuum models (which are integrable in the general case) and some perfect fluid models with barotropic equations of state. All of them contain a component of the F field appearing as an additional scalar in 4 dimensions. A two-parameter family of spatially flat models and four one-parameter fa…
This thesis is concerned with the development and application of conformal techniques to numerical calculations of asymptotically flat spacetimes. The conformal compactification technique enables us to calculate spatially unbounded domains, thereby avoiding the introduction of an artificial timelike outer boundary. We construct in spherical symmetry an explicit scri-fixing gauge, i.e. a conformal and a coordinate gauge in which the spatial coordinate location of null infinity is independent of time so that no resolution loss in the physical part of the conformal extension appears. Going beyond…
A spatially flat Robertson-Walker spacetime driven by a cosmological constant is non-conformally coupled to a massless scalar field. The equations of semiclassical gravity are explicitly solved for this case, and a self-consistent de Sitter solution associated with the Bunch-Davies vacuum state is found (the effect of the quantum field is to shift slightly the effective cosmological constant). Furthermore, it is shown that the corrected de Sitter spacetime is stable under spatially-isotropic perturbations of the metric and the quantum state. These results are independent of the free renormaliz…
We consider the classical stochastic fluctuations of spacetime geometry induced by quantum fluctuations of massless non-conformal matter fields in the Early Universe. To this end, we supplement the stress-energy tensor of these fields with a stochastic part, which is computed along the lines of the Feynman-Vernon and Schwinger-Keldysh techniques; the Einstein equation is therefore upgraded to a so called Einstein-Langevin equation. We consider in some detail the conformal fluctuations of flat spacetime and the fluctuations of the scale factor in a simple cosmological modelintroduced by Hartle,…
This work was mainly driven by the desire to explore, to what extent embedding some given geometry in a higher dimensional flat one is useful for understanding the causal structure of classical fields traveling in the former, in terms of that in the latter. We point out, in the 4D spatially flat FLRW universe, that the causal structure of transverse-traceless (TT) gravitational waves can be elucidated by first reducing the problem to a 2D Minkowski wave equation with a time dependent potential, where the relevant Green's function is pure tail -- waves produced by a physical source propagate st…
Simply-connected homogeneous spacetimes for kinematical and aristotelian Lie algebras (with space isotropy) have recently been classified in all dimensions. In this paper, we continue the study of these "maximally symmetric" spacetimes by investigating their local geometry. For each such spacetime and relative to exponential coordinates, we calculate the (infinitesimal) action of the kinematical symmetries, paying particular attention to the action of the boosts, showing in almost all cases that they act with generic non-compact orbits. We also calculate the soldering form, the associated viel…
It is well-known that the $(1+1)$ dimensional Schwarzschild and spatially flat FLRW spacetimes are conformally flat. This work examines entanglement harvesting from the conformal field vacuums in these spacetimes between two Unruh-DeWitt detectors, moving along outgoing null trajectories. In $(1+1)$ dimensional Schwarzschild spacetime, we considered the Boulware and Unruh vacuums for our investigations. In this analysis, one observes that while entanglement harvesting is possible in $(1+1)$ dimensional Schwarzschild and $(1+3)$ dimensional de Sitter spacetimes, it is not possible in the $(1+1)…
We consider the conformal Einstein equations for massless collisionless gas cosmologies which admit an isotropic singularity. After developing the general theory, we restrict to spatially-homogeneous cosmologies. We show that the Cauchy problem for these equations is well-posed with data consisting of the limiting particle distribution function at the singularity.
In this work we would like to address the problem of the effect of bulk matter on the brane cosmological evolution in a general way. We assume that the spatial part of the brane metric is not maximally symmetric, therefore spatially inhomogeneous. However we retain the conformal flatness property of the standard cosmological model (FRW) i.e. the Weyl tensor of the induced 4D geometry is zero. We refer to it as Spatially Inhomogeneous Irrotational (SII) brane. It is shown that the model can be regarded as the 5D generalization of the SII spacetimes found recently [1].
