Higher-dimensional Black Holes Research Articles

Ehrenfest scheme of higher dimensional AdS black holes in the third-order Lovelock–Born–Infeld gravity

Interpreting the cosmological constant as a thermodynamic pressure and its conjugate quantity as a thermodynamic volume, we reconsider the investigation of P–V critical behaviors of (1 + n)-dimensional AdS black holes in Lovelock–Born–Infeld gravity. In particular, we derive an explicit expression of the universal number [Formula: see text] in terms of the space dimension n. Then, we examine the phase transitions at the critical points of such black holes for 6 ≤ n < 11 as required by the physical condition of the thermodynamical quantities including criticality behaviors. More precisely, the Ehrenfest equations have been checked and they reveal that the black hole system undergoes a second phase transition at the critical points.

Vacuum polarization on the brane

We compute the renormalized expectation value of the square of a massless, conformally coupled, quantum scalar field on the brane of a higher-dimensional black hole. Working in the AADD brane-world scenario, the extra dimensions are flat and we assume that the compactification radius is large compared with the size of the black hole. The four-dimensional on-brane metric corresponds to a slice through a higher-dimensional Schwarzschild-Tangherlini black hole geometry and depends on the number of bulk space-time dimensions. The quantum scalar field is in a thermal state at the Hawking temperature. An exact, closed-form expression is derived for the renormalized expectation value of the square of the quantum scalar field on the event horizon of the black hole. Outside the event horizon, this renormalized expectation value is computed numerically. The answer depends on the number of bulk space-time dimensions, with a magnitude which increases rapidly as the number of bulk space-time dimensions increases.

Constraints on the Generalized Uncertainty Principle from black-hole thermodynamics

In this paper, we calculate the modification to the thermodynamics of a Schwarzschild black hole in higher dimensions due to the Generalized Uncertainty Principle (GUP). We use the fact that the leading-order corrections to the entropy of a black hole has to be logarithmic in nature to restrict the form of the GUP. We observe that in six dimensions, the usual GUP produces the correct form for the leading-order corrections to the entropy of a black hole. However, in five and seven dimensions a linear GUP, which is obtained by a combination of DSR with the usual GUP, is needed to produce the correct form of the corrections to the entropy of a black hole. Finally, we demonstrate that in five dimensions, a new form of GUP containing quadratic and cubic powers of the momentum also produces the correct form for the leading-order corrections to the entropy of a black hole.

Killing(-Yano) tensors in string theory

We construct the Killing(-Yano) tensors for a large class of charged black holes in higher dimensions and study general properties of such tensors, in particular, their behavior under string dualities. Killing(-Yano) tensors encode the symmetries beyond isometries, which lead to insights into dynamics of particles and fields on a given geometry by providing a set of conserved quantities. By analyzing the eigenvalues of the Killing tensor, we provide a prescription for constructing several conserved quantities starting from a single object, and we demonstrate that Killing tensors in higher dimensions are always associated with ellipsoidal coordinates. We also determine the transformations of the Killing(-Yano) tensors under string dualities, and find the unique modification of the Killing-Yano equation consistent with these symmetries. These results are used to construct the explicit form of the Killing(-Yano) tensors for the Myers-Perry black hole in arbitrary number of dimensions and for its charged version.

Anomalies, Chern-Simons terms and black hole entropy

Recent derivations of Cardy-like formulae in higher dimensional field theories have opened up a way of computing, via AdS/CFT, universal contributions to black hole entropy from gravitational Chern-Simons terms. Based on the manifestly covariant formulation of the differential Noether charge for Chern-Simons terms proposed in arXiv:1407.6364, we compute the entropy and asymptotic charges for the rotating charged AdS black holes in higher dimensions at leading order of the fluid/gravity derivative expansion in the Einstein-Maxwell-Chern-Simons system. This gives a result that exactly matches the field theory predictions from Cardy-like formulae.

