We propose a new model of the spherical symmetric quantum black hole in the reduced phase space formulation. We deparametrize gravity by coupling to the Gaussian dust which provides the material coordinates. The foliation by dust coordinates covers both the interior and exterior of the black hole. After the spherical symmetry reduction, our model is a 1+1 dimensional field theory containing infinitely many degrees of freedom. The effective dynamics of the quantum black hole is generated by an improved physical Hamiltonian ${\bf H}_Δ$ where the holonomy correction is implemented by the $\barμ$-scheme regularization with a Planckian area scale $Δ$. The effective dynamics recovers the semiclassical Schwarzschild geometry at low curvature regime and resolves the black hole singularity with Planckian curvature. Our model predicts that the evolution of the black hole at late time reaches the charged Nariai geometry ${\rm dS}_2\times S^2$ with Planckian radii. The Nariai geometry is stable under linear perturbations but may be unstable by nonperturbative quantum effects. Our model suggests the existence of quantum tunneling of the Nariai geometry and a scenario of black-hole-to-white-hole transition. During the transition, the linear perturbations exhibit chaotic dynamics with Lyapunov exponent $λ=2πT_{\rm dS}\sim Δ^{-1/2}$ relating to the Hawking temperature $T_{\rm dS}$ of ${\rm dS}_2$. In addition, the Nariai geometry in our model provides an interesting example of Wheeler's bag of gold and contains infinitely many infrared soft modes with zero energy density. These infrared modes span a Hilbert space carrying a representation of 1-dimensional spatial diffeomorphisms (or the Witt/Virasoro algebra) which are conserved charges of the effective dynamics by ${\bf H}_Δ$.
We study the problem of a four-dimensional brane lying in the five-dimensional degenerate Schwarzschild-de Sitter (Nariai) black hole, in five-dimensional $F(R)$-gravity. We show that there cannot exist the brane in the Nariai bulk space except the case that the brane tension vanishes. We demonstrate that the five-dimensional Nariai bulk is unstable in a large region of the parameter space. In particular, the Nariai bulk can have classical (anti-)evaporation instabilities. The bulk instability back-reacts on the four-dimensional brane, in case that the brane tension vanishes, and the unstable …
In this paper, we have presented interesting properties of the static charged Born-Infeld-de Sitter black hole. They can have time-like as well as space-like singularities depending on the parameters of the theory. The degenerate black holes lead to cold, ultra cold and Nariai black holes. The geometry of such black holes are discussed. A comparison is done with the Reissner-Nordstrom-de Sitter black holes.
The product spacetimes of constant curvature describe in Einstein gravity, which is linear in Riemann curvature, Nariai metric which is a solution of $Λ$-vacuum when curvatures are equal, $k_1=k_2$, while it is Bertotti-Robinson metric describing uniform electric field when curvatures are equal and opposite, $k_1=-k_2$. We probe pure Lovelock gravity by these simple product spacetimes and prove that the same characterization of these solutions is indeed true in general for pure Lovelock gravitational equation of order $N$ in $d=2N+2$ dimension. We also consider these solutions for the conventi…
Cosmological solutions derived by Nariai and Tomita (1971) and by Starobinsky (1980) are compared, and it is shown that the former derived de Sitter expansion in the R^2 modified gravity (without cosmological constant) at the earliest stage, and nine years later the latter derived the well-known inflationary solution. Next the property of their simplified models is described using the method of conformal transformations, and how the inflation arises and the singularity is avoided is shown. Finally the initial and final states of the inflation are discussed.
We discuss semiclassical Nariai black holes in the framework of $f(T)$-gravity. For a diagonal choice of tetrades, stable Nariai metrics can be found, emitting Bekenstein-Hawking radiation in semiclassical limit. However, for a non-diagonal choice of tetrades, evaporation and antievaporation instabilities are turned on. In turn, this causes a back-reaction effect suppressing the Bekenstein-Hawking radiation. In particular, evaporation instabilities produce a new radiation -- different by Bekenstein-Hawking emission -- non-violating unitarity in particle physics sector.
