Dimensional Black Hole Spacetimes Research Articles

Holographic Phase Transitions in $$(2+1)$$-Dimensional Black Hole Spacetimes in NMG

Holographic Phase Transitions in $$(2+1)$$-Dimensional Black Hole Spacetimes in NMG

Holographic entanglement entropy with Power-Maxwell electrodynamics in higher dimensional AdS black hole spacetime* *Supported by the National Natural Science Foundation of China (11665015), the Guizhou Provincial Science and Technology Planning Project of China (qiankehejichu-ZK[2021]yiban026), and the Guizhou Province ordinary institutions of higher learning top science and technology talents Support plan of China (qianjiaoheKY[2019]062).

We investigate the behaviors of the scalar operator and holographic entanglement entropy in the metal/superconductor phase transition with Power-Maxwell electrodynamics in a higher dimensional background away from the probe limit. We observe that the larger parameters b and q make the condensation of the scalar operator more difficult, and the critical temperature decreases more slowly as the factors increase. In the belt geometry, the value of the entanglement entropy in the metal and superconductor phases is not only related to the the strength of the Power-Maxwell field but also to the width of the strip geometry. At the phase transition point, the discontinuous slope of entanglement entropy is universal for different model factors. It turns out that holographic entanglement entropy is a powerful tool to probe the properties of the phase transition in this holographic superconductor model.

Fisher information of a black hole spacetime

Relativistic quantum metrology is the study of optimal measurement procedures within systems that have both quantum and relativistic components. Here we use Unruh-DeWitt detectors coupled to a massless scalar field as probes of thermal parameters in different spacetimes via a relativistic quantum metrology analysis. We consider both (2 + 1)-dimensional anti-de Sitter and BTZ black hole spacetimes. We compute the Fisher information to identify characteristics of the black hole spacetime and to compare it to a uniformly accelerating detector in anti-de Sitter space. We find the dependence of the Fisher information on temperature, detector energy gap, black hole mass, interaction time, and the initial state of the detector. We identify strategies that maximize the Fisher information and therefore the precision of estimation.

Quantum kicks near a Cauchy horizon

We analyze a quantum observer who falls geodesically toward the Cauchy horizon of a (1 + 1)-dimensional eternal black hole spacetime with the global structure of the non-extremal Reissner–Nordström solution. The observer interacts with a massless scalar field, using an Unruh–DeWitt detector coupled linearly to the proper time derivative of the field, and by measuring the local energy density of the field. Taking the field to be initially prepared in the Hartle–Hawking–Israel (HHI) state or the Unruh state, we find that both the detector's transition rate and the local energy density generically diverge on approaching the Cauchy horizon, respectively, proportionally to the inverse and the inverse square of the proper time to the horizon, and in the Unruh state the divergences on approaching one of the branches of the Cauchy horizon are independent of the surface gravities. When the outer and inner horizons have equal surface gravities, the divergences disappear altogether in the HHI state and for one of the Cauchy horizon branches in the Unruh state. We conjecture, on grounds of comparison with the Rindler state in 1 + 1 and 3 + 1 Minkowski spacetimes, that similar properties hold in 3 + 1 dimensions for a detector coupled linearly to the quantum field, but with a logarithmic rather than inverse power-law divergence.

Geodesics and bending of light around a BTZ black hole surrounded by quintessential matter

Various observations from cosmic microwave background radiation (CMBR), type Ia supernova and baryon acoustic oscillations (BAO) are strongly suggestive of an accelerated expansion of the universe which can be explained by the presence of mysterious energy known as dark energy. The quintessential matter coupled with gravity minimally is considered one of the possible candidates to represent the presence of such dark energy in our universe. In view of this scenario, we study the geodesic of massless particles as well as massive particles around a (2 + 1)-dimensional BTZ black hole (BH) spacetime surrounded by the quintessence. The effect of parameters involved in the deflection of light by such a BH spacetime is investigated in detail. The results obtained are then compared with a usual non-rotating BTZ BH spacetime.