Quasi-normal Modes for Spin-3/2 Fields

With the Large Hadron Collider already able to produce collisions with an energy of 8 TeV, the formation of higher dimensional black holes may soon be possible. In order to determine if we are detecting these higher dimensional black holes we need to have a theoretical understanding of what the signatures of such black holes could be. As such we shall discuss quasi-normal modes (QNMs) for spin-3/2 fields as they travel through a black hole background. We will begin by studying possible QNMs for N-dimensional Schwarzschild black holes and extend by looking at N-dimensional Kerr black holes. We will use the Wentzel-Kramers-Brillouin approximation to determine the QNMs for the two types of black holes described above.

Accretion of dark energy onto higher dimensional charged BTZ black hole

In this work, we have studied the accretion of $(n+2)$-dimensional charged BTZ black hole (BH). The critical point and square speed of sound have been obtained. The mass of the BTZ BH has been calculated and we have observed that the mass of the BTZ BH is related with square root of the energy density of dark energy which accretes onto BH in our accelerating FRW universe. We have assumed modified Chaplygin gas (MCG) as a candidate of dark energy which accretes onto BH and we have found the expression of BTZ BH mass. Since in our solution of MCG, this model generates only quintessence dark energy (not phantom) and so BTZ BH mass increases during the whole evolution of the accelerating universe. Next we have assumed 5 kinds of parametrizations of well known dark energy models. These models generate both quintessence and phantom scenarios i.e., phantom crossing models. So if these dark energies accrete onto the BTZ BH, then in quintessence stage, BH mass increases upto a certain value (finite value) and then decreases to a certain finite value for phantom stage during whole evolution of the universe. We have shown these results graphically.

New modes for massive Dirac field in higher-dimensional black holes

In this paper, we derive new modes for massive Dirac field in the background of a higher-dimensional Schwarzschild black hole. We use in our approach the Cartesian gauge defined in local frames. We work in the context of Arkani-Hamed, Dimopoulos and Dvali (ADD)-like theories, assuming that the Standard Model fields (fermions and bosons) live only on a (3+1)-dimensional brane and the extra dimensions of space can be large in size.

Instabilities of Extremal Rotating Black Holes in Higher Dimensions

Recently, Durkee and Reall have conjectured a criterion for linear instability of rotating, extremal, asymptotically Minkowskian black holes in $d\ge 4$ dimensions, such as the Myers-Perry black holes. They considered a certain elliptic operator, $\cA$, acting on symmetric trace-free tensors intrinsic to the horizon. Based in part on numerical evidence, they suggested that if the lowest eigenvalue of this operator is less than the critical value $-1/4$ ( called "effective BF-bound"), then the black hole is linearly unstable. In this paper, we prove an extended version of their conjecture. Our proof uses a combination of methods such as (i) the "canonical energy method" of Hollands-Wald, (ii) algebraically special properties of the near horizon geometries associated with the black hole, (iii) the Corvino-Schoen technique, and (iv) semiclassical analysis. Our method of proof is also applicable to rotating, extremal asymptotically Anti-deSitter black holes. In that case, we find additional instabilities for ultra-spinning black holes. Although we explicitly discuss in this paper only extremal black holes, we argue that our results can be generalized to {\em near} extremal black holes.

Corrections to the Hawking tunneling radiation in extra dimensions

Although the tunneling approach is fully established for black hole radiation, much work has been done to support the extension of this approach to more general settings. In this paper the Parikh–Kraus–Wilczeck tunneling proposal of black hole tunneling radiation is considered. The thermodynamics of the higher dimensional Schwarzschild black hole is studied based on the generalized uncertainty principle (GUP) and the modified dispersion relation (MDR) analysis, separately. It is shown that entropy and the rate of the higher dimensional Schwarzschild black hole tunneling radiation receive some corrections. The leading-order corrections does not contain the logarithmic term of the entropy, if the dimensions of the space–time is an odd number. Through the comparison, it is found that the results of these two alternative approaches are identical if one uses the suitable expansion coefficients.

