Exotic Black Holes Research Articles

Exotic black hole thermodynamics in third-order Lovelock gravity

The generalisation of Birkhoff’s theorem to higher dimensions in Lovelock gravity allows for black hole solutions with horizon geometries of non-constant curvature. We investigate thermodynamic aspects of these ‘exotic’ black hole solutions, with a particular emphasis on their phase transitions. We consider an extended phase space where the cosmological constant acts as a thermodynamic pressure, and examine both uncharged and U(1) charged solutions. In d = 7, black hole solutions are restricted to having constant curvature horizon base manifolds. Uncharged d = 7 black holes possess novel triple point phenomena analogous to those recently uncovered in exotic d = 6 black holes in Gauss–Bonnet gravity, while their charged counterparts generically undergo small-large black hole phase transitions. In d = 8, we find that both charged and uncharged black holes exhibit triple point behaviour and small-large black hole transitions. We also show that a wide range of ‘exotic’ horizon geometries can be ruled out due to the appearance of naked singularities.

Negative mass black holes in de Sitter space

We show that asymptotically de Sitter black holes of negative mass can exist in Lovelock gravity. Such black holes have horizon geometries with non-constant curvature and are known as Exotic Black Holes. We explicitly examine the case of Gauss-Bonnet gravity. We briefly discuss the positive mass case where we show how the transverse space geometry affects whether a black hole will exist or not.For negative mass solutions we shown how three different black hole spacetimes are possible depending on the transverse space geometry. We also provide closed form expressions for the geometric parameters to ensure that a black hole spacetime is observed. We close with a discussion of the massless case, where there are many different spacetimes that are permitted.

There is More Than Just One “Corona” That Can Kill Us All

When most people hear the phrase "space exploration", they imagine preparing the colonisation of Mars, studying distant planets, searching for alien life or studying exotic black holes. Many times, however, mankind tends to leap before looking and focus on the exotic and the interesting instead of that which might not seem that special to most of us, but which which can be crucial for our survival. This way, many major and important issues in astrophysics - and sciences in general - can become overlooked and take very long to resolve. One such major issue in astrophysics is the behaviour of our closest star, the Sun. While we generally assume that we have a good idea about the most significant processes in the solar interior acting as its main energy source, our attempts at explaining the dynamics and structure of the solar atmosphere (the so-called corona) are still merely an educated guesswork at best. Due to several of the magnetohydrodynamic processes which we do not yet fully understand, the temperature of the solar atmosphere is very high compared to the layers underneath and reaches millions of Kelvins. Since this is where the major mass ejections occur, some of which might be directed towards the Earth causing geomagnetic storms, it is crucial that we start not only to fully understand these processes, but also to be able to accurately predict their outcomes. As will be shown in this text however, it is not only our limited understanding of the physics which prevents us from doing that; it is also the lack of computational resources. This paper firstly briefly discusses the basic physics behind the behaviour of the solar coronal plasma. Afterwards, it discusses the coronal heating problem in more detail and finally, it outlines the major challenges we currently face which seem to prevent us from efficient simulation and complete understanding of the behaviour of our closest star.

Thermodynamics of exotic black holes in Lovelock gravity

We examine the thermodynamics of a new class of asymptotically AdS black holes with non-constant curvature event horizons in Gauss-Bonnet Lovelock gravity, with the cosmological constant acting as thermodynamic pressure. We find that non-trivial curvature on the horizon can significantly affect their thermodynamic behaviour. We observe novel triple points in 6 dimensions between large and small uncharged black holes and thermal AdS. For charged black holes we find a continuous set of triple points whose range depends on the parameters in the horizon geometry. We also find new generalizations of massless and negative mass solutions previously observed in Einstein gravity.

BTZ entropy from topological M-theory

By determining the relation between topological M-theory and the Chern-Simons actions for a gauge field constructed from the Lie algebra of either SL(2,R)x SL(2,R) or SL(2,C)x SL(2,C), depending on the sign of the space-time curvature, we show that the standard and exotic actions of 3-dimensional gravity can be recovered from topological M-theory. With this result, we provide a concrete realisation of a conjecture by Dijkgraaf et al. stating that the partition function of topological M-theory is equivalent to the partition function of a black hole in a related theory. We do this for the standard and exotic BTZ black holes in 3-dimensional gravity.

