In the study of spherical degenerate stars such as neutron stars, general relativistic effects are incorporated by using Tolman-Oppenheimer-Volkoff equations to describe their interior spacetime. However, the equation of states employed in such studies are invariably computed in flat spacetime. We show that the equation of states computed in the curved spacetime of these stars depend explicitly on the metric function. Further, we show that ignoring such metric-dependent gravitational time dilation effect leads one to grossly underestimate the mass limits of these compact stars.
We compute the equation of state for an ensemble of degenerate fermions by using the curved spacetime of a slowly rotating axially symmetric star. We show that the equation of state computed in such curved spacetime depends on the gravitational time dilation as well as on the dragging of inertial frames, unlike an equation of state computed in a globally flat spacetime. The effect of gravitational time dilation leads to a significant enhancement of the maximum mass limit of a degenerate neutron star. However, such an enhancement due to the frame-dragging effect is extremely small. Nevertheless…
We investigate the instanton solution between the degenerate vacua in curved space. We show that there exist $O(4)$-symmetric solutions not only in de Sitter but also in both flat and anti-de Sitter space. The geometry of the new type of solutions is finite and preserves the $Z_2$ symmetry. The nontrivial solution corresponding to the tunneling is possible only if gravity is taken into account. The numerical solutions as well as the analytic computations using the thin-wall approximation are presented. We expect that these solutions do not have any negative mode as in the instanton solution.
We study the existence and stability of spherical membranes in curved spacetimes. For Dirac membranes in the Schwarzschild--de Sitter background we find that there exists an equilibrium solution. By fine--tuning the dimensionless parameter $ΛM^2,$ the static membrane can be at any position outside the black hole event horizon, even at the stretched horizon, but the solution is unstable. We show that modes having $l=0$ (and for $ΛM^2<16/243$ also $l=1$) are responsible for the instability. We also find that spherical higher order membranes (membranes with extrinsic curvature corrections), contr…
It is shown that the calculation of Dirac operator for the spherical coordinate system with spherical Dirac matrices and using the spin connection formalism is in the contradiction with the definition of standard Dirac operator in the spherical Minkowski coordinate system. It is shown that such contradiction one can avoid by introducing a canonical conjugated covariant derivative for the spinor field. The Dirac equation solution on the Reissner - Nordström background is obtained. The solution describes a bound state of a charged particle.
Aim of the paper is to obtain 2d analogue of the backreaction equation which will be useful to study final state of quantum perturbed spherically symmetric curved space times. Thus we take Einstein-massless-scalar $ψ$ tensor gravity model described on class of spherically symmetric curved space times. We rewrite the action functional in 2d analogue in terms of dimensionless dilaton-matter field $(χ=Φψ)$ where dilaton field $Φ$ is conformal factor of 2-sphere. Then we seek renormalized expectation value of quantum dilaton-matter field stress tensor operator by applying Hadamard rennormalization…
In this paper the generalization of the Gribov pendulum equation in the Coulomb gauge for curved spacetimes is analyzed on static spherically symmetric backgrounds. A rigorous argument for the existence and uniqueness of solution is provided in the asymptotically AdS case. The analysis of the strong and weak boundary conditions is equivalent to analyzing an effective one-dimensional Schrodinger equation. Necessary conditions in order for spherically symmetric backgrounds to admit solutions of the Gribov pendulum equation representing copies of the vacuum satisfying the strong boundary conditio…
Propagation of a localised wave function of a massive scalar field is investigated in its rest frame. The complete orthogonal Hermite-Gauss basis is presented, and the Gouy phase and Rayleigh scale notions are adapted. The leading and sub-leading gravitational corrections to a localised quantum wave function propagating in a general curved spacetime geometry are calculated within the Fermi coordinates around the time-like geodesic of its rest frame, and cross-talk coefficients among the modes are derived. It is observed that spherically symmetric modes propagate along the geodesic. However, no…
In this manuscript, we present an alternative method for calculating null geodesics in General Static Isotropic Metrics in General Relativity and Extended Theories of Gravity. By applying a conformal transformation, we are able to consider an analogue gravity model, where curvature is encoded in the dielectric and magnetic properties of a medium. In other words, we pass from curved to flat space-times, where instead of the Einstein field equations, the Maxwell equations are solved. Within this geometrical background, the photon geodesics are calculated. Then, given different black hole and wor…
A spherically symmetric wormhole in Newtonian gravitation in curved space, enhanced with a connection between the mass density and the Ricci scalar, is presented. The wormhole, consisting of two connected asymptotically flat regions, inhabits a spherically symmetric curved space. The gravitational potential, gravitational field and the pressure that supports the fluid that permeates the Newtonian wormhole are computed. Particle dynamics and tidal effects in this geometry are studied. The possibility of having Newtonian black holes in this theory is sketched.
