Greybody factor for a scalar field coupling to Einstein's tensor

We study the greybody factor and Hawking radiation for a scalar field coupling to Einstein's tensor in the background of Reissner–Nordström black hole in the low-energy approximation. We find that the presence of the coupling terms modifies the standard results in the greybody factor and Hawking radiation. Our results show that both the absorption probability and Hawking radiation increase with the coupling constant. Moreover, we also find that for the stronger coupling, the charge of black hole enhances the absorption probability and Hawking radiation of the scalar field, which is different from those of ones without coupling to Einstein's tensor in the black hole spacetime.     

Holographic Superconductor of Regular Phantom Black Hole

Holographic superconductors containing a non-minimal derivative coupling for the scalar field in a regular phantom plane symmetric black hole have been considered. We show that the parameter of the regular black hole b as well as the non-minimal derivative coupling parameter η affect the formation of the condensate as well as the conductivity in the superconductor. Moreover, b has a critical value in which the critical temperature T_c increases without a bound.     

A New Regular Black Hole

A spherically symmetric uncharged regular black hole is proposed in this paper. The black hole’s density in proportion to $r^{3n}e^{-r^{3n+3}}$ , and the curvature tensor in the region of r=0 keep finity. When n=0 in our model, this spacetime is no other than Dymnikova regular black hole. What’s more, there are better properties in this spacetime when n>0. We then discuss the temperature and Hawking radiation of the black hole’s horizon.     

Three-variable solution in the $$$$-dimensional null-surface formulation

The null-surface formulation of general relativity (NSF) describes gravity by using families of null surfaces instead of a spacetime metric. Despite the fact that the NSF is (to within a conformal factor) equivalent to general relativity, the equations of the NSF are exceptionally difficult to solve, even in 2+1 dimensions. The present paper gives the first exact \((2+1)\)-dimensional solution that depends nontrivially upon all three of the NSF’s intrinsic spacetime variables. The metric derived from this solution is shown to represent a spacetime whose source is a massless scalar field that satisfies the general relativistic wave equation and the Einstein equations with minimal coupling. The spacetime is identified as one of a family of \((2+1)\)-dimensional general relativistic spacetimes discovered by Cavaglià.     

Ricci nilsoliton black holes

We follow a constructive approach and find higher-dimensional black holes with Ricci nilsoliton horizons. The spacetimes are solutions to the Einstein equation with a negative cosmological constant and generalise therefore, Anti-de Sitter black hole spacetimes. The approach combines a work by Lauret–which relates the so-called Ricci nilsolitons and Einstein solvmanifolds–and an earlier work by the author. The resulting black hole spacetimes are asymptotically Einstein solvmanifolds and thus, are examples of solutions which are not asymptotically Anti-de Sitter. We show that any nilpotent group in dimension n≤6$n\le 6$ has a corresponding Ricci nilsoliton black hole solution in dimension (n+2)$(n+2)$. Furthermore, we show that in dimensions (n+2)>8$(n+2)>8$, there exist an infinite number of locally distinct Ricci nilsoliton black hole metrics.     

Black holes in the generalized Proca theory

We investigate static and spherically symmetric black hole solutions in the generalized Proca theory which corresponds to the generalization of the shift-symmetric scalar–tensor Horndeski theory to the vector–tensor theory. Any solution obtained in this paper possesses a constant spacetime norm of the vector field, \(X:=-\frac{1}{2}g^{\mu \nu }A_\mu A_\nu =X_0=\mathrm{constant}\). The solutions in the theory with generalized quartic coupling \(G_4(X)\) generalize the stealth Schwarzschild and the Schwarzschild- (anti-) de Sitter solutions obtained in the theory with the nonminimal coupling to the Einstein tensor \(G^{\mu \nu } A_\mu A_\nu \). While in the vector–tensor theory with the coupling \(G^{\mu \nu }A_\mu A_\nu \) the electric charge does not explicitly affect the spacetime geometry, in more general cases with nonzero \(G_{4XX}(X_0)\ne 0\) this property does not hold in general. The solutions in the theory with generalized cubic coupling \(G_3(X)\) are given by the Schwarzschild- (anti-) de Sitter spacetime, where the dependence on \(G_3(X)\) does not appear in the metric function.     

