We consider electromagnetic fields and charged particle dynamics around non-singular black holes in conformal gravity immersed in an external, asymptotically uniform magnetic field. First, we obtain analytic solutions of the electromagnetic field equation around rotating non-singular black holes in conformal gravity. We show that the radial components of the electric and magnetic fields increase with the increase of the parameters $L$ and $N$ of the black hole solution. Second, we study the dynamics of charged particles. We show that the increase of the values of the parameters $L$ and $N$ and of magnetic field causes a decrease in the radius of the innermost stable circular orbits (ISCO) and the magnetic coupling parameter can mimic the effect of conformal gravity giving the same ISCO radius up to $ω_{\rm B}\leq 0.07$ when $N=3$.
This paper discusses the effect that conformal symmetry can have on a charged wormhole. The analysis yields a physical interpretation of the conformal factor in terms of the electric charge. The rate of change of the conformal factor determines much of the outcome, which ranges from having no solution to wormholes having either one or two throats.
We study the Klein-Gordon equation of a scalar field conformally coupled to a charged BTZ black hole. The background metric is obtained by coupling a non-linear and conformal invariant Maxwell field to (2+1) gravity. We show that the radial part is generally solved by a Heun function and, in the pure gravity limit, by a hypergeometric function.
Considering cylindrical topology we present the static solution for a charged black hole in conformal gravity. We show that unlike the general relativistic case there are two different solutions, both including a factor that when set to zero recovers the familiar static charged black string solution in Einstein's theory. This factor gives rise to a linear term in the potential that also features in the neutral case and may have significant ramifications for particle trajectories.
We continue our study in 4-dimension to derive non-charged and charged (Anti)-de Sitter black hole solutions in conformal teleparallel equivalent of general relativity. The non-charged and charged equations of motion are applied to a spherically symmetric tetrad and the non-linear differential equations are derived. It is shown that the output solutions of the two cases are identical to those obtained in teleparallel equivalent theory to general relativity. As a result, it is found that in the conformal teleparallel equivalent theory to general relativity, the scalar field cannot influence on …
Motivated by the recent work of the hidden conformal symmetry of the Kerr black hole, we investigate the hidden conformal symmetry of a Kerr-Sen black hole and a Kerr-Newman-Kasuya black hole. Our result shows the conformal symmetry is spontaneously broken due to the periodicity of the azimuthal angle. The absorption across section is in consistence with the finite temperature absorption cross section for a 2D CFT. The entropies of the black holes are reproduced by the Cardy formula.
Using a C-metric-type ansatz, we obtain an exact solution to conformal gravity coupled to a Maxwell electromagnetic field. The solution resembles a C-metric spacetime carrying an electromagnetic charge. The metric is cast in a factorised form which allows us to study the domain structure of its static coordinate regions. This metric reduces to the well-known Mannheim-Kazanas metric under an appropriate limiting procedure, and also reduces to the (Anti-)de Sitter C-metric of Einstein gravity for a particular choice of parameters.
In this paper, model of charged gravastar under $f(T)$ modified gravity is obtained. The model has been explored by taking the diagonal tetrad field of static spacetime together with electric charge. To solve the Einstein-Maxwell field equations, along with $f(T)$ gravity, we assume the existence of a conformal Killing vector which relates between geometry and matter through the Einstein-Maxwell field equations by an inheritance symmetry. We study several cases of interest to explore physically valid features of the solutions. Some physical properties of the model are discussed and we match ou…
We propose a new model of a {\it gravastar} admitting conformal motion. While retaining the framework of the Mazur-Mottola model, the gravastar is assumed to be internally charged, with an exterior defined by a Reissner-Nordstr{ö}m rather than a Schwarzschild line element. The solutions obtained involve (i) the interior region, (ii) the shell, and (iii) the exterior region of the sphere. Of these three cases the first case is of primary interest since the total gravitational mass vanishes for vanishing charge and turns the total gravitational mass into an {\it electromagnetic mass} under certa…
We present a generalisation of the charged C-metric conformally coupled with a scalar field in the presence of a cosmological constant. The solution is asymptotically flat or a constant curvature spacetime. The spacetime metric has the geometry of a usual charged C-metric with cosmological constant, where the mass and charge are equal. When the cosmological constant is absent it is found that the scalar field only blows up at the angular pole of the event horizon. The presence of the cosmological constant can generically render the scalar field regular where the metric is regular, pushing the …