Biconformal symmetry and static Maxwell fields near higher-dimensional black holes

We study an electric field created by a static electric charge near the higher-dimensional Reissner-Nordstr\om black hole. The relation between the static Green functions on the $D$-dimensional Reissner-Nordstr\om background and on the $(D+2)$-dimensional homogeneous Bertotti-Robinson spacetime is found. Using the biconformal symmetry we obtain a simple integral representation for the static Maxwell Green functions in arbitrary dimensions. We show that in a four-dimensional spacetime the static Green function obtained by the biconformal method correctly reproduces known results. We also find a closed form for the exact static Green functions and vector potentials in the five-dimensional Reissner-Nordstr\om spacetime.

Stable bound orbits in six-dimensional Myers-Perry black holes

The existence of stable bound orbits of test particles is one of the most characteristic properties in black hole spacetimes. In higher-dimensional black holes, due to the dimensionality of gravity, there is no stable bound orbit balanced by Newtonian gravitational monopole force and centrifugal force as in the same mechanism of the four-dimensional Kerr black hole case. In this paper, however, the existence of stable bound orbits of massive and massless particles is shown in six-dimensional singly spinning Myers-Perry black holes with a value of the spin parameter larger than a critical value. The innermost stable circular orbits and the outermost stable bound orbit are found on the rotational axis.

Phase transition and Clapeyron equation of black holes in higher dimensional AdS spacetime

Using Maxwell's equal area law, we study the phase transition in higher dimensional anti-de Sitter (AdS) Reissner–Nordström black holes and Kerr black holes in this paper. The coexisting region of the two phases involved in the phase transition is found and some coexisting curves are shown in figures. We also analytically investigate the parameters that affect the phase transition. To better compare with a general thermodynamic system, the Clapeyron equation is derived for the higher dimensional AdS black holes.

New geometries for black hole horizons

AbstractWe construct several classes of worldvolume effective actions for black holes by integrating out spatial sections of the worldvolume geometry of asymptotically flat black branes. This provides a generalisation of the blackfold approach for higher-dimensional black holes and yields a map between different effective theories, which we exploit by obtaining new hydrodynamic and elastic transport coefficients via simple integrations. Using Euclidean minimal surfaces in order to decouple the fluid dynamics on different sections of the worldvolume, we obtain local effective theories for ultraspinning Myers-Perry branes and helicoidal black branes, described in terms of a stress-energy tensor, particle currents and non-trivial boost vectors. We then study in detail and present novel compact and non-compact geometries for black hole horizons in higher-dimensional asymptotically flat space-time. These include doubly-spinning black rings, black helicoids and helicoidal p-branes as well as helicoidal black rings and helicoidal black tori in D ≥ 6.

On heat properties of AdS black holes in higher dimensions

We investigate the heat properties of AdS Black Holes in higher dimensions. We consider the study of the corresponding thermodynamical properties including the heat capacity explored in the determination of the black hole stability. In particular, we compute the heat latent. To overcome the instability problem, the Maxwell construction, in the (T,S)-plane, is elaborated. This method is used to modify the the Hawking-Page phase structure by removing the negative heat capacity regions. Then, we discuss the thermodynamic cycle and the heat engines using the way based on the extraction of the work from a black hole solution.

Lovelock black holes in the presence of nonlinear electrodynamics

In this paper, we consider third-order Lovelock–Maxwell gravity with additional (Fμν Fμν)2 term as a nonlinearity correction of the Maxwell theory. We obtain black hole solutions with various horizon topologies (and various number of horizons) in which their asymptotical behavior can be flat or anti-de Sitter with an effective cosmological constant. We investigate the effects of Lovelock and electrodynamic corrections on properties of the solutions. Then, we restrict ourselves to asymptotically flat solutions and calculate the conserved and thermodynamic quantities. We check the first law of thermodynamics for these black hole solutions and calculate the heat capacity to analyze stability. Although higher dimensional black holes in Einstein gravity are unstable, here we look for suitable constraints on the black hole radius to find thermally stable black hole solutions.

Do all D-dimensional Schwarzschild black holes behave as one-dimensional entropy emitters?

