Black Brane Research Articles

From rotating to charged black holes and back again

The mild form of the Weak Gravity Conjecture (WGC) requires higher derivative corrections to extremal charged black holes to increase their charge-to-mass ratio. This allows decay via emission of a smaller extremal black hole. In this paper, we investigate if similar constraints hold for extremal rotating black holes. We do so by considering the leading higher derivative corrections to the four-dimensional Kerr black hole and five-dimensional Myers-Perry black hole. We use a known mapping of these rotating solutions to a four-dimensional non-rotating dyonic Kaluza-Klein black hole and impose the WGC on this charged solution. Going back again to the rotating solutions, this fixes the sign of the corrections to the rotating extremality bounds. The sign of the corrections is non-universal, depending on the black hole under consideration. We argue that this is not at odds with black hole decay, because of the presence of a superradiant instability that persists in the extremal limit. When this instability is present, the WGC is implied for the four-dimensional charged black hole.

Bound orbits around charged black strings

We study the geodesics of 5d Reissner–Nordstrom and nonsingular black strings, and establish a rational bound orbit taxonomy for both massive as well as null test particles. For the timelike case, test particles with high energy (that would have made them plunge into or scatter off a black hole) could still form bound orbits around the black strings. We calculate the accumulated angles of the corresponding radial periods and show that they are higher than their 4d counterparts. For the null case, we found the existence of stable null orbits outside their respective horizons, which do not exist in the four dimensions except at their extremal limit.

Weak gravity conjecture, black branes and violations of universal thermodynamics relation

The universal thermodynamic relations between corrections to entropy and extremality for various black hole solutions, like rotating-AdS black holes, charged black holes, rotating black holes in massive gravity, etc., have been studied by modifying general relativity. In this paper, we consider a number of the black brane in different structures, such as black brane solution in Rastall AdS massive gravity, Einstein–Yang–Mills AdS black brane solution in massive gravity, and general anisotropic black brane in Horava–Lifshitz gravity. Then, we study universal thermodynamic relations by using a small constant correction added to the action. We conclude that black brane violates the universal thermodynamic relations. In other words, these universal thermodynamic relations are not valid in the black brane structure.

BRST symmetry and the convolutional double copy

Motivated by the results of Anastasiou et al., we consider the convolutional double copy for BRST and anti-BRST covariant formulations of gravitational and gauge theories in more detail. We give a general BRST and anti-BRST invariant formulation of linearised mathcal{N} = 0 supergravity using superspace methods and show how this may be obtained from the square of linearised Yang-Mills theories. We demonstrate this relation for the Schwarzschild black hole and the ten-dimensional black string solution as two concrete examples.

Analytic approach to the formation of a three-dimensional black string from a dust cloud

In three-dimensional low-energy string theory,we study the formation of a black string from a dust cloud.We analytically obtain two distinct classes of exact solutions with arbitrary functionsresponsible for mass distributions ofthe dust cloud. The first and second kinds of solutions may describe collapsing dusts butthe first kind is only for inhomogeneous dust distribution while the second kind has a homogeneous limit.The finite collapse time and the Israel junction conditions tell us thatthe first kind solution describesa desired collapsing phenomenon, whereasthe scale factor in the inner spacetime for the second kindturns out to be trivial.In the first kind solution, specific collapsing models can be realized by choosing anappropriate inhomogeneousdust distribution consistent with the Israel junction conditions.Consequently, the inhomogeneous dust cloud eventually collapses to theblack string although the homogeneous dust clouddoes not guarantee the formation of the black string in our setting.The space-like curvature singularities occur at the finite collapse time andthey can be cloaked by the horizon of the black string.

Thermodynamics of Taub-NUT and Plebanski solutions

We observe the parallel between the null Killing vector on the horizon and degenerate Killing vectors at both north and south poles in Kerr-Taub-NUT and general Plebanski solutions. This suggests a correspondence between the pairs of the angular momentum/velocity and the NUT charge/potential. We treat the time as a real line such that the Misner strings are physical. We find that the NUT charge spreads along the Misner strings, analogous to that the mass in the Schwarzschild black hole sits at its spacetime singularity. We develop procedures to calculate all the thermodynamic quantities and we find that the results are consistent with the first law (Wald formalism), the Euclidean action and the Smarr relation. We also apply the Wald formalism, the Euclidean action approach, and the (generalized) Komar integration to the electric and magnetic black holes in a class of EMD theories, and also to boosted black strings and Kaluza-Klein monopoles in five dimensions, to gain better understandings of how to deal with the subtleties associated with Dirac and Misner strings.