In a very interesting paper, Cunha, Berti, and Herdeiro have recently claimed that ultra-compact objects, self-gravitating horizonless solutions of the Einstein field equations which have a light ring, must possess at least {\it two} (and, in general, an even number of) light rings, of which the inner one is {\it stable}. In the present compact paper we explicitly prove that, while this intriguing theorem is generally true, there is an important exception in the presence of degenerate light rings which, in the spherically symmetric static case, are characterized by the simple dimensionless rel…
We calculate the one-loop divergences for different vector field models in curved spacetime. We introduce a classification scheme based on their degeneracy structure, which encompasses the well-known models of the non-degenerate vector field, the Abelian gauge field and the Proca field. The renormalization of the generalized Proca model, which has important applications in cosmology, is more complicated. By extending standard heat-kernel techniques, we derive a closed form expression for the one-loop divergences of the generalized Proca model.
A recent analysis by one of the authors\cite{Perivolaropoulos:2018cgr} has pointed out that Derrick's theorem can be evaded in curved space. Here we extend that analysis by demonstrating the existence of a static metastable solution in a wide class of metrics that include a Schwarzschild-Rindler-AntideSitter spacetime (Grumiller metric) defined as $ds^2= f(r) dt^2 - f(r)^{-1} dr^2 - r^2 (dθ^2 +\sin^2θdϕ^2)$ with $f(r)=1-\frac{2Gm}{r}+2br-\fracΛ{3} r^2$ ($Λ<0\; b<0$). This metric emerges generically as a spherically symmetric vacuum solution in a class of scalar-tensor theories\cite{Grumiller:2…
Conformal matter collineations of the energy-momentum tensor for a general spherically symmetric static spacetime are studied. The general form of these collineations is found when the energy-momentum tensor is non-degenerate, and the maximum number of independent conformal matter collineations is \emph{fifteen}. In the degenerate case of the energy-momentum tensor it is found that these collineations have infinite degrees of freedom. In some subcases of degenerate energy-momentum, the Ricci tensor is non-degenerate, that is, there exist non-degenerate Ricci inheritance collineations.
We analyse the dynamics of the collision of two spherical massive shells in a generally spherically symmetric background, obtaining an expression from the conservation law that imposes a constraint between the different parameters involved. We study the light-like limit and make some comparisons of the predictions of our master equation with the results obtained in the case of collision of light-like shells, like the short life of white holes or the mass inflation phenomena. We present some particular cases of the constraint equation.