Weyl type N solutions with null electromagnetic fields in the Einstein–Maxwell <Emphasis Type="Italic">p</Emphasis>-form theory

We consider d-dimensional solutions to the electrovacuum Einstein–Maxwell equations with the Weyl tensor of type N and a null Maxwell \((p+1)\)-form field. We prove that such spacetimes are necessarily aligned, i.e. the Weyl tensor of the corresponding spacetime and the electromagnetic field share the same aligned null direction (AND). Moreover, this AND is geodetic, shear-free, non-expanding and non-twisting and hence Einstein–Maxwell equations imply that Weyl type N spacetimes with a null Maxwell \((p+1)\)-form field belong to the Kundt class. Moreover, these Kundt spacetimes are necessarily \({ CSI}\) and the \((p+1)\)-form is \({ VSI}\). Finally, a general coordinate form of solutions and a reduction of the field equations are discussed.     

Deflection of light by black holes and massless wormholes in massive gravity

Weak gravitational lensing by black holes and wormholes in the context of massive gravity (Bebronne and Tinyakov, JHEP 0904:100, 2009) theory is studied. The particular solution examined is characterized by two integration constants, the mass M and an extra parameter S namely ‘scalar charge’. These black hole reduce to the standard Schwarzschild black hole solutions when the scalar charge is zero and the mass is positive. In addition, a parameter \(\lambda \) in the metric characterizes so-called ‘hair’. The geodesic equations are used to examine the behavior of the deflection angle in four relevant cases of the parameter \(\lambda \). Then, by introducing a simple coordinate transformation \(r^\lambda =S+v^2\) into the black hole metric, we were able to find a massless wormhole solution of Einstein–Rosen (ER) (Einstein and Rosen, Phys Rev 43:73, 1935) type with scalar charge S. The programme is then repeated in terms of the Gauss–Bonnet theorem in the weak field limit after a method is established to deal with the angle of deflection using different domains of integration depending on the parameter \(\lambda \). In particular, we have found new analytical results corresponding to four special cases which generalize the well known deflection angles reported in the literature. Finally, we have established the time delay problem in the spacetime of black holes and wormholes, respectively.     

Hawking Radiation of Reissner-Nordstr<Emphasis Type="Italic">ö</Emphasis>m Black Hole in Electromagnetic Field with Einstein Tensor Corrections

In this paper, we have investigated the absorption probability and Hawking radiation of electromagnetic field while it coupling with Einstein tensor in the background of 4-dimensional Reissner-Nordström(RN) black hole spacetime. Our results indicate that the properties of the absorption probability and Hawking radiation depend not only on the coupling parameter, but also on the parity of the electromagnetic field, which is quite different from those of the usual electromagnetic field without coupling in the 4-dimensional spacetime.The absorption probability, power emission spectra and luminosity of Hawking radiation decreases with the increase of coupling parameter α when the coupled electromagnetic field have odd-parity, and increases with the increase of coupling parameter α when the coupled electromagnetic field have even-parity.     

