The main focus of this paper is to discuss the solutions of Einstein-Maxwell's field equations for compact stars study. We have chosen the MIT bag model equation of state for the pressure-energy density relationship and conformal Killing vectors are used to investigate the appropriate forms for metric coefficients. We impose the boundary conditions, by choosing the Bardeen model to describe as an exterior spacetime. The Bardeen model may provide the analysis with some interesting results. For example, the extra terms involved in the asymptotic representations as compared to the usual Reissner-Nordstrom case may influence the mass of a stellar structure. Both energy density and pressure profiles behave realistically except a central singularity. It is shown that the energy conditions are satisfied in our study. The equilibrium conditions through TOV equation and stability criteria through Adiabatic index for the charged stellar structure study are investigated. Lastly, we have also provided a little review of the case with Reissner-Nordstrom spacetime as an exterior geometry for the matching condition. In both cases, the masses obey the Andreasson's limit $\sqrt{M} \leq \sqrt{R}/3+\sqrt{R/9+q^2/3R}$ requirement for a charged star. Conclusively, the results show that Bardeen model geometry provides more massive stellar objects as compared to usual Reissner-Nordstrom spacetime. In particular, the current study supports the existence of realistic massive structures like PSR J $1614-2230$.
This paper presents an exact solution of Bardeen black hole in presence of massive gravity, which is characterized by the additional parameter $m$. Here, we focus on $4D$ Bardeen AdS massive black hole solutions as example to discuss the thermodynamical properties such as temperature, entropy and specific heat at constant pressure. We also study the critical behaviour of Bardeen AdS massive black holes by considering the cosmological constant $Λ$ as thermodynamical variable (pressure) as well as the parameter associated with the nonlinear electrodynamics. We calculate the critical value of pre…
The Bardeen black hole solution is the first spherically symmetric regular black hole based on the Sakharov and Gliner proposal which is a modification of the Schwarzschild black hole. We present the Bardeen black hole solution in the presence of the de Rham, Gabadaadze, and Tolly (dRGT) massive gravity, which is regular everywhere in the presence of a nonlinear source. The obtained solution reduces to the Bardeen black hole in the absence of a massive gravity parameter, and the Schwarzschild black hole when magnetic charge $g = 0$. We investigated the thermodynamic quantities, that is, mass (…
We give a detailed discussion of the use of the (3+1) decomposition and of Bardeen's variables in massive gravity linearized over a Minkowski as well as over a de Sitter background. In Minkowski space the Bardeen "potential" Φ, that in the massless case is a non-radiative degree of freedom, becomes radiative and describes the helicity-0 component of the massive graviton. Its dynamics is governed by a simple Klein-Gordon action, supplemented by a term (\Box Φ)^2 if we do not make the Fierz-Pauli tuning of the mass term. In de Sitter the identification of the variable that describes the radiativ…
The exact solutions of the Dirac equation that describe a massive, non-charged particle with spin-(1/2) in the curved spacetime geometry of regular Bardeen black hole surrounded by quintessence (BBHSQ) are investigated. We first derive the Dirac equation in the BBHSQ background using a null tetrad in the Newman-Penrose formalism. Afterward, we separate the Dirac equation into ordinary differential equations for the radial and angular parts. The angular equations are solved exactly in terms of standard spherical harmonics. The radial part equations are transformed into a Schrödinger like differ…
First, we obtain the plane wave solution of the linearized massive conformal gravity field equations. It is shown that the theory has seven physical plane waves. In addition, we investigate the gravitational radiation from binary systems in massive conformal gravity. We find that the theory with large graviton mass can reproduce the orbit of binaries by the emission of gravitational waves.
In this article we construct a massive theory of gravity that is invariant under conformal transformations. The massive action of the theory depend on the metric tensor and a scalar field, which are considered as the only field variables. We find the vacuum field equations of the theory and the solution of its Newtonian limit.
In this paper we find the cosmological solutions of the massive conformal gravity field equations in the presence of matter fields. In particular, we show that the solution of negative curvature is in good agreement with the late universe.
We find the linearized gravitational field of a static spherically symmetric mass distribution in massive conformal gravity and test it with some solar system experiments. The result is that the theory agrees with the general relativistic observations in the solar system for a determined lower bound on the graviton mass.