D = 5 static, charged black holes, strings and rings with resonant, scalar Q-hair

A mechanism for circumventing the Mayo-Bekenstein no-hair theorem allows endowing four dimensional (D = 4) asymptotically flat, spherical, electro-vacuum black holes with a minimally coupled U (1)-gauged scalar field profile: Q-hair. The scalar field must be massive, self-interacting and obey a resonance condition at the threshold of (charged) superradiance. We establish generality for this mechanism by endowing three different types of static black objects with scalar hair, within a D = 5 Einstein-Maxwell-gauged scalar field model: asymptotically flat black holes and black rings; and black strings which asymptote to a Kaluza-Klein vacuum. These D = 5 Q-hairy black objects share many of the features of their D = 4 counterparts. In particular, the scalar field is subject to a resonance condition and possesses a Q-ball type potential. For the static black ring, the charged scalar hair can balance it, yielding solutions that are singularity free on and outside the horizon.

Nonlinear effective dynamics of a Brownian particle in magnetized plasma

An effective description is presented for a Brownian particle in a magnetized plasma. In order to systematically capture various corrections to linear Langevin equation, we construct effective action for the Brownian particle, to quartic order in its position. The effective action is first derived within nonequilibrium effective field theory formalism, and then confirmed via a microscopic holographic model consisting of an open string probing magnetic fifth-dimensional anti--de Sitter (${\mathrm{AdS}}_{5}$) black brane. For practical usage, the non-Gaussian effective action is converted into Fokker-Planck-type equation, which is an Euclidean analog of Schr\"odinger equation and describes time evolution of probability distribution for particle's position and velocity.

Improved Wald formalism and first law of dyonic black strings with mixed Chern-Simons terms

We study the first law of thermodynamics of dyonic black strings carrying a linear momentum in type IIA string theory compactified on K3 with leading order α′ corrections. The low energy effective action contains mixed Chern-Simons terms of the form −2B(2) ^ tr(R(Γ±) ^ R(Γ±)) which is equivalent to 2H(3) ^ CS(3)(Γ±) up to a total derivative. We find that the naive application of Wald entropy formula leads to two different answers associated with the two formulations of the mixed Chern-Simons terms. Surprisingly, neither of them satisfies the first law of thermodynamics for other conserved charges computed unambiguously using the standard methods. We resolve this problem by carefully evaluating the full infinitesimal Hamiltonian at both infinity and horizon, including contributions from terms proportional to the Killing vector which turn out to be nonvanishing on the horizon and indispensable to establish the first law. We find that the infinitesimal Hamiltionian associated with −2B(2) ^ tr(R(Γ±) ^ R(Γ±)) requires an improvement via adding a closed but non-exact term, which vanishes when the string does not carry either the magnetic charge or linear momentum. Consequently, both formulations of the mixed Chern-Simons terms yield the same result of the entropy that however does not agree with the Wald entropy formula. In the case of extremal black strings, we also contrast our result with the one obtained from Sen’s approach.

On the entropy of strings and branes

We show that the entropy of strings that wind around the Euclidean time circle is proportional to the Noether charge associated with translations along the T-dual time direction. We consider an effective target-space field theory which includes a large class of terms in the action with various modes, interactions and α′ corrections. The entropy and the Noether charge are shown to depend only on the values of fields at the boundary of space. The classical entropy, which is proportional to the inverse of Newton’s constant, is then calculated by evaluating the appropriate boundary term for various geometries with and without a horizon. We verify, in our framework, that for higher-curvature pure gravity theories, the Wald entropy of static neutral black hole solutions is equal to the entropy derived from the Gibbons-Hawking boundary term. We then proceed to discuss horizonless geometries which contain, due to the back-reaction of the strings and branes, a second boundary in addition to the asymptotic boundary. Near this “punctured” boundary, the time-time component of the metric and the derivatives of its logarithm approach zero. Assuming that there are such non-singular solutions, we identify the entropy of the strings and branes in this geometry with the entropy of the solution to all orders in α′. If the asymptotic region of an α′-corrected neutral black hole is connected through the bulk to a puncture, then the black hole entropy is equal to the entropy of the strings and branes. Later, we discuss configurations similar to the charged black p-brane solutions of Horowitz and Strominger, with the second boundary, and show that, to leading order in the α′ expansion, the classical entropy of the strings and branes is equal exactly to the Bekenstein-Hawking entropy. This result is extended to a configuration that asymptotes to AdS.