Higher-dimensional black holes with Dirac–Born–Infeld (DBI) global defects

It is well-known that the exact solution of non-linear \(\sigma \) model coupled to gravity can be perceived as an exterior gravitational field of a global monopole. Here we study Einstein’s equations coupled to a non-linear \(\sigma \) model with Dirac–Born–Infeld (DBI) kinetic term in D dimensions. The solution describes a metric around a DBI global defects. When the core is smaller than its Schwarzschild radius it can be interpreted as a black hole having DBI scalar hair with deficit conical angle. The solutions exist for all D, but they can be expressed as polynomial functions in r only when D is even. We give conditions for the mass M and the scalar charge \(\eta \) in the extremal case. We also investigate the thermodynamic properties of the black holes in canonical ensemble. The monopole alter the stability differently in each dimensions. As the charge increases the black hole radiates more, in contrast to its counterpart with ordinary global defects where the Hawking temperature is minimum for critical \(\eta \). This behavior can also be observed for variation of DBI coupling, \(\beta \). As it gets stronger (\(\beta \ll 1\)) the temperature increases. By studying the heat capacity we can infer that there is no phase transition in asymptotically-flat spacetime. The AdS black holes, on the other hand, undergo a first-ordered phase transition in the Hawking–Page type. The increase of the DBI coupling renders the phase transition happen for larger radius.     

Black holes in the Brans-Dicke

It is shown that a stationary space containing a black hole is a solution of the Brans-Dicke field equations if and only if it is a solution of the Einstein field equations. This implies that when the star collapses to form a black hole, it loses that fraction (about 7%) of its measured gravitational mass that arises from the scalar interaction. This mass loss is in addition to that caused by emission of scalar or tensor gravitational radiation. Another consequence is that there will not be any scalar gravitational radiation emitted when two black holes collide.     

Quasinormal modes for tensor and vector type perturbation of Gauss Bonnet black hole using third order WKB approach

We obtain the quasinormal modes for tensor perturbations of Gauss–Bonnet (GB) black holes in d = 5, 7, 8 dimensions and vector perturbations in d = 5, 6, 7 and 8 dimensions using third order WKB formalism. The tensor perturbation for black holes in d = 6 is not considered because of the fact that the black hole is unstable to tensor mode perturbations. In the case of uncharged GB black hole, for both tensor and vector perturbations, the real part of the QN frequency increases as the Gauss–Bonnet coupling (α′) increases. The imaginary part first decreases upto a certain value of α′ and then increases with α′ for both tensor and vector perturbations. For larger values of α′, the QN frequencies for vector perturbation differs slightly from the QN frequencies for tensorial one. It has also been shown that as α′ → 0, the quasinormal frequencies for tensor and vector perturbations of the Schwarzschild black hole can be obtained. We have also calculated the quasinormal spectrum of the charged GB black hole for tensor perturbations. Here we have found that the real oscillation frequency increases, while the imaginary part of the frequency falls with the increase of the charge. We also show that the quasinormal frequencies for scalar field perturbations and the tensor gravitational perturbations do not match as was claimed in the literature. The difference in the result increases if we increase the GB coupling.     

$$$$-Dimensional charged black holes with scalar hair in Einstein–Power–Maxwell Theory

In \((2+1)\)-dimensional AdS spacetime, we obtain new exact black hole solutions, including two different models (power parameter \(k=1\) and \(k\ne 1\)), in the Einstein–Power–Maxwell (EPM) theory with nonminimally coupled scalar field. For the charged hairy black hole with \(k\ne 1\), we find that the solution contains a curvature singularity at the origin and is nonconformally flat. The horizon structures are identified, which indicates the physically acceptable lower bound of mass in according to the existence of black hole solutions. Later, the null geodesic equations for photon around this charged hairy black hole are also discussed in detail.     

Dilatons and the dynamical collapse of charged scalar field

We studied the influence of dilaton field on the dynamical collapse of a charged scalar one. Different values of the initial amplitude of dilaton field as well as the altered values of the dilatonic coupling constant were considered. We described structures of spacetimes and properties of black holes emerging from the collapse of electrically charged scalar field in dilaton gravity. Moreover, we provided a meaningful comparison of the collapse in question with the one in Einstein gravity, when dilaton field is absent and its coupling with the scalar field is equal to zero. The course and results of the dynamical collapse process seem to be very sensitive to the amplitude of dilaton field and to the value of the coupling constant in the underlying theory.     