We investigate the future evolution of Nariai black hole which is extremal limit of Schwarzschild-de Sitter one in modified gravity. The perturbations equations around Nariai black hole are derived in static and cosmological patches for general $F(R)$-gravity. The analytical and numerical study of several realistic $F(R)$-models shows the occurence of rich variety of scenarios: instabilities, celebrated Hawking evaporation and anti-evaporation of black hole. The realization of specific scenario depends on the model under consideration. It is remarkable that the presence of such primordial blac…
In recent work, the Schwarzschild interior of a black hole was investigated, incorporating quantum gravitational modifications due to loop quantum gravity. The central Schwarzschild singularity was shown to be replaced by a Nariai type universe. In this brief report we show that this interior solution is stable with respect to small perturbations, in contrast to the classical Nariai universe.
We discuss the evaporation and antievaporation instabilities of Nariai solution in extended theories of gravity. These phenomena were explicitly shown in several different extensions of General Relativity, suggesting that a universal cause is behind them. We show that evaporation and antievaporation are originated from deformations of energy conditions on the Nariai horizon. Energy conditions get new contributions from the extra propagating degrees of freedom, which can provide extra focalizing or antifocalizing terms in the Raychanduri equation. We also show two explicit examples in $f(R)$-gr…
We studied the anti-evaporation of degenerate Schwarzschild-de Sitter black hole (so-called Nariai space-time) in modified $F(R)$ gravity. The analysis of perturbations of the Nariai black hole is done with the conclusion that anti-evaporation may occur in such a theory already on classical level. For several power-law $F(R)$ gravities which may describe the inflation and/or dark energy eras we presented the theory parameters bounds for occurrence of anti-evaporation and conjectured creation of infinite number of horizons.
The semiclassical effects of antievaporating black holes can be discussed in the framework of $f(R)$ gravity. In particular, the Bousso-Hawking-Nojiri-Odinstov antievaporation instability of degenerate Schwarzschild-de Sitter black holes (the so called Nariai space-time) leads to a dynamical increasing of black hole horizon in $f(R)$ gravity. This phenomenon causes the following transition: emitting marginally trapped surfaces become space-like surfaces before the effective Bekenstein-Hawking emission time. As a consequence, Bousso-Hawking thermal radiation cannot be emitted in an antievaporat…
Using the improved quantization technique to the mini-superspace approximation of loop quantum gravity, we study the evolution of black holes supported by a cosmological constant. The addition of a cosmological constant allows for classical solutions with planar, cylindrical, toroidal and higher genus black holes. Here we study the quantum analog of these space-times. In all scenarios studied, the singularity present in the classical counter-part is avoided in the quantized version and is replaced by a bounce, and in the late evolution, a series of less severe bounces. Interestingly, although …
Extremal cosmological black holes are analysed in the framework of the most general second order scalar-tensor theory, the~so-called Horndeski gravity. Such~extremal black holes are a particular case of Schwarzschild-De Sitter black holes that arises when the black hole horizon and the cosmological one coincide. Such~metric is induced by a particular value of the effective cosmological constant and is known as Nariai spacetime. The~existence of this type of solutions is studied when considering the Horndeski Lagrangian and its stability is analysed, where the so-called anti-evaporation regime …
The wave function of the universe is usually taken to be a functional of the three-metric on a spacelike section, Sigma, which is measured. It is sometimes better, however, to work in the conjugate representation, where the wave function depends on a quantity related to the second fundamental form of Sigma. This makes it possible to ensure that Sigma is part of a Lorentzian universe by requiring that the argument of the wave function be purely imaginary. We demonstrate the advantages of this formalism first in the well-known examples of the nucleation of a de Sitter or a Nariai universe. We th…
We construct solutions of higher-dimensional Einstein gravity coupled to nonlinear $σ$-model with cosmological constant. The $σ$-model can be perceived as exterior configuration of a spontaneously-broken $SO(D-1)$ global higher-codimensional "monopole". Here we allow the kinetic term of the $σ$-model to be noncanonical; in particular we specifically study a quadratic-power-law type. This is some possible higher-dimensional generalization of the Bariola-Vilenkin (BV) solutions with $k$-global monopole studied recently. The solutions can be perceived as the exterior solution of a black hole swal…