Perfect black-body emitters in a flat three-dimensional space are characterized by the well-known relation S˙flat3D=(32π2AP3/1215ħ3)1/4, where S˙flat3D and P are respectively the entropy and energy emission rates out of the 3-D hot body, and A is the 2-D surface area of the emitting body. However, Bekenstein and Mayo have pointed out that three-dimensional Schwarzschild black holes are characterized by a qualitatively different relation: S˙BH3D=CBH3D×(P/ħ)1/2, where CBH3D is a numerically computed proportionality coefficient. Thus, in their entropy emission properties, these three-dimensional black holes effectively behave as one-dimensional entropy emitters: in particular, they respect Pendry's upper bound S˙flat1D=Cflat1D×(P/ħ)1/2 on the entropy emission rate out of one-dimensional flat-space thermal bodies, where Cflat1D=(π/3)1/2. One naturally wonders whether this intriguing property of the three-dimensional black holes is a generic feature of all D-dimensional Schwarzschild black holes? In this paper we shall show that the answer to this question (and to the question raised in the title) is ‘Yes and No’. ‘Yes’, because we shall prove that all D-dimensional Schwarzschild black holes are characterized by the one-dimensional functional relation S˙BHD=CBHD×(P/ħ)1/2. ‘No’, because we shall show that, in the large-D limit, the analytically calculated coefficients CBHD are larger than Cflat1D=(π/3)1/2, implying that higher-dimensional black holes may violate Pendry's upper bound on the entropy emission rate of one-dimensional physical systems.

Study of motion around a static black hole in Einstein and Lovelock gravity

We study motion around a static Einstein and pure Lovelock black hole in higher dimensions. It is known that in higher dimensions, bound orbits exist only for pure Lovelock black hole in all even dimensions, D=2N+2, where N is degree of Lovelock polynomial action. In particular, we compute periastron shift and light bending and the latter is given by one of transverse spatial components of Riemann curvature tensor. We also consider pseudo-Newtonian potentials and Kruskal coordinates.

Absence of black holes at LHC due to gravity's rainbow

In this paper, we investigate the effect of Planckian deformation of quantum gravity on the production of black holes at colliders using the framework of gravity's rainbow. We demonstrate that a black hole remnant exists for Schwarzschild black holes in higher dimensions using gravity's rainbow. The mass of this remnant is found to be greater than the energy scale at which experiments were performed at the LHC. We propose this as a possible explanation for the absence of black holes at the LHC. Furthermore, we demonstrate that it is possible for black holes in six (and higher) dimensions to be produced at energy scales that will be accessible in the near future.

Greybody factors for rotating black holes in higher dimensions

We perform a thorough study of greybody factors for minimally-coupled scalar fields propagating on the background of rotating black holes (BHs) in higher (odd) dimensions with all angular momenta set equal. For this special case, the solution enjoys an enhanced symmetry, which translates into the advantageous feature of being cohomogeneity-1, i.e., these backgrounds depend on a single radial coordinate. Our analysis contemplates three distinct situations, with the cosmological constant being zero, positive or negative. Using the technique of matched asymptotic expansions we analytically compute the greybody factors in the low-frequency regime, restricting to s-wave scattering. Our formulas generalize those obtained previously in the literature for the static and spherically symmetric case, with corrections arising from the change in the horizon area due to rotation. It is also proven that, for this family of BHs, the horizon area is a decreasing function of the spin parameter, without regard to the dimensionality and cosmological constant. Through an improvement on a calculation specific to the class of small BHs in anti-de Sitter (AdS) and not restricted to the usual low-frequency regime, we uncover a rich structure of the greybody spectrum, more complex than previously reported but also enjoying a certain degree of universality. We complement our low-frequency analytic results with numerical computations valid over a wide range of frequencies and extend them to higher angular momentum quantum numbers, . This allows us to probe the superradiant regime that is observed for corotating wavefunctions. We point out that the maximum amplification factor for intermediate-size BHs in AdS can be surprisingly large.