We study 4-dimensional non-charged and charged spherically symmetric spacetimes in conformal teleparallel equivalent of general relativity. We apply the gravitational field equations in non-charged and charged spacetimes to the diagonal and non-diagonal vierbeins and derive their sets of the non-linear differential equations. It is demonstrated that the Schwarzschild, for the non-charged case, and the Reissner-Nordström, for the charged case, are the only black hole solutions for the spherically symmetric case in the framework of the conformal teleparallel equivalent of general relativity theo…
In this work, we study the issue of the past and future cosmological singularities in the context of the fourth-order conformal Weyl gravity. In particular, we investigate the emergent universe scenario proposed by Ellis {\it et al}, and find the stability conditions of the corresponding Einstein static state using the fixed point approach. We show that depending on the values of the parameters of the conformal Weyl gravity theory, there are possibilities for having initially stable emergent states for an FRW universe with both the positive and negative spatial curvatures. This represents that…
We study the sparsity of Hawking radiation from nonrotating singularity-free black holes in conformal gravity. We give a rigorous bound on the greybody factor for massless scalar field and calculate the sparsity of Hawking radiation from the black hole. Besides, we investigate the dependence of the greybody factor and the sparsity of Hawking radiation on the conformal parameters. Our study shows that the Hawking radiation from the black hole is extremely sparse. When the conformal parameters are large, the increase of conformal parameters will lead to an even more sparse Hawking radiation, whi…
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…
Conformal gravity can elegantly solve the problem of spacetime singularities present in Einstein's gravity. For every physical spacetime, there is an infinite family of conformally-equivalent singularity-free metrics. In the unbroken phase, every non-singular metric is equivalent and can be used to infer the physical properties of the spacetime. In the broken phase, a Higgs-like mechanism should select a certain vacuum, which thus becomes the physical one. However, in the absence of the complete theoretical framework we do not know how to select the right vacuum. In this paper, we study the en…
New solutions for $(2+1)$-dimensional Einstein-Maxwell space-time are found for a static spherically symmetric charged fluid distribution with the additional condition of allowing conformal killing vectors (CKV). We discuss physical properties of the fluid parameters. Moreover, it is shown that the model actually represents two structures, namely (i) Gravastar as an alternative of black hole and (ii) Electromagnetic Mass model depending on the nature of the equation state of the fluid. Here the gravitational mass originates from electromagnetic field alone. The solutions are matched with the e…
This paper investigates the influence of charge on physical features of gravastars in the framework of energy-momentum squared gravity. A gravastar is an alternate model to a black hole that comprises of three distinct regions, namely the intermediate shell, inner and outer sectors. Different values of the barotropic equation of state parameter provide the mathematical formulation for these regions. We construct the structure of a gravastar admitting conformal motion for a specific model of energy-momentum squared gravity. The field equations are formulated for a spherically symmetric spacetim…
We consider the family of singularity-free rotating black hole solutions in Einstein's conformal gravity found in Bambi, Modesto & Rachwal (2017) and we constrain the value of the conformal parameter $L$ from the analysis of a 30 ks NuSTAR observation of the stellar-mass black hole in GS 1354-645 during its outburst in 2015. Our new constraint is much stronger than that found in previous work. Here we obtain $L/M < 0.12$ (99% confidence level, statistical uncertainty only).
An exact analytical solution describing the interior of a charged strange quark star is found under the assumption of spherical symmetry and the existence of a one-parameter group of conformal motions. The solution describes a unique static charged configuration of quark matter with radius $R=9.46$ km and total mass $M=2.86M_{\odot}$.
A non-singular exact black hole solution in General Relativity is presented. The source is a non-linear electromagnetic field, which reduces to the Maxwell theory for weak field. The solution corresponds to a charged black hole with |q| \leq 2s_c m \approx 0.6 m, having metric, curvature invariants, and electric field bounded everywhere.
We study analytically the spacelike singularity inside a spherically-symmetric, charged black hole coupled to a self-gravitating spherical massless scalar field. We assume spatial homogeneity, and find a generic solution in terms of a formal series expansion. This solution is tested against fully-nonlinear and inhomogeneous numerical simulations. We find full compliance between our analytical solution and the pointwise behavior of the singularity in the numerical simulations. This is a strong scalar-curvature monotonic spacelike singularity, which connects to a weak null singularity at asympto…
In this paper we study the Hawking radiation in Reissner-Nordstrom and Kerr-Newman black holes by considering the charge to be the function of radial coordinate.