A new (original) set of Quasi-normal modes in spherically symmetric AdS black hole spacetimes

From black hole perturbation theory, quasi-normal modes (QNMs) in spherically symmetric AdS black hole spacetimes are usually studied with the Horowitz and Hubeny methods [1] by imposing the Dirichlet or vanishing energy flux boundary conditions. This method was constructed using the scalar perturbation case and box-like effective potentials, where the radial equation tends to go to infinity when the radial coordinate approaches infinity. These QNMs can be realized as a different set of solutions from those obtained by the barrier-like effective potentials. However, in some cases the existence of barrier-like effective potentials in AdS black hole spacetimes can be found. In these cases this means that we would obtain a new (original) set of QNMs by the purely ingoing and purely outgoing boundary conditions when the radial coordinate goes to the event horizon and infinity, respectively. Obtaining this set of QNMs in AdS black hole cases is the main focus of this paper.     

On the Backward Stability of the Schwarzschild Black Hole Singularity

We study the backwards-in-time stability of the Schwarzschild singularity from a dynamical PDE point of view. More precisely, considering a spacelike hypersurface \({\Sigma_0}\) in the interior of the black hole region, tangent to the singular hypersurface \({\{r = 0\}}\) at a single sphere, we study the problem of perturbing the Schwarzschild data on \({\Sigma_0}\) and solving the Einstein vacuum equations backwards in time. We obtain a local backwards well-posedness result for small perturbations lying in certain weighted Sobolev spaces. No symmetry assumptions are imposed. The perturbed spacetimes all have a singularity at a “collapsed” sphere on \({\Sigma_0}\), where the leading asymptotics of the curvature and the metric match those of their Schwarzschild counterparts to a suitably high order. As in the Schwarzschild backward evolution, the pinched initial hypersurface \({\Sigma_0}\) ‘opens up’ instantly, becoming a regular spacelike (cylindrical) hypersurface. This result thus yields classes of examples of non-symmetric vacuum spacetimes, evolving forward-in-time from regular initial data, which form a Schwarzschild type singularity at a collapsed sphere. We rely on a precise asymptotic analysis of the Schwarzschild geometry near the singularity which turns out to be at the threshold that our energy methods can handle.     

Gravitational collapse of charged scalar fields

In order to study the gravitational collapse of charged matter we analyze the simple model of an self-gravitating massless scalar field coupled to the electromagnetic field in spherical symmetry. The evolution equations for the Maxwell–Klein–Gordon sector are derived in the \(3+1\) formalism, and coupled to gravity by means of the stress–energy tensor of these fields. To solve consistently the full system we employ a generalized Baumgarte–Shapiro–Shibata–Nakamura formulation of General Relativity that is adapted to spherical symmetry. We consider two sets of initial data that represent a time symmetric spherical thick shell of charged scalar field, and differ by the fact that one set has zero global electrical charge while the other has non-zero global charge. For compact enough initial shells we find that the configuration doesn’t disperse and approaches a final state corresponding to a sub-extremal Reissner–Nördstrom black hole with \(|Q| . By increasing the fundamental charge of the scalar field \(q\) we find that the final black hole tends to become more and more neutral. Our results support the cosmic censorship conjecture for the case of charged matter.     

A no-hair theorem for spherically symmetric black holes in $$R^2$$ gravity

In a recent paper Cañate (Class Quantum Grav 35:025018, 2018) proved a no hair theorem to static and spherically symmetric or stationary axisymmetric black holes in general f(R) gravity. The theorem applies for isolated asymptotically flat or asymptotically de Sitter black holes and also in the case when vacuum is replaced by a minimally coupled source having a traceless energy momentum tensor. This theorem excludes the case of pure quadratic gravity, \(f(R) = R^2\). In this paper we use the scalar tensor representation of general f(R) theory to show that there are no hairy black hole in pure \(R^2\) gravity. The result is limited to spherically symmetric black holes but does not assume asymptotic flatness or de-Sitter asymptotics as in most of the no-hair theorems encountered in the literature. We include an example of a static and spherically symmetric black hole in \(R^2\) gravity with a conformally coupled scalar field having a Higgs-type quartic potential.