Black Holes In String Theory Research Articles

From black holes to flux throats

Supersymmetry‐breaking is a key ingredient for string theory models to be phenomenologically viable. We review the strong analogy in the physics and methods used for describing non‐supersymmetric flux vacua and non‐supersymmetric black holes in string theory. We also show how the polarized state could be the key to describing a well‐behaved back‐reaction of anti‐branes in flux backgrounds, shedding a new light on a recent debate in the literature.

Absorption of scalars by nonextremal charged black holes in string theory

We analyze the low frequency absorption cross section of minimally coupled massless scalar fields by different kinds of charged static black holes in string theory, namely the D1-D5 system in d=5 and a four dimensional dyonic four-charged black hole. In each case we show that this cross section always has the form of some parameter of the solution divided by the black hole Hawking temperature. We also verify in each case that, despite its explicit temperature dependence, such quotient is finite in the extremal limit, giving a well defined cross section. We show that this precise explicit temperature dependence also arises in the same cross section for black holes with string alpha' corrections: it is actually induced by them.

On the temperature dependence of the absorption cross-section for black holes in string theory

We study the low frequency absorption cross-section of spherically symmetric nonextremal d-dimensional black holes. In the presence of α′ corrections, this quantity must have an explicit dependence on the Hawking temperature of the form 1/TH. This property of the low frequency absorption cross-section is shared by the D1-D5 system from type IIB superstring theory already at the classical level, without α′ corrections. We apply our formula to the simplest example, the classical d-dimensional Reissner–Nordström solution, checking that the obtained formula for the cross-section has a smooth extremal limit. We also apply it for a d-dimensional Tangherlini-like solution with α′3 corrections.

Physical Kinetics of Loop Quantum Gravity and Blackhole Dynamics: Kinetic Theory of Quantum Spacetime, Blackhole Phase Transition Theory and Blackhole Fission.

In the following chapter, a sincere endeavor is made to build a physically as well as in most later aspects a mathematically simple but rigorous physical kinetics of spacetime and of blackholes. Starting with a 3-volume quantization result of the now standard Ashtekar-Lewandowski Quantum Riemannian Geometry, and based on the work of the author on time as a vortex, a 4-volume spacetime quantum, a rapidly fluctuating one is developed and the foundations seem to look shaky in the very beginning, but start to get stronger and stronger as one starts to enter the end of the section on the physical kinetics of blackholes. Thus, experimental tests and observational predictions have been made whenever seem required or appropriate for justification, examples from laboratory table-top physics provided. Once the framework of kinetic theory has been developed, the author has entered into the realm of blackhole phase transitions nucleating from backgroung spacetime as well as other blackhole phase transitions. The equations of phase transitions have been rigorously analyzed and physical interpretations and physical predictions provided. Also certain the Bardeen-Carter-Hawking standard zeroeth law of blackhole dynamics been deduced in the context of equilibrium phase transitions in blackholes. The possibility of splitting of the Kerr-Newman blackhole akin to nuclear fission is obtained. An interesting work is the conception and extensin of the stretched horizon which was constructed by Ashoke Sen in the context of unphysical extremal blackholes in string theory -to that of isolated horizons in the context of arbitrary blackholes as proposed by Rovelli . Quantum gravitational dispersion as well as diffraction of light and gravitational waves by discrete nature of quantum spacetime geometry has been predicted in phenomenology. The paper predicts the gravi-electric Meissner effect in the wake of the Galilean superconductivity in the form of locally Lorentzian spacetimes as a critical behavior in the context of a second order phase transition. The property of the blackholes to undergo fission is demonstrated in the equations of phase transitions. This is used to explain the astrophysical phenomenon of Quasars. An iso-Higgs multiplet is qualitatively predicted as basic constituents of the blackhole. A liquid droplet model is suggested to explain the newly predicted phenomenon of blackhole fission in this paper.The chapter as a whole builds the foundations of the subject of the title of the paper.

Effect of the deformation operator in the D1D5 CFT

The D1D5 CFT gives a holographic dual description of a near-extremal black hole in string theory. The interaction in this theory is given by a marginal deformation operator, which is composed of supercharges acting on a twist operator. The twist operator links together different copies of a free CFT. We study the effect of this deformation operator when it links together CFT copies with winding numbers M and N to produce a copy with winding M+N, populated with excitations of a particular form. We compute the effect of the deformation operator in the full supersymmetric theory, firstly on a Ramond-Ramond ground state and secondly on states with an initial bosonic or fermionic excitation. Our results generalize recent work which studied only the bosonic sector of the CFT. Our findings are a step towards understanding thermalization in the D1D5 CFT, which is related to black hole formation and evaporation in the bulk.