We study static black hole solutions in Einstein and Einstein-Gauss-Bonnet gravity with product two-spheres topology, ${\bf SO(n) \times SO(n)}$, in higher dimensions. There is an unusual new feature of Gauss-Bonnet black hole that the avoidance of non-central naked singularity prescribes a mass range for black hole in terms of $Λ>0$. For Einstein-Gauss-Bonnet black hole a limited window of negative values for $Λ$ is also permitted. This topology encompasses black string and brane as well as a generalized Nariai metric. We also give new solutions with product two-spheres of constant curvatures…
We study static black holes in quadratic gravity with planar and hyperbolic symmetry and non-extremal horizons. We obtain a solution in terms of an infinite power-series expansion around the horizon, which is characterized by two independent integration constants -- the black hole radius and the strength of the Bach tensor at the horizon. While in Einstein's gravity, such black holes require a negative cosmological constant $Λ$, in quadratic gravity they can exist for any sign of $Λ$ and also for $Λ=0$. Different branches of Schwarzschild-Bach-(A)dS or purely Bachian black holes are identified…
We propose a new $\barμ$-scheme Hamiltonian effective dynamics in the spherical symmetric sector of Loop Quantum Gravity (LQG). The effective dynamics is generally covariant as derived from a covariant Lagrangian. The Lagrangian belongs to the class of extended mimetic gravity Lagrangians in 4 dimensions. We apply the effective dynamics to both cosmology and black hole. The effective dynamics reproduces the non-singular Loop-Quantum-Cosmology (LQC) effective dynamics. From the effective dynamics, we obtain the non-singular black hole solution, which has a killing symmetry in addition to the sp…
Kaluza-Klein reduction of 3D gravity with minimal scalars leads to 2D dilaton-Maxwell gravity with dilaton coupled scalars. Evaluating the one-loop effective action for dilaton coupled scalars in large $N$ and s-wave approximation we apply it to study quantum evolution of BTZ black hole. It is shown that quantum-corrected BTZ BH may evaporate or else anti-evaporate similarly to 4D Nariai BH as is observed by Bousso and Hawking. Instable higher modes in the spectrum indicate also the possibility of proliferation of BTZ BH.
Owing to the quadratic nature of the theory, Einstein-Gauss-Bonnet gravity generically permits two distinct vacuum solutions. One solution (the "Einstein" vacuum) has a well defined limit as the Gauss-Bonnet coupling goes to zero, whereas the other solution (the "stringy" vacuum) does not. There has been some debate regarding the stability of these vacua, most recently from Deser and Tekin who have argued that the corresponding black hole solutions have positive mass and as such both vacua are stable. Whilst the statement about the mass is correct, we argue that the stringy vacuum is still per…
We study gravitational perturbations of electrically charged black holes in (3+1)-dimensional Einstein-Born-Infeld gravity with a positive cosmological constant. For the axial perturbations, we obtain a set of decoupled Schrodinger-type equations, whose formal expressions, in terms of metric functions, are the same as those without cosmological constant, corresponding to the Regge-Wheeler equation in the proper limit. We compute the quasi-normal modes (QNMs) of the decoupled perturbations using the Schutz-Iyer-Will's WKB method. We discuss the stability of the charged black holes by investigat…
Limits on the Statistical Description of Charged de Sitter Black Holes
University of Minnesota Duluth（明尼苏达大学德卢斯分校）；University of Wisconsin-Madison（威斯康星大学麦迪逊分校）；University of Amsterdam（阿姆斯特丹大学）；KTH Royal Institute of Technology（瑞典皇家理工学院）；Stockholm University（斯德哥尔摩大学）
We study the quantum modifications of classical, spherically symmetric Schwarzschild (Anti-) de Sitter black holes within Quantum Einstein Gravity. The quantum effects are incorporated through the running coupling constants $G_k$ and $Λ_k$, computed within the exact renormalization group approach, and a common scale-setting procedure. We find that, in contrast to common intuition, it is actually the cosmological constant that determines the short-distance structure of the RG-improved black hole: in the asymptotic UV the structure of the quantum solutions is universal and given by the classical…
We derive the field equations for topologically massive gravity coupled with the most general quadratic curvature terms using the language of exterior differential forms and a first order constrained variational principle. We find variational field equations both in the presence and absence of torsion. We then show that spaces of constant negative curvature (i.e. the anti de-Sitter space $AdS_3$) and constant torsion provide exact solutions.