The spherically symmetric static spacetimes are classified according to their matter collineations. These are studied when the energy-momentum tensor is degenerate and also when it is non-degenerate. We have found a case where the energy-momentum tensor is degenerate but the group of matter collineations is finite. For the non-degenerate case, we obtain either {\it four}, {\it five}, {\it six} or {\it ten} independent matter collineations in which four are isometries and the rest are proper. We conclude that the matter collineations coincide with the Ricci collineations but the constraint equa…
The Hamiltonian formulation of modified dispersion relations (MDRs) allows for their implementation on generic curved spacetimes. In turn it is possible to derive phenomenological effects. I will present how to construct the kappa-Poincare dispersion relation on curved spacetimes, its spherically symmetric realizations, among them the kappa deformation of Schwarzschild spacetime, and its implementation on Friedmann-Lemaitre-Robertson-Walker spacetimes with arbitrary scale factor. In addition we will construct the general first order modifications of the general relativistic dispersion relation…
Derrick's theorem is an important result that decides the existence of soliton configurations in field theories in different dimensions. It is proved using the extremization of finite energy of configurations under the scaling transformation. According to this theorem, the $2+1$ dimension is the critical dimension for the existence of solitons in scalar field theories without the gauge fields. In the present article, Derrick's theorem is extended in a generic curved spacetime in a covariant manner. Moreover, the existence of solitons in conformally flat spacetimes and spherically symmetric spa…
We generalize our previous thick shell formalism to incorporate any codimension-1 thick wall with a peculiar velocity and proper thickness bounded by arbitrary spacetimes. Within this new formulation we obtain the equation of motion of a spherically symmetric dust thick shell immersed in vacuum as well as in Friedmann-Robertson-Walker spacetimes.
We demonstrate how the Einstein's equations for the $D$-dimensional spherical gravity can be written in the covariant vector-like form. These equations reveal easily the causal structure of curved spherically symmetric manifolds and may appear useful in investigation of different models of brane universes.
Particle Physics in Curved Spacetime and Dark Matter
Università di Salerno（萨莱诺大学）；INFN – Gruppo Collegato di Salerno（意大利国家核物理研究所萨莱诺联合小组）；Università degli Studi di Napoli Federico II（那不勒斯费德里科二世大学）；Scuola Superiore Meridionale（南方高等学院）；University of Camerino（卡梅里诺大学）
General-relativistic stable spacetimes can be made unstable under the presence of certain nonminimally coupled free scalar fields. In this paper, we analyze the evolution of linear scalar-field perturbations in spherically symmetric spacetimes and compare the classical stability analysis with a recently discussed quantum field one. In particular, it is shown that vacuum fluctuations lead to natural seeds for the unstable phase, whereas in the classical framework the presence of such seeds in the initial conditions must be assumed.
We consider the computation of the entanglement entropy in curved backgrounds with event horizons. We use a Hamiltonian approach to the problem and perform numerical computations on a spherical lattice of spacing $a$. We study the cosmological case and make explicit computations for the Friedmann-Robertson-Walker universe. Our results for a massless, minimally coupled scalar field can be summarized by $S_{ent}=0.30 r_H^2/a^2$,which resembles the flat space formula, although here the horizon radius, $r_H$, is time-dependent.