This is the first of two papers where we study the asymptotics of the generalized Nariai solutions and its relation to the cosmic no-hair conjecture. According to the cosmic no-hair conjecture, generic expanding solutions of Einstein's field equations in vacuum with a positive cosmological constant isotropize and approach the de-Sitter solution asymptotically. The family of solutions which we introduce as "generalized Nariai solutions", however, shows quite unusual asymptotics and hence should be non-generic in some sense. In this paper, we list basic facts for the Nariai solutions and charact…
The only efficient and robust method of generating consistent initial data in general relativity is the conformal technique initiated by Lichnerowicz and perfected by York. In the spatially compact case, the complete scheme consists of the Arnowitt-Deser-Misner (ADM) Hamiltonian and momentum constraints, the ADM Euler-Lagrange equations, York's constant-mean-curvature (CMC) condition, and a lapse-fixing equation (LFE) that ensures propagation of the CMC condition by the Euler-Lagrange equations. The Hamiltonian constraint is rewritten as the Lichnerowicz-York equation for the conformal factor …
A new approach is suggested for the study of geometric symmetries in general relativity, leading to an invariant characterization of the evolutionary behaviour for a class of Spatially Homogeneous (SH) vacuum and orthogonal $γ-$law perfect fluid models. Exploiting the 1+3 orthonormal frame formalism, we express the kinematical quantities of a generic symmetry using expansion-normalized variables. In this way, a specific symmetry assumption lead to geometric constraints that are combined with the associated integrability conditions, coming from the existence of the symmetry and the induced expa…
We consider averaged null energy conditions (ANEC) for strongly coupled quantum field theories in even (two and four) dimensional curved spacetimes by applying the no-bulk-shortcut principle in the context of the AdS/CFT duality. In the same context but in odd-dimensions, the present authors previously derived a conformally invariant averaged null energy condition (CANEC), which is a version of the ANEC with a certain weight function for conformal invariance. In even-dimensions, however, one has to deal with gravitational conformal anomalies, which make relevant formulas much more complicated …
The problem of cosmological particle creation for a spatially flat, homogeneous and isotropic Universes is discussed in the context of f(R) theories of gravity. Different from cosmological models based on general relativity theory, it is found that a conformal invariant metric does not forbid the creation of massless particles during the early stages (radiation era) of the Universe.
A Penrose diagram is constructed for a spatially coherent black hole that smoothly begins an accretion, then excretes symmetrically as measured by a distant observer, with the initial and final states described by a metric of Minkowski form. Coordinate curves on the diagram are computationally derived. Causal relationships between space-time regions are briefly discussed. The life cycle of the black hole demonstrably leaves asymptotic observers in an unaltered Minkowski space-time of uniform conformal scale.
We study phases of equilibrium Hawking radiation in $d$-dimensional holographic CFTs on spatially compact spacetimes with two black holes. In the particular phases chosen the dual $(d+1)$-dimensional bulk solutions describe a variety of black funnels and droplets. In the former the CFT readily conducts heat between the two black holes, but it in the latter such conduction is highly suppressed. While the generic case can be understood in certain extreme limits of parameters on general grounds, we focus on CFTs on specific geometries conformally equivalent to a pair of $d \ge 4$ AdS${}_d$-Schwar…
An anisotropic cosmic fluid with radial heat flux which sources a time dependent Rindler-like geometry is investigated. Even though its energy density $ρ$ is positive, the radial and transversal pressures are negative and the strong energy condition is not satisfied. The congruence of "static" observers is not geodesic and the heat flux is oriented outward. We computed the Misner-Sharp energy associated with the Rindler-type metric embedded in a spatially flat FLRW universe and found that the Weyl energy is vanishing thanks to the conformally flat form of the spacetime. The null geodesic expan…
The ``Newtonian'' theory of spatially unbounded, self--gravitating, pressureless continua in Lagrangian form is reconsidered. Following a review of the pertinent kinematics, we present alternative formulations of the Lagrangian evolution equations and establish conditions for the equivalence of the Lagrangian and Eulerian representations. We then distinguish open models based on Euclidean space $\R^3$ from closed models based (without loss of generality) on a flat torus $\T^3$. Using a simple averaging method we show that the spatially averaged variables of an inhomogeneous toroidal model form…
Constraints on cosmological parameters and CMB first acoustic peak in conformal Killing gravity
Università degli Studi di Napoli Federico II（那不勒斯费德里科二世大学）；Istituto Nazionale di Fisica Nucleare (INFN)（意大利国家核物理研究所）；Scuola Superiore Meridionale（南方高等学院）；Università degli Studi di Milano（米兰大学）；Osservatorio Astronomico di Capodimonte (OACN), Istituto Nazionale di Astrofisica (INAF)（卡波迪蒙特天文台，意大利国家天体物理研究所）
We propose and analyze a new metric that has two conformal factors a(t) and b(t) that combine the expansion of the universe and its effects on the spatial and temporal part of the Schwarzschild metric in isotropic coordinates. We present the solutions, their descriptions and we comment on their shortcomings. In the spatially flat case of an expanding universe, we derive from the proposed metric the special solutions of the field equations for the dust approximation and the McVittie metric. We show that the presence of a black hole does not modify the a(t) proportional to t^{2/3} law for dust a…
We consider the dynamics of a spatially flat universe dominated by a self-interacting nonminimally coupled scalar field. The structure of the phase space and complete phase portraits for the conformal coupling case are given. It is shown that the non-minimal coupling modifies drastically the dynamics of the universe. New cosmological behaviors are identified, including superinflation ($\dot{H}>0$), avoidance of big bang singularities through classical birth of the universe from empty Minkowski space, and spontaneous entry into and exit from inflation. The relevance of this model to the descrip…