In this paper, we study the quasinormal modes of the massless Dirac field for charged black holes in Rastall gravity. The spherically symmetric black hole solutions in question are characterized by the presence of a power-Maxwell field, surrounded by the quintessence fluid. The calculations are carried out by employing the WKB approximations up to the thirteenth order, as well as the matrix method. The temporal evolution of the quasinormal modes is investigated by using the finite difference method. Through numerical simulations, the properties of the quasinormal frequencies are analyzed, incl…
The theory of massive gravity in three dimensions recently proposed by Bergshoeff, Hohm and Townsend (BHT) is considered. At the special case when the theory admits a unique maximally symmetric solution, a conformally flat space that contains black holes and gravitational solitons for any value of the cosmological constant is found. For negative cosmological constant, the black hole is characterized in terms of the mass and the "gravitational hair" parameter, providing a lower bound for the mass. For negative mass parameter, the black hole acquires an inner horizon, and the entropy vanishes at…
We examine the Schwarzschild interior of a black hole, incorporating quantum gravitational modifications due to loop quantum gravity. We consider an improved loop quantization using techniques that have proven successful in loop quantum cosmology. The central Schwarzschild singularity is resolved and the implications for the fate of an in-falling test particle in the interior region is discussed. The singularity is replaced by a Nariai type Universe. We discuss the resulting conformal diagram, providing a clear geometrical interpretation of the quantum effects.
We propose a new derivation from the full Loop Quantum Gravity (LQG) to the Loop Quantum Cosmology (LQC) improved $\barμ$-scheme effective dynamics, based on the reduced phase space formulation of LQG and a proposal of effective Hamiltonian/action in the full LQG. A key step of our program is an improved regularization of the full LQG Hamiltonian on a cubic lattice. The improved Hamiltonian uses a set of "dressed holonomies" $h_Δ(\mathfrak{s})$ which not only depend on the connection $A$ but also depend on the length of the curve $\mathfrak{s}$. With the improved Hamiltonian, we propose a quan…
We investigate some properties of n(\ge 4)-dimensional spacetimes having symmetries corresponding to the isometries of an (n-2)-dimensional maximally symmetric space in Lovelock gravity under the null or dominant energy condition. The well-posedness of the generalized Misner-Sharp quasi-local mass proposed in the past study is shown. Using this quasi-local mass, we clarify the basic properties of the dynamical black holes defined by a future outer trapping horizon under certain assumptions on the Lovelock coupling constants. The C^2 vacuum solutions are classified into four types: (i) Schwarzs…
We have investigated the problem of traversability of wormholes in the framework of quantum improvement of gravity theory arising from functional renormalization group methods to describe the asymptotic safe quantum gravity. We have shown that improved pseudospherical wormholes could be traversable with non--exotic matter, while spherical ones could not. This is done within a specific model of improvement.
We generalize $f(R)$-theory of anti-evaporation/evaporation for a Reissner-Nordström black hole in $n$-dimensional space-time. We consider non-linear conformally invariant Maxwell field. By perturbing the fields over Nariai-like space-time associated with degenerate horizon, we describe dynamical behavior of horizon. We show that $f(R)$-gravity can offer both anti-evaporation and evaporation in $n$-dimensional Reissner-Nordström black hole depending on the dimension $n$ and the functional form of $f(R)$. Furthermore, we argue that, in one class of non-oscillatory solution, stable and unstable …
Theories such as massive Galileons and massive gravity can satisfy the presently known improved positivity bounds provided they are weakly coupled. We discuss the form of the EFT Lagrangian for a weakly coupled UV completion of massive gravity which closely parallels the massive Galileon, and perform the power counting of corrections to the scattering amplitude and the positivity bounds. The Vainshtein mechanism which is central to the phenomenological viability of massive gravity is entirely consistent with weak coupling since it is classical in nature. We highlight that the only implication …
The improved lattice regularization method of the Ashtekar connection holonomy representation in loop quantum gravity is described in this article. The approach is based on the geometric expansion of holonomies into power series up to the quadratic order terms in the regularization parameter. As a result, a more accurate procedure than the currently established approach to the canonical lattice quantization of gravity is obtained. Moreover, if holonomies are defined along linear links, this procedure becomes exact. Furthermore, in the improved method, the symmetry of holonomies assigned to lin…
The choice of the regularization scheme in Loop Quantum Cosmology (LQC) is crucial for the predicted phenomenology. We outline how the improved scheme can be naturally realized in Quantum Reduced Loop Gravity, describing the Universe as an ensemble of microstates labeled by different graphs. The new effective dynamics presents corrections to LQC, which do not significantly affect the bouncing scenario for the most relevant kinds of matter fields in cosmology $(w \leq 1)$.