Extended thermodynamics and complexity in gravitational Chern-Simons theory

We study several aspects of the extended thermodynamics of BTZ black holes with thermodynamic mass M=alpha m+gamma frac{j}{ell } and angular momentum J = αj + γℓm, for general values of the parameters (α, γ) ranging from regular (α = 1, γ = 0) to exotic (α = 0, γ = 1). We show that there exist two distinct behaviours for the black holes, one when α > γ (“mostly regular”), and the other when γ < α (“mostly exotic”). We find that the Smarr formula holds for all (α, γ). We derive the corresponding thermodynamic volumes, which we find to be positive provided α and γ satisfy a certain constraint. The dependence of pressure on volume is unremarkable and strictly decreasing when α > γ, but a maximum volume emerges for large J ≫ T when γ > α; consequently an exotic black hole of a given horizon circumference and temperature can exist in two distinct anti de Sitter backgrounds. We compute the reverse isoperimetric ratio, and study the Gibbs free energy and criticality conditions for each. Finally we investigate the complexity growth of these objects and find that they are all proportional to the complexity of the BTZ black hole. Somewhat surprisingly, purely exotic BTZ black holes have vanishing complexity growth.

Thermodynamic instabilities of generalized exotic BTZ black holes

We examine the conjecture that black holes violating the reverse isoperimetric inequality have negative specific heat at constant volume CV [1]. We test this conjecture on the family of generalized exotic Bañados, Teitelboim and Zanelli (BTZ) black holes and find that CV can be positive even when the reverse isoperimetric inequality is violated, providing a counter example to the conjecture. However in all cases where CV is positive, the specific heat at constant pressure CP is negative, indicating that generalized exotic black holes are thermodynamically unstable, suggesting that a broader version of the conjecture might hold.

On black hole thermodynamics with a momentum relaxation

We investigate black hole thermodynamics involving a scalar hair which is dual to a momentum relaxation of the dual field theory. This black hole geometry is able to be classified by two parameters. One is a momentum relaxation and the other is a mass density of another matter localized at the center. Even though all parameters are continuous, there exists a specific point where its thermodynamic interpretation is not continuously connected to the one defined in the other parameter regime. The similar feature also appears in a topological AdS black hole. In this work, we show why such an unusual thermodynamic feature happens and provide a unified way to understand such an exotic black hole thermodynamically in the entire parameter range.

Phase transitions of an anisotropic N=4 super Yang-Mills plasma via holography

Black hole solutions of type IIB supergravity were previously found that are dual to N=4 supersymmetric Yang-Mills plasma with an anisotropic spatial deformation. In the zero temperature limit, these black holes approach a Liftshitz like scaling solution in the IR. It was recently shown that these black holes are unstable, and at low temperatures there is a new class of black hole solutions that are thermodynamically preferred. We extend this analysis, by considering consistent truncations of the Kaluza-Klein reduction of IIB supergravity on a five-sphere that preserves multiple scalar and $U(1)$ gauge fields. We show that the previously constructed black holes become unstable at low temperatures, and construct new classes of exotic black hole solutions. We study the DC thermo-electric conductivity of these $U(1)$ charged black holes, and find a diverging DC conductivity at zero temperature due to the divergence of the gauge field coupling.

The mass formula for an exotic BTZ black hole

An exotic Bañados–Teitelboim–Zanelli (BTZ) black hole has an angular momentum larger than its mass in three dimension (3D), which suggests the possibility that cosmic censorship could be violated if angular momentum is extracted by the Penrose process. In this paper, we propose a mass formula for the exotic BTZ black hole and show no violation of weak cosmic censorship in the gedanken process above by understanding properly its mass formula. Unlike the other black holes, the total energy of the exotic BTZ black hole is represented by the angular momentum instead of the mass, which supports a basic point of view that the same geometry should be determined by the same energy in 3D general relativity whose equation of motion can be given either by normal 3D Einstein gravity or by exotic 3D Einstein gravity. However, only the mass of the exotic black hole is related to the thermodynamics and other forms of energy are “dumb”, which is consistent with the earlier thermodynamic analysis about exotic black holes.