In spinor formalism, since any massless free-field spinor with spin higher than $1/2$ can be constructed with spin-1/2 spinors (Dirac-Weyl spinors) and scalars, we introduce a map between Weyl fields and Dirac-Weyl fields. We determine the corresponding Dirac-Weyl spinors in a given empty spacetime. Regarding them as basic units, other higher spin massless free-field spinors are then identified. Along this way, we find some hidden fundamental features related to these fields. In particular, for non-twisting vacuum Petrov type N solutions, we show that all higher spin massless free-field spinor…
Within the framework of the theory of strongly-interacting quantum Bose liquids, we consider a general relativistic model of self-interacting complex scalar fields with logarithmic nonlinearity taken from dense superfluid models. We demonstrate the existence of gravitational equilibria in this model, described by spherically symmetric nonsingular finite-mass asymptotically-flat solutions. These equilibrium configurations can describe both massive astronomical objects, such as bosonized superfluid stars or cores of neutron stars, and finite-size particles and non-topological solitons, such as Q…
Using a Legendre transformation, we compute the unconstrained Hamiltonian of a spinning test-particle in a curved spacetime at linear order in the particle spin. The equations of motion of this unconstrained Hamiltonian coincide with the Mathisson-Papapetrou-Pirani equations. We then use the formalism of Dirac brackets to derive the constrained Hamiltonian and the corresponding phase-space algebra in the Newton-Wigner spin supplementary condition (SSC), suitably generalized to curved spacetime, and find that the phase-space algebra (q,p,S) is canonical at linear order in the particle spin. We …
In this paper we discuss matter inheritance collineations by giving a complete classification of spherically symmetric static spacetimes by their matter inheritance symmetries. It is shown that when the energy-momentum tensor is degenerate, most of the cases yield infinite dimensional matter inheriting symmetries. It is worth mentioning here that two cases provide finite dimensional matter inheriting vectors even for the degenerate case. The non-degenerate case provides finite dimensional matter inheriting symmetries. We obtain different constraints on the energy-momentum tensor in each case. …
We prove the theorem: The necessary and sufficient condition for a spherically symmetric spacetime to represent an isothermal perfect fluid (barotropic equation of state with density falling off as inverse square of the curvature radius) distribution without boundary is that it is conformal to the ``minimally'' curved (gravitation only manifesting in tidal acceleration and being absent in particle trajectory) spacetime.
We use our previously developed identification of dispersion relations with Hamilton functions on phase space to locally implement the $κ$-Poincaré dispersion relation in the momentum spaces at each point of a generic curved spacetime. We use this general construction to build the most general Hamiltonian compatible with spherical symmetry and the Plank-scale-deformed one such that in the local frame it reproduces the $κ$-Poincaré dispersion relation. Specializing to Planck-scale-deformed Schwarzschild geometry, we find that the photon sphere around a black hole becomes a thick shell since pho…
We consider a massless scalar field propagating in a weakly curved spacetime whose metric is a solution to the linearized Einstein field equations. The spacetime is assumed to be stationary and asymptotically flat, but no other symmetries are imposed -- the spacetime can rotate and deviate strongly from spherical symmetry. We prove that the late-time behavior of the scalar field is identical to what it would be in a spherically-symmetric spacetime: it decays in time according to an inverse power-law, with a power determined by the angular profile of the initial wave packet (Price falloff theor…
Newton's theorem of revolving orbits states that one can multiply the angular speed of a Keplerian orbit by a factor $k$ by applying a radial inverse cubed force proportional to $(1-k^2)$. In this paper we derive an extension of this theorem in general relativity, valid for the motion of massive particles in any static, spherically symmetric metrics. We verify the Newtonian limit of this extension and demonstrate that there is no such generalization for rotating metrics. Further we also extend the theory to the case of charged particles in the Einstein-Maxwell and Kaluza-Klein theories.
We investigate the vacuum and charged spherically symmetric static solutions of the Einstein equations on cosmological background. The background metric is not flat, but curved, with constant - curvature spatial sections. Both vacuum and charged cases contain two branches. The first branches transform into the Schwarzschild and Reissner-Nordström solutions if the background metric goes to the Minkovski one. The second branches describe wormholes and have no Einstein limit.
We investigate the linear dynamics of an electromagnetic field propagating in curved spacetime in the presence of plasma. The dynamical equations are generically more involved and richer than the effective Proca equation adopted as a model in previous work. We discuss the general equations and focus on the case of a cold plasma in the background of a spherically-symmetric black hole, showing that the system admits plasma-driven, quasibound electromagnetic states that are prone to become superradiantly unstable when the black hole rotates. The quasibound states are different from those of the P…
We consider a spherically symmetric, Petrov-type D, spacetime with hyper-surface orthogonal, radial, homothetic Killing vector. In this work, some general properties of this spacetime for non-singular and non-degenerate data are presented. We also present the source-free electromagnetic fields in this spacetime. We then discuss general astrophysical relevance of the results obtained for this spacetime.