We study static spherically symmetric solutions to the vacuum field equations of quadratic gravity in the presence of a cosmological constant $Λ$. Motivated by the trace no-hair theorem, we assume the Ricci scalar to be constant throughout a spacetime. Furthermore, we employ the conformal-to-Kundt metric ansatz that is valid for all static spherically symmetric spacetimes and leads to a considerable simplification of the field equations. We arrive at a set of two ordinary differential equations and study its solutions using the Frobenius-like approach of (infinite) power series expansions. Whi…
When it comes to searches for extensions to general relativity, large efforts are being dedicated to accurate predictions for the power spectrum of density perturbations. While this observable is known to be sensitive to the gravitational theory, its efficiency as a diagnostic for gravity is significantly reduced when Solar System constraints are strictly adhered to. We show that this problem can be overcome by studying weigthed density fields. We propose a transformation of the density field for which the impact of modified gravity on the power spectrum can be increased by more than a factor …
Improvement of the classical gravity with the running gravitational coupling obtained from asymptotically safe gravity, is a good way of considering the effects of quantum gravity. This is usually done for metric theories of gravity. Here we investigate the effects of such an improvement for pure affine theories of gravity. To motivate the approach, we first consider the effects of quantum improvement on the connection using metric theory and investigate the effects on the causal structure of black hole solution. Next in the framework of Schrödinger-Eddington affine theory, the general way of …
We consider a very general dilaton-axion system coupled to Einstein-Hilbert gravity in arbitrary dimension and we carry out holographic renormalization for any dimension up to and including five dimensions. This is achieved by developing a new systematic algorithm for iteratively solving the radial Hamilton-Jacobi equation in a derivative expansion. The boundary term derived is valid not only for asymptotically AdS backgrounds, but also for more general asymptotics, including non-conformal branes and Improved Holographic QCD. In the second half of the paper, we apply the general result to Impr…
As an extension of previous works on classical tests of Kaluza-Klein (KK) gravity and as an attempt to find more stringent constraints on this theory, its effects on physical experiments and astronomical observations conducted in the Solar System are studied. We investigate the gravitational time delay at inferior conjunction caused by KK gravity, and use new Solar System ephemerides and the observation of \textit{Cassini} to strengthen constraints on KK gravity by up to two orders of magnitude. These improved upper bounds mean that the fifth-dimensional space in the soliton case is a very fla…
When the semi-positive cosmological constant is dynamical, the naive Euclidean Einstein action is unbounded from below and the Hartle-Hawking wavefunction of the universe is not normalizable. With the inclusion of back-reaction (a crucial point), the presence of the metric perturbative modes (as well as matter fields) as the environment (that is, to be integrated or traced out) introduces a correction term that provides a bound to the Euclidean action. So the improved wavefunction is normalizable. That is, decoherence plays an essential role in the consistency of quantum gravity. In the sponta…
A set of features of the renormalization group improved Kerr spacetime taking into account the running of Newton's constant is presented. This set includes: Behavior of the critical surfaces and corrections to the mass and angular momentum of the Kerr black hole.
General relativity has two fundamental problems that render it unsuitable for tackling the gravitational field's quantization. The first problem is the lack of a genuine gravitational variable representing gravitation only, inertial forces apart. The second problem is its incompatibility with quantum mechanics, a problem inherited from the more fundamental conflict of special relativity with quantum mechanics. A procedure to overcome these difficulties is outlined, which amounts to replacing general relativity with its teleparallel equivalent and the Poincaré-invariant special relativity with …
Usually, General Relativity (GR) is known to be unrenormalizable perturbatively from the viewpoint of quantum field theory. But in the modern sense of renormalizability, there still remains the possibility to investigate whether GR is "nonpertubatively" renormalizable or not. Here I review the basics and results in this topic based on the "Effective Average Action" approach which was proposed by M.Reuter, and discuss its application to the balck hole geometry.
We hereby derive the Newtonian metric potentials for the fourth-derivative gravity including the one-loop logarithm quantum corrections. It is explicitly shown that the behavior of the modified Newtonian potential near the origin is improved respect to the classical one, but this is not enough to remove the curvature singularity in $r=0$. Our result is grounded on a rigorous proof based on numerical and analytic computations.
We consider the notion of improved and perfect actions within Regge calculus. These actions are constructed in such a way that they - although being defined on a triangulation - reproduce the continuum dynamics exactly, and therefore capture the gauge symmetries of General Relativity. We construct the perfect action in three dimensions with cosmological constant, and in four dimensions for one simplex. We conclude with a discussion about Regge Calculus with curved simplices, which arises naturally in this context.