An Alexandrov–Fenchel-Type Inequality in Hyperbolic Space with an Application to a Penrose Inequality

We prove a sharp Alexandrov-Fenchel-type inequality for star-shaped, strictly mean convex hypersurfaces in hyperbolic $n$-space, $n\geq 3$. The argument uses two new monotone quantities along the inverse mean curvature flow. As an application we establish, in any dimension, an optimal Penrose inequality for asymptotically hyperbolic graphs carrying a minimal horizon, with the equality occurring if and only if the graph is an anti-de Sitter-Schwarzschild solution. This sharpens previous results by Dahl-Gicquaud-Sakovich and settles, for this class of initial data sets, the conjectured Penrose inequality for time-symmetric space-times with negative cosmological constant. We also explain how our methods can be easily adapted to derive an optimal Penrose inequality for asymptotically locally hyperbolic graphs in any dimension $n\geq 3$. When the horizon has the topology of a compact surface of genus at least one, this provides an affirmative answer, for this class of initial data sets, to a question posed by Gibbons, Chrusciel and Simon on the validity of a Penrose-type inequality for exotic black holes.

THE DISCOVERY OF PERIODIC MODULATIONS IN THE OPTICAL SPECTRA OF GALAXIES, POSSIBLY DUE TO ULTRARAPID LIGHT BURSTS FROM THEIR MASSIVE CENTRAL BLACK HOLES

A Fourier transform analysis of 2.5 million spectra in the SDSS survey was carried out to detect periodic modulations contained in their intensity versus frequency spectrum. A statistically significant signal was found for 223 galaxies while the spectra of 0.9 million galaxies were observed. A plot of the periods as a function of redshift clearly shows that the effect is real without any doubt, because they are quantized at two base periods that increase with redshift in two very tight parallel linear relations. I suggest that it could be caused by light bursts separated by times of the order of 10-13 seconds because it was the original reason for searching for the spectral periodicity but other causes may be possible. As another possible cause, I investigate the hypothesis that the modulation is generated by the Fourier transform of spectral lines, concluding that it is not valid. Although the light bursts suggestion implies absurdly high temperatures, it is supported by the fact that the Crab pulsar also has extremely short unresolved pulses (<0.5 nanosecond) that also imply absurdly high temperatures. Furthermore, the radio spectrum of the Crab pulsar also has spectral bands similar to those that have been detected. Finally, decreasing the signal to noise threshold of detection gave results consistent with beamed signals having a small beam divergence, as expected from non-thermal sources that send a jet, like those seen in pulsars. Considering that galaxy centers contain massive black holes, exotic black hole physics may be responsible for the spectral modulation. However, at this stage, this is only a hypothesis to be confirmed with further work.

Thermodynamics of "exotic" Bañados-Teitelboim-Zanelli black holes.

A number of three-dimensional (3D) gravity models, such as 3D conformal gravity, admit "exotic" black hole solutions: the metric is the same as the Bañados-Teitelboim-Zanelli metric of 3D Einstein gravity but with reversed roles for mass and angular momentum, and an entropy proportional to the length of the inner horizon instead of the event horizon. Here we show that the Bañados-Teitelboim-Zanelli solutions of the exotic 3D Einstein gravity (with parity-odd action but Einstein field equations) are exotic black holes, and we investigate their thermodynamics. The first and second laws of black hole thermodynamics still apply, and the entropy still has a statistical interpretation.

Eling–Oz formula for exotic hairy black holes

We checked Eling–Oz formula (Eling and Oz, 2011, [1]) for the bulk viscosity of the holographic fluid dual to the exotic black holes (Buchel and Pagnutti, 2010, [2]). Initially, Eling and Oz argued that the formula is valid in the high temperature and adiabatic limits. In Buchel (2011) [3] the validity of the formula for N=2⁎ plasma and cascading gauge theory was pushed forward for arbitrary temperatures. We successfully verified the formula with the computations of the bulk viscosity (Buchel and Pagnutti, 2010, 2011, [4,5]) for a wide range of the temperatures. Moreover, it correctly reproduces the critical behavior in the vicinity of the critical point, where the bulk-to-shear viscosity diverges.

Heterotic horizons, Monge-Ampère equation and del Pezzo surfaces

Heterotic horizons preserving 4 supersymmetries have sections which are T^2 fibrations over 6-dimensional conformally balanced Hermitian manifolds. We give new examples of horizons with sections S^3 X S^3 X T^2 and SU(3). We then examine the heterotic horizons which are T^4 fibrations over a Kahler 4-dimensional manifold. We prove that the solutions depend on 6 functions which are determined by a non-linear differential system of 6 equations that include the Monge-Ampere equation. We show that this system has an explicit solution for the Kahler manifold S^2 X S^2. We also demonstrate that there is an associated cohomological system which has solutions on del Pezzo surfaces. We raise the question of whether for every solution of the cohomological problem there is a solution of the differential system, and so a new heterotic horizon. The horizon sections have topologies which include ((k-1) S^2 X S^4 # k (S^3 X S^3)) X T^2$ indicating the existence of exotic black holes. We also find an example of a horizon section which gives rise to two different near horizon geometries.