Deconfinement transition as black hole formation by the condensation of QCD strings

We argue that the deconfinement transition of large-$N$ Yang-Mills theory is the condensation of very long and self-intersecting chromo-electric flux strings (QCD string), which is analogous to the formation of a black hole in string theory. We do this by using lattice gauge theory and matrix models. As evidence, we derive an analytic formula for the deconfinement temperature in the strong coupling limit and confirm it numerically. Dual gravity descriptions interpreted in this manner should make it possible to understand the details of the formation of black holes in terms of fundamental strings. We argue that very simple matrix models capture the essence of the formation of black holes.

Empty black holes, firewalls, and the origin of Bekenstein–Hawking entropy

We propose a novel solution for the endpoint of gravitational collapse, in which spacetime ends (and is orbifolded) at a microscopic distance from black hole event horizons. This model is motivated by the emergence of singular event horizons in the gravitational aether theory, a semiclassical solution to the cosmological constant problem(s) and thus suggests a catastrophic breakdown of general relativity close to black hole event horizons. A similar picture emerges in fuzzball models of black holes in string theory, as well as the recent firewall proposal to resolve the information paradox. We then demonstrate that positing a surface fluid in thermal equilibrium with Hawking radiation, with vanishing energy density (but nonvanishing pressure) at the new boundary of spacetime, which is required by Israel junction conditions, yields a thermodynamic entropy that is identical to the Bekenstein–Hawking area law, SBH, for charged rotating black holes. To our knowledge, this is the first derivation of black hole entropy that only employs local thermodynamics. Furthermore, a model for the microscopic degrees of freedom of the surface fluid (which constitute the microstates of the black hole) is suggested, which has a finite, but Lorentz-violating, quantum field theory. Finally, we comment on the effects of physical boundary on Hawking radiation and show that relaxing the assumption of equilibrium with Hawking radiation sets SBH as an upper limit for Black Hole entropy.

Bogoliubov coefficients for the twist operator in the D1D5 CFT

The D1D5 CFT is a holographic dual of a near-extremal black hole in string theory. The interaction in this theory involves a twist operator which joins together different copies of a free CFT. Given a large number of D1 and D5 branes, the effective length of the circle on which the CFT lives is very large. We develop a technique to study the effect of the twist operator in the limit where the wavelengths of excitations are short compared to this effective length, which we call the ‘continuum limit’. The method uses Bogoliubov coefficients to compute the effect of the twist operator in this limit. For bosonic fields, we use the method to reproduce recent results describing the effect of the twist operator when it links together CFT copies with windings M and N, producing a copy of winding M+N. We also comment on possible generalizations of our results. The methods developed here may help in understanding the twist interaction at higher orders. This in turn should provide insight into the thermalization process in the D1D5 CFT, which gives a holographic description of black hole formation.

Electrodynamics of black holes in STU supergravity

External magnetic fields can probe the composite structure of black holes in string theory. With this motivation we study magnetised four-charge black holes in the STU model, a consistent truncation of maximally supersymmetric supergravity with four types of electromagnetic fields. We employ solution generating techniques to obtain Melvin backgrounds, and black holes in these backgrounds. For an initially electrically charged static black hole immersed in magnetic fields, we calculate the resultant angular momenta and analyse their global structure. Examples are given for which the ergoregion does not extend to infinity. We calculate magnetic moments and gyromagnetic ratios via Larmor's formula. Our results are consistent with earlier special cases. A scaling limit and associated subtracted geometry in a single surviving magnetic field is shown to lift to $AdS_3\times S^2$. Magnetizing magnetically charged black holes give static solutions with conical singularities representing strings or struts holding the black holes against magnetic forces. In some cases it is possible to balance these magnetic forces.

Microscopic and macroscopic entropy of extremal black holes in string theory

This is a short review summarizing the current status of the comparison between microscopic and macroscopic entropy of extremal BPS black holes in string theory.