In this paper, we use a suitable conformal rescaling to construct static and rotating regular black holes in conformal massive gravity. The new metric is characterized by the mass $M$, the "scalar charge" $Q$, the angular momentum parameter $a$, the "hair parameter" $λ$, and the conformal scale factor encoded in the parameter $L$. We explore the shadow images and the deflection angles of relativistic massive particles in the spacetime geometry of a rotating regular black hole. For $λ\neq 0$ and $Q > 0$, the shadow is larger than the shadow of a Kerr black hole. In particular, if $λ< 0$, the sh…
Recently, in Phys. Rev. D 98, 084002 (2018), an investigation was carried out on the gravitational radiation from binary systems in conformal gravity and massive conformal gravity. According to the authors of the paper, these two theories differ only by the sign of a parameter in the matter action of a general conformal theory. For a negative parameter the general conformal theory indeed corresponds to conformal gravity. However, here, we argue that for a positive parameter the general conformal theory does not correspond to massive conformal gravity.
We investigate the new massive conformal gravity which is not invariant under conformal transformations, in comparison to the massive conformal gravity. We find five polarization modes of gravitational waves propagating on the Minkowski spacetimes. The stability of Minkowski spacetimes is guaranteed if the mass squared is not negative and the linearized Ricci tenor is employed to describe a massive spin-2 graviton. However, the small Schwarzschild black hole is unstable against the $s$-mode massive graviton perturbations.
In a recent paper in EPJC March 2016, Faria has shown that quantum massive conformal gravity is renormalizable but has ghost states. We comment this paper on the aspect of renormalizability.
Recently in (Eur. Phys. J. C 76:341, 2016) [arXiv:1604.08706], Myung has suggested that the renormalizability of massive conformal gravity is meaningless unless the massive ghost states of the theory are stable. Here we show that massive conformal gravity can be renormalizable having unstable ghost states.
We study the dynamics of the early universe in massive conformal gravity. In particular, we show that the theory is consistent with the observed values of the primordial abundances of light elements if we consider the existence of right-handed sterile neutrinos.
We analyze the classical stability of Schwarzschild black hole in massive conformal gravity which was recently proposed for another massive gravity model. This model in the Jordan frame is conformally equivalent to the Einstein-Weyl gravity in the Einstein frame. The coupled linearized Einstein equation is decomposed into the traceless and trace equation when one chooses $6m^2φ=δR$. Solving the traceless equation exhibits unstable modes featuring the Gregory-Laflamme $s$-mode instability of five-dimensional black string, while we find no unstable modes when solving the trace equation. It is sh…
We first find the linear approximation of the second plus fourth order derivative massive conformal gravity action. Then we reduce the linearized action to separated second order derivative terms, which allows us to quantize the theory by using the standard first order canonical quantization method. It is shown that quantum massive conformal gravity is renormalizable but has ghost states. A possible decoupling of these ghost states at high energies is discussed.
We investigate the black holes in the new massive conformal gravity which is not invariant under conformal transformations because of the presence of the Einstein-Hilbert term. First, we show that the small Schwarzschild black hole is unstable against the $s$-mode of linearized Ricci tensor by solving the Lichnerowicz-Ricci tensor equation. This instability induces the appearance of the non-BBMB (Bocharova-Bronnikov-Melnikov-Bekenstein) black hole that has both Ricci tensor and conformal scalar hair.
The presence of an unstable massive spin-2 ghost state in the renormalizable theory of massive conformal gravity leads to a pair of complex poles appearing in the first sheet of the energy plane. Here we show that the positions of these poles are gauge dependent, which makes the theory unitary.
In this work, a correspondence between black hole solutions of conformal and massive theories of gravity is found. It is seen that this correspondence imposes some constraints on parameters of these theories. What is more, a relation between the mass of black holes and the parameters of massive gravity is found. Indeed, the acceptable ranges of massive gravity parameters ($c_{1}$\ and $c_{2}$) are found. It is shown that by considering the positive mass of black holes, some ranges of $c_{1}$\ and $c_{2}$ are acceptable.
Extending researches on Hawking radiation to conformal gravity theory, we discuss Hawking radiation of different particles across charged rotating AdS black holes in conformal gravity, including charged massive particles, complex scalar and spin-$1/2$ Dirac particles. To make the study of rotating black holes' tunneling radiation get rid of the dependence on dragging coordinate systems, we investigate the radiation without dragging coordinate transformations. The previous geodesic derivation existed some shortcomings. Not only did geodesics of massive and massless particles are derived by usin…
By taking the massless limit of linearized massive conformal gravity coupled to a source, we show that the theory is free from the vDVZ discontinuity. This result is confirmed when we take the massless limit of the gravitational potential of the theory, which is shown to be finite at the origin.