The covariant phase technique is used to compute the constraint algebra of the stationary axisymmetric charged black hole. A standard Virasoro subalgebra with corresponding central charge is constructed at a Killing horizon with Carlip's boundary conditions. For the Kerr-Newman black hole and the Kerr-Newman-AdS black hole, the density of states determined by conformal fields theory methods yields the statistical entropy which agrees with the Bekenstein-Hawking entropy.
This paper studies the effects of charge on a peculiar stellar object, recognized as gravastar, under the influence of $f(R,T)$ gravity by considering the conjecture of Mazur and Mottola in general relativity. The gravastar is also known as an alternative to a black hole and is expressed by three distinct domains named as (i) the interior domain, (ii) the intermediate shell and (iii) the exterior domain. We analyze these domains for a specific $f(R,T)$ gravity model conceding the conformal Killing vectors. In the interior domain, we assume that pressure is equal to negative energy density whic…
The extended thermodynamics of static charged AdS black holes in conformal gravity is analyzed. The $P-V$ criticality of these black holes has some unusual features. There exists a single critical point with critical temperature $T_c$ and critical pressure $P_c$. At fixed $T>T_c$ (or at fixed $P>P_c$), there are two zeroth order phase transition points but no first order phase transition points. The systems favors large pressure states at constant $T$, or high temperature states at constant $P$.
We study analytically the features of the Cauchy horizon (CH) singularity inside a spherically-symmetric charged black hole, nonlinearly perturbed by a self-gravitating massless scalar field. We derive exact expressions for the divergence rate of the blue-shift factors, namely the derivatives in the outgoing direction of the scalar field $Φ$ and the area coordinate $r$. Both derivatives are found to grow along the contracting CH exactly like $1/r$. Our results are valid everywhere along the CH singularity, up to the point of full focusing. These exact analytic expressions are verified numerica…
We construct a conformal scattering theory for Dirac fields in the interior of a Reissner-Nordström-like black hole, between the black hole event horizon and the Cauchy horizon. The main result is a resolution of the characteristic Cauchy problem for the Dirac equation on the horizons by solving a system of wave equations and re-interpreting its solution as the components of the required Dirac solution.
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…
Original abstract: Consider the worldline of a charged particle in a static spacetime. Contraction of the time-translation Killing field with the retarded electromagnetic energy-momentum tensor gives a conserved electromagnetic energy vector which can be used to define the radiated electromagnetic energy. This note points out that for a conformally flat spacetime, the radiated energy is the same as for a flat spacetime (i.e. Minkowski space). This appears to be inconsistent with an equation of motion for such particles derived by DeWitt and Brehme and later corrected by Hobbs [End of original …
Inspired by the observations of supermassive black hole M87* in \emph{Event Horizon Telescope }(EHT) experiment, a remarkable surge in black hole physics is to use the black hole shadow's observables to distinguish general relativity (GR) and modified theories of gravity (MoG), which could also help to disclose the astrophysical nature of the center black hole in EHT observation. In this paper, we shall extensively carry out the study of a charged rotating black hole in conformal gravity, in which the term related with the charge has different falloffs from the usual Kerr-Newman (KN) black hol…
A widespread solution-generating technique of general relativity consists of conformally transforming known `seed' solutions. It is shown that these new solutions always solve the field equations of a pathological Brans-Dicke theory. Furthermore, when interpreted as effective Einstein equations,those field equations exhibit, in the case of a cosmological `background', an induced imperfect fluid as an additional effective source besides the original sources of the `seed' solutions. As an application, the charged non-rotating Thakurta black hole conformal to Reissner-Nordstrom is used to demonst…
The time-like naked singularities of the electrically and magnetically charged black hole solutions obtained in a model of nonlinear electrodynamics proposed by Kruglov is investigated within the framework of quantum mechanics. In view of quantum mechanics, the space-time is quantum regular provided that the time evolution of the test quantum wave packet uniquely propagates on an underlying background. Rigorous calculations have shown that when the singularity is probed with specific quantum wave/particle modes, the quantum wave operator turns out to be essentially self-adjoint. Thus, the time…
We obtain the charged rotating black hole in conformal gravity. The metric is asymptotic to the (anti-)de Sitter spacetime. The contribution to the metric from the charges has a slower falloff than that in the Kerr-Newman AdS black hole. We analyse the global structure and obtain all the thermodynamical quantities including the mass, angular momentum, electric/magnetic charges and their thermodynamical conjugates. We verify that the first law of thermodynamics holds. We also obtain the new neutral rotating black holes that are beyond Einstein metrics. In contrast to the static ones, these rota…
We study some general properties of two black hole solutions in Einstein's conformal gravity. Both solutions can be obtained from the Kerr metric with a suitable conformal rescaling, which leads, respectively, to a regular and a singular spacetime. In addition to the mass $M$ and the spin angular momentum $J$ of the black hole, these solutions are characterized by a new parameter, $L$, which may be expected to be of the order of the black hole mass. We study the geodesic motion and we calculate the radiative efficiency of a putative accretion disk around these black holes, which allows us to g…
We study the stability of new neutral and electrically charged four-dimensional black hole solutions of Einstein's equations with a positive cosmological constant and conformally coupled scalar field. The neutral black holes are always unstable. The charged black holes are also shown analytically to be unstable for the vast majority of the parameter space of solutions, and we argue using numerical techniques that the configurations corresponding to the remainder of the parameter space are also unstable.