State-Space Geometry, Statistical Fluctuations, and Black Holes in String Theory

We study the state-space geometry of various extremal and nonextremal black holes in string theory. From the notion of the intrinsic geometry, we offer a state-space perspective to the black hole vacuum fluctuations. For a given black hole entropy, we explicate the intrinsic geometric meaning of the statistical fluctuations, local and global stability conditions, and long range statistical correlations. We provide a set of physical motivations pertaining to the extremal and nonextremal black holes, namely, the meaning of the chemical geometry and physics of correlation. We illustrate the state-space configurations for general charge extremal black holes. In sequel, we extend our analysis for various possible charge and anticharge nonextremal black holes. From the perspective of statistical fluctuation theory, we offer general remarks, future directions, and open issues towards the intrinsic geometric understanding of the vacuum fluctuations and black holes in string theory.

Umbral moonshine

We describe surprising relationships between automorphic forms of various kinds, imaginary quadratic number fields and a certain system of six finite groups that are parameterised naturally by the divisors of twelve. The Mathieu group correspondence recently discovered by Eguchi-Ooguri-Tachikawa is recovered as a special case. We introduce a notion of extremal Jacobi form and prove that it characterises the Jacobi forms arising by establishing a connection to critical values of Dirichlet series attached to modular forms of weight two. These extremal Jacobi forms are closely related to certain vector-valued mock modular forms studied recently by Dabholkar-Murthy-Zagier in connection with the physics of quantum black holes in string theory. In a manner similar to monstrous moonshine the automorphic forms we identify constitute evidence for the existence of infinite-dimensional graded modules for the six groups in our system. We formulate an umbral moonshine conjecture that is in direct analogy with the monstrous moonshine conjecture of Conway-Norton. Curiously, we find a number of Ramanujan's mock theta functions appearing as McKay-Thompson series. A new feature not apparent in the monstrous case is a property which allows us to predict the fields of definition of certain homogeneous submodules for the groups involved. For four of the groups in our system we find analogues of both the classical McKay correspondence and McKay's monstrous Dynkin diagram observation manifesting simultaneously and compatibly.

String black hole: can it be a particle accelerator?

In this paper we have studied the possibility of the center-of-mass energy of two particles colliding near the horizon of a static charged black hole in string theory. Various cases corresponding to the electric charge and the angular momentum of the particles were considered. The studies were done for the general black hole as well as for the extreme black hole. There were two scenarios where the center-of-mass energy reach very large values if the appropriate properties of the particles are chosen.

Stability of charged black holes in string theory under charged massive scalar perturbations

Similar to the superradiant effect in Reissner-Nordstr\"{o}m black hole, a charged scalar field can be amplified when impinging on the charged black hole in string theory. According to the black-hole bomb mechanism,the mass term of the incident field can works as the reflecting mirror, which may trigger the instability of black hole. We study the possible instability triggered by superradiant effect and demonstrate that the charged black hole in string theory is stable against the massive charged scalar perturbation. The reason is that there is no trapping potential well in the black hole exterior which is separated from the horizon by a potential barrier and there is no bound states in the superradiant regime.

Asymptotically AdS charged black holes in string theory with Gauss-Bonnet correction in various dimensions

We study charged black hole solutions in Einstein-Maxwell-Gauss-Bonnet theory with the dilaton field which is the low-energy effective theory of the heterotic string. The spacetime is $D$ dimensional and assumed to be static and plane symmetric with the ($D\ensuremath{-}2$)-dimensional constant curvature space and asymptotically anti--de Sitter. By imposing the boundary conditions of the existence of the regular black hole horizon and proper behavior at infinity where the Breitenlohner-Freedman bound should be satisfied, we construct black hole solutions numerically. We give the relations among the physical quantities of the black holes such as the horizon radius, the mass, the temperature, and so on. The properties of the black holes do not depend on the dimensions qualitatively, which is different from the spherically symmetric and asymptotically flat case. There is nonzero lower limit for the radius of the event horizon below which no solution exists. The temperature of the black hole becomes smaller as the horizon radius is smaller but remains nonzero when the lower limit is attained.

Scattering of spherically symmetric d-dimensional α′-corrected black holes in string theory

We study scattering of minimally coupled massless scalar fields by non-extremal spherically symmetric black holes in d dimensions with string-theoretical α′ corrections. We then obtain a formula for the low frequency absorption cross section for every black hole of this kind, which we apply to known black hole solutions. We compare the α′ corrections for the absorption cross section with those for the black hole entropy, obtained through Wald’s formula, in each case concluding that these corrections are different. We find a general covariant formula for the absorption cross section including α′ corrections, in terms of the horizon area and temperature.