The quantum Casimir condensate of a conformal massive scalar field in a compact Friedmann universe is considered in the static approximation. The Abel-Plana formula is used for renormalization of divergent series in the condensate calculation. A differential relation between the static Casimir energy density and static Casimir condensate is derived.
We extend the recently proposal of hidden conformal symmetry to the self-dual warped AdS$_3$ black holes in topological massive gravity. It is shown that the wave equation of massive scalar field with sufficient small angular momentum can be reproduced by the SL(2, R) Casimir quadratic operator. Due to the periodic identification in the $ϕ$ direction, it is found that only the left section of hidden conformal symmetry is broken to U(1), while the right section is unbroken, which only gives the left temperature of dual CFT. As a check of the dual CFT conjecture of self-warped AdS$_3$ black hole…
A massive scalar field in a curved spacetime can propagate along the light cone, a causal pathology, which can, in principle, be eliminated only if the scalar couples conformally to the Ricci curvature of spacetime. This property mandates conformal coupling for the field driving inflation in the early universe. During slow-roll inflation, this coupling can cause super-acceleration and, as a signature, a blue spectrum of primordial gravitational waves.
According to Witten [1], the conformal boundary condition of gravity, which specifies the conformal geometry of the boundary and the trace of the extrinsic curvature, is elliptic and leads to well-defined perturbation theory of gravity about any classical solution. The conformal boundary condition was previously considered in [2, 3] in the context of AdS/BCFT, wherein the equation of motion of the end-of-the-world was derived and emphasized. In this paper, we investigate further other consequences of the conformal boundary condition in AdS/BCFT. We derive the boundary central charges of the ho…
We study the generalized massive gravity in three dimensional flat spacetime. A massive logarithmic mode is propagating in the flat spacetime at the critical point where two masses degenerate. Furthermore, we discuss the logarithmic extension of the Galilean conformal algebra (GCA) which may arise from the exotic and standard rank-2 logarithmic conformal field theory (LCFT) on the boundary of AdS3 spacetime.
The graviton 1-loop partition function is calculated for Euclidean generalised massive gravity (GMG) using AdS heat kernel techniques. We find that the results fit perfectly into the AdS/(L)CFT picture. Conformal Chern-Simons gravity, a singular limit of GMG, leads to an additional contribution in the 1-loop determinant from the conformal ghost. We show that this contribution has a nice interpretation on the conformal field theory side in terms of a semi-classical null vector at level two descending from a primary with conformal weights (3/2,-1/2).
We show how the equations for the scalar field (including the massive, massless, minimally and conformally coupled cases) on de Sitter and Anti-de Sitter spaces can be obtained from both the SO$(2,4)$-invariant equation $\square ϕ= 0$ in $\mathbb{R}^6$ and two geometrical constraints defining the (A)dS space. Apart from the equation in $\mathbb{R}^6$, the results only follow from the geometry.
It is shown that solutions to Einstein's field equations with positive cosmological constant can include non-zero rest-mass fields which coexist with and travel unimpeded across a smooth conformal boundary. This is exemplified by the coupled Einstein-massive-scalar field equations for which the mass $m$ is related to the cosmological constant $λ$ by the relation $3\,m^2 = 2\,λ$. Cauchy data for the conformal field equations can in this case be prescribed on the (compact, space-like) conformal boundary ${\cal J}^+$. Their developments backwards in time induce a set of standard Cauchy data on sp…
We hereby show that the Kasner spacetime turns out to be singularity-free in Einstein's conformal gravity in vacuum or in presence of matter. Such a statement is based on the regularity of the curvature invariants and on the geodesic completion of the spacetime when it is probed by massive, massless, and conformally coupled particles. As a universal feature of the regular metric, nothing can reach the singularity located in t=0 in a finite amount of proper time (for massive particles and conformally coupled particles) or for finite values of the affine parameter (for massless particles).