Stability analysis of geodesics and quasinormal modes of a dual stringy black hole via Lyapunov exponents

We investigate the stability of both timelike as well as null circular geodesics in the vicinity of a dual (3+1) dimensional stringy black hole (BH) spacetime by using an excellent tool so-called Lyapunov exponent. The proper time (\(\tau \)) Lyapunov exponent (\(\lambda _{p}\)) and coordinate time (t) Lyapunov exponent (\(\lambda _{c}\)) are explicitly derived to analyze the stability of equatorial circular geodesics for the stringy BH spacetime with electric charge parameter (\(\alpha \)) and magnetic charge parameter (Q). By computing these exponents for both the cases of BH spacetime, it is observed that the coordinate time Lyapunov exponent of magnetically charged stringy BH for both timelike and null geodesics are independent of magnetic charge parameter (Q). The variation of the ratio of Lyapunov exponents with radius of timelike circular orbits (\(r_{0}/M\)) for both the cases of stringy BH are presented. The behavior of instability exponent for null circular geodesics with respect to charge parameters (\(\alpha \) and Q) are also observed for both the cases of BH. Further, by establishing a relation between quasinormal modes (QNMs) and parameters related to null circular geodesics (like angular frequency and Lyapunov exponent), we deduced the QNMs (or QNM frequencies) for a massless scalar field perturbation around both the cases of stringy BH spacetime in the eikonal limit. The variation of scalar field potential with charge parameters and angular momentum of perturbation (l) are visually presented and discussed accordingly.

Harvesting entanglement with detectors freely falling into a black hole

We carry out the first investigation of the entanglement and mutual information harvesting protocols for detectors freely falling into a black hole. Working in $(1+1)$-dimensional Schwarzschild black hole spacetime, we consider two pointlike Unruh-DeWitt (UDW) detectors in different combinations of free-falling and static trajectories. Employing a generalization of relative velocity suitable for curved spacetimes, we find that the amount of correlations extracted from the black hole vacuum, at least outside the near-horizon regime, is largely kinematic in origin (i.e. it is mostly due to the relative velocities of the detectors). Second, correlations can be harvested purely from the black hole vacuum even when the detectors are causally disconnected by the event horizon. Finally, we show that the previously known `entanglement shadow' near the horizon is indeed absent for the case of two free-falling-detectors, since their relative gravitational redshift remains finite as the horizon is crossed, in accordance with the equivalence principle.

Scalar field quasinormal modes of noncommutative high dimensional Schwarzschild-Tangherlini black hole spacetime with smeared matter sources

We investigate the massless scalar quasinormal modes (QNMs) of the noncommutative D-dimensional Schwarzschild-Tangherlini black hole spacetime in this paper. By using the Wentzel-Kramers-Brillouin (WKB) approximation method, the asymptotic iterative method (AIM) and the inverted potential method (IPM), we made a detail analysis of the massless scalar QNM frequencies by varying the general smeared matter distribution and the allowable characteristic parameters (k and θ) corresponding to different dimensions. It is found that the nonconvergence of the high order WKB approximation exists in the QNMs frequencies of scalar perturbation around the noncommutative D-dimensional Schwarzschild black holes. We conclude that the 3rd WKB result should be more reliable than those of the high order WKB method since our numerical results are also verified by the AIM method and the IPM method. In the dimensional range of 4≤D≤7, the scalar QNMs as a function of the different parameters (the noncommutative parameter θ, the smeared matter distribution parameter k, the multipole number l and the main node number n) are obtained. Moreover, we study the dynamical evolution of a scalar field in the background of the noncommutative high dimensional Schwarzschild-Tangherlini black hole.

Conformal vacuum and the fluctuation-dissipation theorem in a de Sitter universe and black hole spacetimes

In the studies of quantum field theory in curved spacetime, the ambiguous concept of vacuum state and the particle content is a long-standing debatable aspect. So far it is well known to us that in the background of the curved spacetime, some privileged class of observers detect particle production in the suitably chosen vacuum states of the quantum matter fields. In this work we aim to study the characteristics behaviour of these produced particles in the background of the de-Sitter (dS) Friedmann-Lama\^{i}tre-Robertson-Walker (FLRW) Universe (both for $(1+1)$ and $(3+1)$ dimensions) and $(1+1)$-dimensional Schwarzschild black hole (BH) spacetime, from the point of view of the respective privileged class of observers. Here the analysis is confined to the observers who perceive particle excitations in the conformal vacuum. We consider some test particles in the thermal bath of the produced particles and calculate the correlation function of the fluctuation of the random force as exerted by the produced quanta on the test particles. We obtain that the correlation function abides by the fluctuation-dissipation theorem, which in turn signifies that the test particles execute Brownian-like motion in the thermal bath of the produced quanta.