Einstein-Gauss-Bonnet metrics: black holes, black strings and a staticity theorem

We find the general solution of the 6-dimensional Einstein-Gauss-Bonnet equations in a large class of space and time-dependent warped geometries. Several distinct families of solutions are found, some of which include black string metrics, space and time-dependent solutions and black holes with exotic horizons. Among these, some are shown to verify a Birkhoff type staticity theorem, although here, the usual assumption of maximal symmetry on the horizon is relaxed, allowing exotic horizon geometries. We provide explicit examples of such static exotic black holes, including ones whose horizon geometry is that of a Bergman space. We find that the situation is very different from higher-dimensional general relativity, where Einstein spaces are admissible black hole horizons and the associated black hole potential is not even affected. In Einstein-Gauss-Bonnet theory, on the contrary, the non-trivial Weyl tensor of such exotic horizons is exposed to the bulk dynamics through the higher order Gauss-Bonnet term, severely constraining the allowed horizon geometries and adding a novel charge-like parameter to the black hole potential. The latter is related to the Euler characteristic of the four-dimensional horizon and provides, in some cases, additional black hole horizons.

THOUGHTS ON THE AREA THEOREM

Hawking's area theorem can be understood from a quasistationary process in which a black hole accretes positive energy matter, independent of the details of the gravity action. I use this process to study the dynamics of the inner as well as the outer horizons for various black holes which include the recently discovered exotic black holes and three-dimensional black holes in higher derivative gravities as well as the usual Banados–Teitelboim–Zanelli (BTZ) black hole and the Kerr black hole in four dimensions. I find that the area for the inner horizon "can decrease," rather than increase, with the quasistationary process. However, I find that the area for the outer horizon "never decrease" such as the usual area theorem still works in our examples, though this is quite nontrivial in general. I also find that the recently proposed new entropy formulae for the above mentioned, recently discovered black holes satisfy the second law of thermodynamics.

Notes on the area theorem

Hawking's area theorem can be understood from a quasi-stationary process in which a black hole accretes positive energy matter, independent of the details of the gravity action. I use this process to study the dynamics of the inner as well as the outer horizons for various black holes which include the recently discovered exotic black holes and three-dimensional black holes in higher derivative gravities as well as the usual BTZ black hole and the Kerr black hole in four dimensions. I find that the area for the inner horizon ‘can decrease’, rather than increase, with the quasi-stationary process. However, I find that the area for the outer horizon ‘never decreases’ such that the usual area theorem still works in our examples, though this is quite non-trivial in general. There exists an instability problem of the inner horizons but it seems that the instability is not important in my analysis. I also find a generalized area theorem by combining those of the outer and inner horizons.

Bicycling black rings

We present detailed physics analyses of two different 4+1-dimensional asymptotically flat vacuum black hole solutions with spin in two independent planes: the doubly spinning black ring and the bicycling black ring system (``bi-rings''). The latter is a new solution describing two concentric orthogonal rotating black rings which we construct using the inverse scattering technique. We focus particularly on extremal zero-temperature limits of the solutions. We construct the phase diagram of currently known zero-temperature vacuum black hole solutions with a single event horizon, and discuss the non-uniqueness introduced by more exotic black hole configurations such as bi-rings and multi-ring saturns.

Can Hawking temperatures be negative?

It has been widely believed that the Hawking temperature for a black hole is uniquely determined by its metric and positive. But, I argue that this might not be true in the recently discovered black holes which include the exotic black holes and the black holes in the three-dimensional higher curvature gravities. I argue that the Hawking temperatures, which are measured by the quantum fields in thermal equilibrium with the black holes, might not be the usual Hawking temperature but the new temperatures that have been proposed recently and can be negative. The associated new entropy formulae, which are defined by the first and second laws of thermodynamics, versus the black hole masses show some genuine effects of the black holes which do not occur in the spin systems. Some cosmological implications and physical origin of the discrepancy with the standard analysis are noted also.