Higher-order curvature corrections involving the conformally-invariant Weyl-squared action have played a role in two recent investigations of four-dimensional gravity; in critical gravity, where it is added to the standard cosmological Einstein-Hilbert action with a coefficient tuned to make the massive ghostlike spin-2 excitations massless, and in a pure Weyl-squared action considered by Maldacena, where the massive spin-2 modes are removed by the imposition of boundary conditions. We exhibit the connections between the two approaches, and we also generalise critical gravity to a wider class …
A version of massive gravity, namely conformal massive gravity, is employed to study the behavior of thermodynamic geometry for both the static and the rotating regular black holes. Whereas in thermodynamic geometry singularity can be interpreted as the second phase transition, seeing such phenomena as heat capacity behavior for both cases is investigated in detail. In addition, other thermodynamic quantities like the entropy and the temperature are analyzed as well. Another important property of the black holes is the so-called stability, in which utilizing the first phase transition of the h…
Various massive gravity theories in three dimensions are conjecturally dual to logarithmic conformal field theories (LCFTs). We summarise the status of these conjectures. LCFTs are characterised by the values of the central charges and the so-called "new anomalies". We employ a short-cut to calculate these new anomalies in generalised massive gravity and in the recently proposed higher-derivative gravity theories with holographic c-theorem. Both cases permit LCFTs exhibiting intriguing features, like rank three Jordan cells or non-zero central charges. Finally, as an example we discuss in some…
We elaborate on conformal higher-spin gauge theory in three-dimensional (3D) curved space. For any integer $n>2$ we introduce a conformal spin-$\frac{n}{2}$ gauge field $h_{(n)} =h_{α_1\dots α_n}$ (with $n$ spinor indices) of dimension $(2-n/2)$ and argue that it possesses a Weyl primary descendant $C_{(n)}$ of dimension $(1+n/2)$. The latter proves to be divergenceless and gauge invariant in any conformally flat space. Primary fields $C_{(3)}$ and $C_{(4)}$ coincide with the linearised Cottino and Cotton tensors, respectively. Associated with $C_{(n)}$ is a Chern-Simons-type action that is bo…
Three-dimensional topologically massive AdS gravity has a complicated constraint algebra, making it difficult to count nonperturbative degrees of freedom. I show that a new choice of variables greatly simplifies this algebra, and confirm that the theory contains a single propagating mode for all values of the mass parameter and the cosmological constant. As an added benefit, I rederive the central charges and conformal weights of the boundary conformal field theory from an explicit analysis of the asymptotic algebra of constraints.
Conformal symmetry is taken as an attribute of theories of massless fields in manifolds with specific dimensionalities. This paper shows that this is not an absolute truth; it is a consequence of the mathematical representation used for the physical interactions. It introduces a new kind of representation where the propagation of massive (invariant mass) and massless interactions are unifiedly described by a single conformally symmetric Green's function. Sources and fields are treated at a same footing, symmetrically, as discrete fields - the fields in this new representation - fields defined …
We extend to study Hawking radiation via tunneling in conformal gravity. We adopt Parikh-Wilczek's semi-classical tunneling method and the method of complex-path integral to investigate Hawking radiation from new rotating AdS black holes in conformal gravity. In this paper, the research on Hawking radiation from the rotating black holes is done in a general system, not limited in dragging coordinate systems any longer. Moreover, there existed some shortcomings in the previous derivation of geodesic equations. Different from the massless case, they used a different approach to derive the geodes…
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 t…
A canonical transformation which relates the model of a massive relativistic particle moving near the horizon of an extremal black hole in four dimensions and the conventional conformal mechanics is constructed in two different ways. The first approach makes use of the action-angle variables in the angular sector. The second scheme relies upon integrability of the system in the sense of Liouville.
Ladder operators can be useful constructs, allowing for unique insight and intuition. In fact, they have played a special role in the development of quantum mechanics and field theory. Here, we introduce a novel type of ladder operators, which map a scalar field onto another massive scalar field. We construct such operators, in arbitrary dimensions, from closed conformal Killing vector fields, eigenvectors of the Ricci tensor. As an example, we explicitly construct these objects in anti-de Sitter spacetime (AdS) and show that they exist for masses above the Breitenlohner-Freedman (BF) bound. S…
A method of calculating the vacuum effective action for massive quantum fields in curved space-time is outlined. Our approach is based on the conformal representation of the fields action and on the integration of the corresponding conformal anomaly. As a relevant cosmological application, we find that if taking the masses of the fields into account, then the anomaly-induced inflation automatically slows down. The only relevant massive fields for this purpose turn out to be the fermion fields. So in supersymmetric theories this mechanism can be specially efficient, for it may naturally provide…