Tensorial perturbations and stability of spherically symmetricd-dimensional black holes in string theory

We compute the tensorial perturbations to a general spherically symmetric metric in d dimensions with string-theoretical corrections quadratic in the Riemann tensor, from which we derive their respective potential. We use this result to study the stability of corresponding black hole solutions under such perturbations.

On the positivity of black hole degeneracies in string theory

Certain helicity trace indices of charged states in N = 4 and N = 8 superstring theory have been computed exactly using their explicit weakly coupled microscopic descrip- tion. These indices are expected to count the exact quantum degeneracies of black holes carrying the same charges. In order for this interpretation to be consistent, these indices should be positive integers. We prove this positivity property for a class of four/five dimen- sional black holes in type II string theory compactified on T 6 /T 5 and on K3 ×T 2 /S 1 . The proof relies on the mock modular properties of the corresponding generating functions. 1. Introduction and statement of results The study of supersymmetric black holes in string theory has been very effective in shedding light on the issue of black hole entropy. The strength of the string theoretic approach lies in the fact that there are two related descriptions of charged black holes. The first (strong string coupling, macroscopic) description is a low energy effective description as general relativity coupled to a set of matter fields. In the second (weak string coupling, microscopic) descrip- tion, a generic state of the theory with the same charges as the black hole is identified as a collection of fundamental objects of string theory namely fundamental strings and branes. The fluctuations of these objects make up the elementary excitations (microstates) of the theory, which can be described by conventional quantum field theoretic methods. The key idea is to identify these two descriptions valid at strong and weak coupling, respectively. At strong coupling, the excitations of the strings and branes exert a gravitational force on each other, and the black hole can be thought of as a quantum mechanical bound state of these microstates. In a class of supersymmetric string theories with sixteen or more unbroken supercharges we now have a practically complete understanding of the spectrum of BPS states (see (27) for a relatively recent review). One can therefore subject the above idea to high precision tests, by comparing the statistical entropy of the ensemble of states and an appropriately defined thermodynamic entropy of the corresponding BPS black hole, beyond a large charge approximation. Since we know the microscopic degeneracies exactly, one can even aim for an

EXOTIC BRANES AND BLACK HOLE MICROSTATES

Besides ordinary branes such as D-branes, string theory is known to contain exotic branes which are related to ordinary branes by U-duality. Exotic branes are codimension-two objects and have non-trivial U-duality monodromies around them. This means that they are intrinsically non-geometric. Even if one starts with a system only with ordinary branes, exotic branes can be spontaneously generated by the supertube effect. We argue that, if one puts together more than two mutually supersymmetric branes, then, by a multi-stage supertube effect, the system will polarize into an exotic brane extending along an arbitrary surface, dubbed as the superstratum. We conjecture that, black holes in string theory, which are constructed by combining multiple ordinary branes, necessarily include exotic superstrata as their microscopic ingredients. We review the argument for the existence of superstrata and the recent progress toward constructing examples of superstrata in the framework of supergravity in six dimensions.

Charged black holes in string theory with Gauss-Bonnet correction in various dimensions

We study charged black hole solutions in Einstein-Gauss-Bonnet theory with the dilaton field which is the low-energy effective theory of the heterotic string. The spacetime is $D$-dimensional and assumed to be static and spherically symmetric with the ($D\ensuremath{-}2$)-dimensional constant curvature space and asymptotically flat. The system of the basic equations is complex and the solutions are obtained numerically. We identify the allowed parameter region where the black hole solutions exist, and show configurations of the field functions in $D=4--6$ and 10. We also show the relations of the physical quantities of the black holes such as the horizon radius, the mass, the temperature, and so on, and find several results. The forms of the allowed parameter regions are different depending on the dimension. There is no extreme black hole solution with $T=0$ that can be obtained by taking the limit of the nonextreme solutions within the parameter range we chose. Entropy of the black holes in the dilatonic theory is always larger than that in the nondilatonic theory. Our analysis includes the higher order term of the dilaton field which is not in our previous works. Its effect remarkably appears in five dimensions and is given in the Appendix. By our analysis it is found that the properties of the black hole solutions strongly depend on the dimension, charge, existence of the dilaton field. Hence both the detailed analyses of the individual systems and the investigations from the systematic point of view are important.