Charged fluids rotating around compact objects can form unique equilibrium structures when ambient large-scale electromagnetic fields combine with strong gravity. Equatorial as well as off-equatorial toroidal structures are among such figures of equilibrium with a direct relevance for astrophysics. To investigate their geometrical shapes and physical properties in the near-horizon regime, where effects of general relativity play a significant role, we commonly employ a scheme based on the energy-momentum conservation written in a standard representation. Here, we develop its interesting altern…
We examine the motion of a charged particle in the vicinity of a weakly magnetized naked singularity. The escape velocity and energy of the particle moving around the naked singularity after being kicked by another particle or photon are investigated. Also at the innermost stable circular orbit (ISCO) escape velocity and energy are examined. Effective potential and angular momentum of the particle are also discussed. We discuss the center of mass energy after collision between two particles having same mass and opposite charges moving along the same circular orbit in the opposite direction. It…
In this paper, we consider $F(R)=R+f(R)$ theory instead of Einstein gravity with conformal anomaly and look for its analytical solutions. Depending on the free parameters, one may obtain both uncharged and charged solutions for some classes of $F(R)$ models. Calculation of Kretschmann scalar shows that there is a singularity located at $r=0$, which the geometry of uncharged (charged) solution is corresponding to the Schwarzschild (Reissner-Nordström) singularity. Further, we discuss the viability of our models in details. We show that these models can be stable depending on their parameters an…
We study the inner-structure of a charged black-hole which is formed from the gravitational collapse of a self-gravitating charged scalar-field. Starting with a regular spacetime, we follow the evolution through the formation of an apparent horizon, a Cauchy horizon and a final central singularity. We find a null, weak, mass-inflation singularity along the Cauchy horizon, which is a precursor of a strong, spacelike singularity along the $r=0$ hypersurface.
We analyse spacetimes with a conformal scalar field source, a cosmological constant and a quartic self-interaction term for the scalar field. We also consider additional matter contents in the form of Maxwell and Yang-Mills fields or radiation fluids. Existence theorems for weakly asymptotically flat spacetimes are given. We give a generalisation of Bekenstein's result [Ann. Phys. 82, 535 (1974)] and use it to derive existence theorems for spacetimes that contain an isotropic singularity. The results are combined to suggest a mathematical setup for Penrose's CCC scenario using a conformal scal…
Quantum effects due to particle creation on a classical sudden singularity have been investigated in a previous work. The conclusion was that quantum effects do not lead to the avoidance nor the modification of the sudden future singularity. In this paper, we investigate quantum corrections coming from conformal anomaly near the sudden future singularity. We conclude that when the equation of state is chosen to be $p=-ρ-Aρ^α$, the conformal anomaly can transform the sudden singularity in the singularity of type III for any $α> 1/2$ and in the singularity of the type I (the big rip) or the big …
The nonextremal Kerr black holes have been considered to be holographically dual to two-dimensional (2D) conformal field theories (CFTs). In this paper, we extend the holography to the case of an asymptotically anti--de Sitter (AdS) rotating charged black holes in $f$($T$) gravity, where $f(T) = T + αT^2$, where $α$ is a constant. We find that the scalar wave radial equation at the near-horizon region implies the existence of the 2D conformal symmetries. We note that the $2π$ identification of the azimuthal angle $ϕ$ in the black hole line element, corresponds to a spontaneous breaking of the …
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).