Einstein-Gauss-Bonnet black strings at large α

The simplest black string in higher-dimensional general relativity (GR) is perhaps the direct product of a Schwarzschild spacetime and a flat spatial direction. However, it is known that the Einstein-Gauss-Bonnet theory does not allow such a trivial and simple solution. We propose a novel analytic technique, which assumes that the Gauss-Bonnet (GB) term becomes dominant over the Einstein-Hilbert (EH) term. Assuming the dimensionless coupling constant α normalized by the horizon scale is large enough, we find that the spacetime is separated into the GB region and GR region, which are matched via the transition region where the GB and EH terms are comparable. Using this large α approximation, we indeed construct new analytic solutions of black strings, from which we analytically compute various physical quantities of black strings at large α. Moreover, we confirm that all these analytic results are consistent with the numerical calculation. We also discuss the possible extension to general Einstein-Lovelock black holes.

Black holes and black strings in the Einstein SU(N) nonlinear sigma model

We construct analytical solutions describing black holes and black strings in the Einstein $SU(N)$-nonlinear sigma model in ($3+1$) dimensions. This construction is carried out using the maximal embedding ansatz of $SU(2)$ together with the Euler parametrization of the $SU(N)$ group, in such a way that the nonlinear sigma model equations are automatically satisfied for arbitrary values of the flavor number $N$ while the Einstein equations can be solved analytically. In particular, we construct black holes with spherical and flat horizons as well as black strings that present the geometry of a three-dimensional charged Ba\~nados-Teitelboim-Zanelli black hole on the transverse section of the string. These configurations are not trivial embeddings of $SU(2)$ into $SU(N)$, which allow us to explicitly show the role that the flavor number plays on the geometry and thermodynamics of the black holes and black strings. Finally, we perform a thermal comparison between these configurations.

Rotating black branes in Lovelock gravity with double-logarithmic electrodynamics

We couple a third order Lovelock gravity with double-logarithmic electrodynamics and compute a new class of d-dimensional magnetically charged rotating solutions with a complete set of possible rotational parameters. These solutions describe horizon flat magnetically charged rotating black branes with inner and outer horizons, extremal black holes and naked singularities according to the choice of parameters of nonlinear electrodynamics and Lovelock gravity. We also work out Hawking temperature, entropy, heat capacity, mass, potential and angular momenta for these black branes with the help of known formulas and methods. The Smarr-type formula has also been derived and the fulfilment of first law has been shown.

Holographic Schwinger effect and electric instability with anisotropy

According to the gauge-gravity duality, we systematically study the Schwinger effect and electric instability with anisotropy in a top-down holographic approach. The anisotropic black brane and bubble (soliton) background in IIB supergravity are employed and the dual theories in these backgrounds are expected to be anisotropic theory at finite temperature and anisotropic theory with confinement respectively. Then performing the potential analysis, we find due to the anisotropy, the potential barrier behaves oppositely with parallel and perpendicular electric fields, and this behavior agrees with the previous study about the quark potential with anisotropy in this system. Afterwards, we evaluate the pair production rate by solving the equation of motion for a fundamental string numerically which reveals the consistent behavior with the potential analysis. Furthermore, the probe D7-brane as flavor is introduced into the bulk in order to investigate the electric instability. The vacuum decay rate can be obtained by evaluating the imaginary part of the D7-brane action which again agrees with our potential analysis. Solving the associated constraint of gauge field strength on the flavor brane, we finally obtain the V-A curve displaying the distinct behavior of the conductivity in parallel and perpendicular direction which is in agreement with some bottom-up and phenomenologically holographic approaches in anisotropic fluid. Accordingly, we believe this work may be remarkable to study the electric features in strongly coupled anisotropic system.

Thermodynamics of black string from Rényi entropy in de Rham–Gabadadze–Tolley massive gravity theory

The de Rham–Gabadadze–Tolley black string solution is a cylindrically symmetric and static solution of the Einstein field equation with graviton mass term. For the asymptotically de Sitter solution, it is possible to obtain the black string with two event horizons corresponding to two thermodynamic systems. The Rényi entropy is one of the entropic forms which is suitable to deal with nonextensive properties of the black string. In this work, we investigated the possibility to obtain a stable black string by using the Rényi entropy in both separated and effective approaches. We found that the nonextensivity provides the thermodynamically stable black string with moderate size in both approaches. The transition from the hot gas phase to the moderate-sized stable black string in the separated/effective description is a first-order/zeroth-order phase transition. The significant ways to distinguish the black string from both approaches are discussed.