Generalized uncertainty principle and black holes in higher dimensional self-complete gravity

In this paper we consider generalized uncertainty principle (GUP) effects in higher dimensional black hole spacetimes via a nonlocal gravity approach. We study three possible modifications of momentum space measure emerging from GUP, including the original Kempf-Mangano-Mann (KMM) proposal. By following the KMM model we derive a family of black hole spacetimes. The case of five spacetime dimensions is a special one. We found an exact black hole solution with a Barriola-Vilenkin monopole at the origin. This object turns out to be the end point of the black hole evaporation. Interestingly for smaller masses, we found a “naked monopole” rather than a generic naked singularity. We also show that the Carr-Lake-Casadio-Scardigli proposal leads to mild modifications of spacetime metrics with respect to the Schwarzschild-Tangherlini solution. Finally, by demanding the same degree of convergence in the ultraviolet regime for any spacetime dimension, we derive a family of black hole solutions that fulfill the gravity self-completeness paradigm. The evaporation of such black holes is characterized by a fluctuating luminosity, which we dub a lighthouse effect.

Exact classical and quantum solutions for a covariant oscillator near the black hole horizon in Stueckelberg-Horwitz-Piron theory

We found exact solutions for canonical classical and quantum dynamics for general relativity in Horwitz general covariance theory. These solutions can be obtained by solving the generalized geodesic equation and Schrödinger-Stueckelberg-Horwitz-Piron (SHP) wave equation for a simple harmonic oscillator in the background of a two dimensional dilaton black hole spacetime metric. We proved the existence of an orthonormal basis of eigenfunctions for generalized wave equation. This basis functions form an orthogonal and normalized (orthonormal) basis for an appropriate Hilbert space. The energy spectrum has a mixed spectrum with one conserved momentum p according to a quantum number n. To find the ground state energy we used a variational method with appropriate boundary conditions. A set of mode decomposed wave functions and calculated for the Stueckelberg-Schrodinger equation on a general five dimensional blackhole spacetime in Hamilton gauge.

Geodesic flows around charged black holes in two dimensions

We study the evolution of timelike geodesics for two dimensional black hole spacetimes arising in string theory and general theory of relativity by solving the Raychaudhuri equation for expansion scalar as an initial value problem. The possibility of geodesic focusing/defocusing is then examined accordingly with different settings of black hole parameters. In view of the geodesic focusing/defocusing, the critical value of expansion scalar is also calculated in each case. The effect of the charge and the cosmological constant on the evolution of expansion scalar for timelike geodesics is discussed in detail.

Higher dimensional numerical relativity: Code comparison

The nonlinear behavior of higher dimensional black hole spacetimes is of interest in several contexts, ranging from an understanding of cosmic censorship to black hole production in high-energy collisions. However, nonlinear numerical evolutions of higher dimensional black hole spacetimes are tremendously complex, involving different diagnostic tools and "dimensional reduction methods". In this work we compare two different successful codes to evolve Einstein's equations in higher dimensions, and show that the results of such different procedures agree to numerical precision, when applied to the collision from rest of two equal-mass black holes. We calculate the total radiated energy to be E/M=9x10^{-4} in five dimensions and E/M=8.1x10^{-4} in six dimensions.

Decay of linear waves on higher-dimensional Schwarzschild black holes

In this paper we consider solutions to the linear wave equation on higher dimensional Schwarzschild black hole spacetimes and prove robust nondegenerate energy decay estimates that are in principle required in a nonlinear stability problem. More precisely, it is shown that for solutions to the wave equation \Box_g\phi=0 on the domain of outer communications of the Schwarzschild spacetime manifold (M^n_m, g) (where n >= 3 is the spatial dimension, and m > 0 is the mass of the black hole) the associated energy flux E[\phi](\Sigma_\tau) through a foliation of hypersurfaces (\Sigma_\tau) (terminating at future null infinity and to the future of the bifurcation sphere) decays, E[\phi](\Sigma_\tau) <= CD/\tau^2, where C is a constant only depending on n and m, and D < \infty is a suitable higher order initial energy on \Sigma_0; moreover we improve the decay rate for the first order energy to E[\partial_t\phi](\Sigma_\tau^R) <= CD/\tau^(4-2\delta) for any \delta > 0 where \Sigma_\tau^R denotes the hypersurface (\Sigma_\tau) truncated at an arbitrarily large fixed radius R < \infty provided the higher order energy D_\delta on \Sigma_0 is finite. We conclude our paper by interpolating between these two results to obtain the pointwise estimate |\phi|_{\Sigma_\tau^R} <= (C D'_\delta) / \tau^(3/2-\delta). In this work we follow the new physical-space approach to decay for the wave equation of Dafermos and Rodnianski.