We present a method to construct conformally curved initial data for charged black hole binaries with spin on arbitrary orbits. We generalize the superposed Kerr-Schild, extended conformal thin sandwich construction from [Lovelace et al., Phys. Rev. D {78}, 084017 (2008)] to use Kerr-Newman metrics for the superposed black holes and to solve the electromagnetic constraint equations. We implement the construction in the pseudospectral code SGRID. The code thus provides a complementary and completely independent excision-based construction, compared to the existing charged black hole initial dat…
We obtain a newly charged BBMB (Bocharova-Bronnikov-Melnikov-Bekenstein) black hole solution from the Einstein-Weyl-Maxwell-conformal (conformally coupled) scalar theory with a positive Weyl coupling parameter $m^2_2$ numerically. This solution has a primary scalar hair, compared to a secondary scalar hair in the charged BBMB black hole solution. The limiting case of $m_2^2\to\infty$ leads to the series form of the charged BBMB black hole solution. However, for $m^2_2<0$, we could not obtain any asymptotically flat black hole solution with scalar hair.
Extending previous work on the formation and the evaporation of black holes in conformal gravity, in the present paper we study the gravitational collapse of a spherically symmetric and electrically charged thin shell of radiation. The process creates a singularity-free black hole. Assuming that in the evaporation process the charge $Q$ is constant, the final product of the evaporation is an extremal remnant with $M=Q$, which is reached in an infinite amount of time. We also discuss the issue of singularity and thermodynamics of black holes in Weyl's conformal gravity.
A new class of four-dimensional, hairy, stationary solutions of the Einstein-Maxwell-Lambda system with a conformally coupled scalar field is constructed in this paper. The metric belongs to the Plebanski-Demianski family and hence its static limit has the form of the charged C-metric. It is shown that, in the static case, a new family of hairy black holes arises. They turn out to be cohomogeneity-two, with horizons that are neither Einstein nor homogenous manifolds. The conical singularities in the C-metric can be removed due to the back reaction of the scalar field providing a new kind of re…
This is an extended version of the previous paper (hep-th/0701272). Quantum fields near horizons can be described in terms of an infinite set of two-dimensional conformal fields. We first generalize the method of Christensen and Fulling to charged black holes to derive fluxes of energy and charge. These fluxes can be obtained by employing a conformal field theory technique. We then apply this technique to obtain the fluxes of higher-spin currents and show that the thermal distribution of Hawking radiation from a charged black hole can be completely reproduced by investigating transformation pr…
We obtain scalar hairy black holes from Einstein-Maxwell-conformally coupled scalar (EMCS) theory with the scalar coupling parameter $α$ to the Maxwell term. In case of $α=0$, the $α=0$ EMCS theory provides constant (charged) scalar hairy black hole and charged BBMB (Bocharova-Bronnikov-Melnikov-Bekenstein) black hole where the former is stable against full perturbations, while the latter remains unstable because it belongs to an extremal black hole. It is noted that for $α\not=0$, the unstable Reissner-Nordström black holes without scalar hair imply infinite branches of $n=0(α\ge 8.019),1(α\g…
Is it possible the no-hair paradigm is violated when a black hole undergoes an instability? Employing massless charged scalar perturbations, we address this question within the context of conformally invariant Einstein-Maxwell theory for some allowed $d$-dimensional ($d=4n+4$ with conformal parameter $n=0,1,2,...$ ) topological small AdS black-holes. We provide numerical analyses that show the non trivial scalar hairy black hole solutions to include planar and spherical horizon topologies in higher dimensions with an even conformal parameter $n$. It is also shown that the solutions presented h…
We study the conformal structure of exotic (non-big-bang) singularity universes using the hybrid big-bang/exotic singularity/big-bang and big-rip/exotic singularity/big-rip models by investigating their appropriate Penrose diagrams. We show that the diagrams have the standard structure for the big-bang and big-rip and that exotic singularities appear just as the constant time hypersurfaces for the time of a singularity and because of their geodesic completeness are potentially transversable. We also comment on some applications and extensions of the Penrose diagram method in studying exotic si…
The infinite cosmological "constant" limit of the de Sitter solutions to Einstein's equation is studied. The corresponding spacetime is a singular, four-dimensional cone-space, transitive under proper conformal transformations, which constitutes a new example of maximally-symmetric spacetime. Grounded on its geometric and thermodynamic properties, some speculations are made in connection with the primordial universe.