Entanglement wedge minimum cross-section for holographic aether gravity

We study the entanglement wedge cross-section (EWCS) in holographic Aether gravity theory, a gravity theory with Lorentz symmetry violation while keeping the general covariance intact. We find that only a limited parameter space is allowed to obtain a black brane with positive Hawking temperature. Subject to these allowed parameter regions, we find that the EWCS could exhibit non-monotonic behaviors with system parameters. Meanwhile, the holographic entanglement entropy (HEE), and the corresponding mutual information (MI), can only exhibit monotonic behaviors. These phenomena suggest that the EWCS could capture much more rich content of the entanglement than that of the HEE and the MI. The role of the Lorentz violation in determining the behaviors of quantum information-related quantities is also analyzed.

Black strings thermodynamics in noncommutative spacetime

Black holes have been a subject of investigation over years not only because they have interesting physical properties, but also because they seem to be the appropriate tool for studying gravity in quantum scale. A lot of effort has been made to understand the aspects of spacetime on the quantum scale. Among several possibilities, the approach which includes noncommutativity of spacetime proves to be promising. In this paper, we use the Hamilton–Jacobi method to study the thermodynamic properties of cylindrical black holes (black strings) in noncommutative spacetime. The behavior of the black string is also investigated in the presence of back reaction as well as its influence on the system can be understood as an anomaly. This work aims to provide an understanding about black strings thermodynamics in noncommutative spacetime since this scale of spacetime is important for the comprehension of the relation between quantum mechanics and general relativity.

The quest for a conifold conformal order

The holographic duality between cascading gauge theory and type IIB supergravity on warped deformed conifold with fluxes reveals exotic thermal phases with nonzero expectation values of certain operators, persistent to high temperatures. These phases, in the limit of vanishing the strong coupling scale of the cascading gauge theory, would realize thermal ordered conformal phases in ℝ3,1 relativistic QFT. We find that the dual Klebanov-Strassler/Klebanov-Tseytlin black branes in this limit are outside the regime of the supergravity approximation, rendering the construction of such conformal ordered states unreliable. While we have been able to construct conformal order in phenomenologically deformed effective theory of type IIB supergravity reduced on warped deformed conifold with fluxes, the removal of the deformation parameter causes the destruction of the thermal conformal ordered phases. Once again, we find that the holographic models with the conformal ordered phases are in the String Theory swampland.

Investigations of strong cosmic censorship in 3-dimensional black strings

Investigating the quasinormal modes of a massive scalar field on the 3-dimensional black string (3dBS), we study the strong cosmic censorship (SCC) conjecture for the 3dBS in the T-dual relationship with the 3-dimensional rotating anti-de-Sitter (BTZ) black hole. It is shown that even though geometries of the two spacetimes are quite different, such as asymptotically AdS for the BTZ black hole and asymptotically flat for the 3dBS, the BTZ black hole and the 3dBS share similar properties for the SCC. Concretely speaking, the SCC conjecture can be violated even for asymptotically flat spacetime, i.e. the 3dBS. These observations lead us to an assumption that the T-dual transformation preserves spacetime symmetries, at least, which are relevant to the SCC. In addition, we find a new feature of the quasinormal mode at the Cauchy horizon: in the case of in the 3dBS, the spectral gap, αBS at the Cauchy horizon is not determined by the ‘ω-frequency mode’, but the ‘m-frequency mode’.

Quasinormal modes of NUT-charged black branes in the AdS/CFT correspondence

We study the scalar, electromagnetic and gravitational perturbations of planar AdS4 black holes with NUT charge. In the context of the AdS/CFT correspondence, these solutions describe a thermal quantum field theory embedded in a Gödel-type Universe with closed time-like curves. For a given temperature and NUT charge, two different planar Taub–NUT solutions exist, but we show that only the one with a positive specific heat contributes to the Euclidean saddle point in the path integral. By using the Newman–Penrose formalism, we then derive the master equations satisfied by scalar, electromagnetic and gravitational perturbations in this background, and show that the corresponding equations are separable. Interestingly, the solutions pile up in the form of Landau levels, and hence are characterized by a single quantum number q. We determine the appropriate boundary conditions satisfied by the master variables and using these we compute the quasinormal modes of scalar and gravitational perturbations. On the other hand, electromagnetic perturbations depend on a free parameter whose determination is problematic. We find that all the scalar and gravitational QNM frequencies lie in the lower half of the complex plane, indicating that these Taub–NUT spacetimes are stable. We discuss the implications of these results in the light of the AdS/CFT correspondence.