Light Glueball Spectrum in Five Dimensional Black Hole with the Perturbed Geometric Function

The five dimensional black hole space-time with perturbed geometric function considered. We use the holographic description of the black hole to investigate the glueball spectra and the effective potential. In this model, glueballs are described by a massless scalar field in the five dimensional black hole with a dilaton background. For the first time we use modified geometric function and discuss the effective potential by using the Schrodinger like equation.

Numerical relativity in higher dimensions

We give a status report on our project targeted at performing numerical simulations of a head-on collision of non-spinning black holes in higher dimensional non-compact space-times. These simulations should help us understand black objects in higher dimensions and their stability properties. They are also relevant for the problem of black hole formation and evaporation in particle accelerators and cosmic rays. We use the symmetries of the system to reduce the problem to an effective 3+1 problem, allowing the use of existing numerical codes. As a simple application of the formalism, we present the results for the evolution of a five dimensional single black hole space-time.

Hidden symmetries and black holes

The paper contains a brief review of recent results on hidden symmetries in higher dimensional black hole spacetimes. We show how the existence of a principal CKY tensor (that is a closed conformal Killing-Yano 2-form) allows one to generate a `tower' of Killing-Yano and Killing tensors responsible for hidden symmetries. These symmetries imply complete integrability of geodesic equations and the complete separation of variables in the Hamilton-Jacobi, Klein-Gordon, Dirac and gravitational perturbation equations in the general Kerr-NUT-(A)dS metrics. Equations of the parallel transport of frames along geodesics in these spacetimes are also integrable.

Ray-tracing in four and higher dimensional black hole spacetimes: An analytical approximation

We study null ray propagation in a spacetime of static Schwarzschild--Tangherlini black holes in an arbitrary number of dimensions. We focus on the bending angle and the retarded time delay for rays emitted in the vicinity of a black hole and propagating to the infinity. We obtain an analytic expression in terms of elementary functions which approximate the bending angle and time delay in these spacetimes with high accuracy. We analyze the relative error of the developed analytic approximations and show that it is quite small in the complete domain of the parameter space for the rays reaching the infinity and for a different number of the spacetime dimensions. Possible applications of the obtained results are briefly discussed.

Eigenvalue Problem of Scalar Fields in BTZ Black Hole Spacetime

We studied the eigenvalue problem of scalar fields in the (2+1)-dimensional BTZ black hole spacetime. The Dirichlet boundary condition at infinity and the Dirichlet or the Neumann boundary condition at the horizon are imposed. Eigenvalues for normal modes are characterized by the principal quantum number (0 ≤ n) and the azimuthal quantum number (−∞ < m < ∞). Effects to eigenvalues of the black hole rotation and of the scalar field mass are studied explicitly. Relation of the black hole rotation to the super-radiant instability is discussed.

Separation of the Dirac equation in the (3 + 1)-dimensional constant curvature black hole background and its solution

The behavior of spin-half particles is discussed in the (3 + 1)-dimensional constant curvature black hole (CCBH) spacetime. We use Schwarzschild-like coordinates, valid outside the black hole event horizon. The constant time surfaces corresponding to the timelike Killing vector are degenerate at the black hole event horizon and also along an axis. We write down the Dirac equation in this spacetime using the Newman–Penrose formalism which is not easily separable unlike that in the Kerr metric. However, with a particular choice of basis system the equation is separable and we obtain the solutions. We discuss the structural difference in the Dirac equation in the CCBH spacetime with that in the Kerr geometry, due to a difference in the corresponding spacetime metrices the resulting complexity arose in separation in the earlier case.