The method of topological renormalization in anti-de Sitter (AdS) gravity consists in adding to the action a topological term which renders it finite, defining at the same time a well-posed variational problem. Here, we use this prescription to work out the thermodynamics of asymptotically locally anti-de Sitter (AlAdS) spacetimes, focusing on the physical properties of the Misner strings of both the Taub-NUT-AdS and Taub-Bolt-AdS solutions. We compute the contribution of the Misner string to the entropy by treating on the same footing the AdS and AlAdS sectors. As topological renormalization is found to correctly account for the physical quantities in the parity preserving sector of the theory, we then investigate the holographic consequences of adding also the Chern-Pontryagin topological invariant to the bulk action; in particular, we discuss the emergence of the parity-odd contribution in the boundary stress tensor.
I show that gravitational entropy can be ascribed to spacetimes containing Misner strings (the gravitational analogues of Dirac strings), even in the absence of any other event horizon (or bolt) structures. This result follows from an extension of proposals for evaluating the stress-energy of a gravitational system which are motivated by the AdS/CFT correspondence.
As shown recently (arXiv:1903.08668), consistent thermodynamics of the Lorentzian Taub-NUT solutions with Misner strings present can be formulated provided a new pair of conjugate quantities (related to the NUT parameter) $ψ-N$ is introduced. In (arXiv:1903.08668) this pair was calculated from the Euclidean action but no geometrical interpretation for the new quantities was provided. In this paper we propose that the potential $ψ$ should be identified with the surface gravity of the Misner string and the conjugate Misner charge $N$ can be obtained by a Komar-type integration over the tubes sur…
Motivated by recent activities in Lorentzian Taub-NUT space thermodynamics, we calculate conserved charges of these spacetimes. We find additional mass, nut, angular momentum, electric and magnetic charge densities distributed along Misner string. These additional charges are needed to account for the difference between the values of the above charges at horizon and at infinity. We propose an unconstrained thermodynamical treatment for Taub-NUT spaces, where we introduce the nut charge $n$ as a relevant thermodynamic quantity with its chemical potential ϕ_n. The internal energy in this treatme…
Special multi-cosmic string metrics are analytically extended to describe configurations of Wheeler-Misner wormholes and ordinary cosmic strings. I investigate in detail the case of flat, asymptotically Minkowskian, Wheeler-Misner wormhole spacetimes generated by two cosmic strings, each with tension $-1/4G$.
We investigate closed string tachyon condensation in Misner space, a toy model for big bang universe. In Misner space, we are able to condense tachyonic modes of closed strings in the twisted sectors, which is supposed to remove the big bang singularity. In order to examine this, we utilize D-instanton as a probe. First, we study general properties of D-instanton by constructing boundary state and effective action. Then, resorting to these, we are able to show that tachyon condensation actually deforms the geometry such that the singularity becomes milder.
Using a boundary counterterm prescription motivated by the AdS/CFT conjecture, I evaluate the energy, entropy and angular momentum of the class of Kerr-NUT/bolt-AdS spacetimes. As in the non-rotating case, when the NUT charge is nonzero the entropy is no longer equal to one-quarter of the area due to the presence of the Misner string. When the cosmological constant is also non-zero, the entropy is bounded from above.
Misner space, also known as the Lorentzian orbifold $R^{1,1}/boost$, is one of the simplest examples of a cosmological singularity in string theory. In this lecture, we review the semi-classical propagation of closed strings in this background, with a particular emphasis on the twisted sectors of the orbifold. Tree-level scattering amplitudes and the one-loop vacuum amplitude are also discussed.
We compute correlation functions of closed strings in Misner space, a big crunch big bang universe. We develop a general method for correlators with twist fields, which are relevant for the investigation on the condensation of winding tachyon. We propose to compute the correlation functions by performing an analytic continuation of the results in C/Z_N Euclidean orbifold. In particular, we obtain a finite result for a general four point function of twist fields, which might be important for the interpretation as the quartic term of the tachyon potential. Three point functions are read off thro…
We address a long-standing problem of describing the thermodynamics of rotating Taub--NUT solutions. The obtained first law is of full cohomogeneity and allows for asymmetric distributions of Misner strings as well as their potential variable strengths---encoded in the gravitational Misner charges. Notably, the angular momentum is no longer given by the Noether charge over the sphere at infinity and picks up non-trivial contributions from Misner strings.
We use D-instantons to probe the geometry of Misner universe, and calculate the world volume field theory action, which is of the 1+0 dimensional form and highly non-local. Turning on closed string tachyons, we see from the deformed moduli space of the D-instantons that the spacelike singularity is removed and the region near the singularity becomes a fuzzy cone, where space and time do not commute. When realized cosmologically there can be controllable trans-planckian effects. And the infinite past is now causally connected with the infinite future, thus also providing a model for big crunch/…
We study D-branes in a two-dimensional Lorentzian orbifold R^{1,1}/Γwith a discrete boost Γ. This space is known as Misner or Milne space, and includes big crunch/big bang singularity. In this space, there are D0-branes in spiral orbits and D1-branes with or without flux on them. In particular, we observe imaginary parts of partition functions, and interpret them as the rates of open string pair creation for D0-branes and emission of winding closed strings for D1-branes. These phenomena occur due to the time-dependence of the background. Open string 2 -> 2 scattering amplitude on a D1-brane is…
Misner space, also known as the Lorentzian orbifold $R^{1,1}/boost$, is one of the simplest examples of a cosmological singularity in string theory. In this work, the study of weakly coupled closed strings on this space is pursued in several directions: (i) physical states in the twisted sectors are found to come in two kinds: short strings, which wind along the compact space-like direction in the cosmological (Milne) regions, and long strings, which wind along the compact time-like direction in the (Rindler) whiskers. The latter can be viewed as infinitely long static open strings, stretching…
Misner space, also known as the Lorentzian orbifold $R^{1,1}/boost$, is the simplest tree-level solution of string theory with a cosmological singularity. We compute tree-level scattering amplitudes involving twisted states, using operator and current algebra techniques. We find that, due to zero-point quantum fluctuations of the excited modes, twisted strings with a large winding number $w$ are fuzzy on a scale $\sqrt{\log w}$, which can be much larger than the string scale. Wave functions are smeared by an operator $\exp(Δ(ν) \partial_+ \partial_-)$ reminiscent of the Moyal-product of non-co…
We show that the first law for the rotating Taub-NUT is straightforwardly established with the surface charge method. The entropy is explicitly found as a charge, and its value is not proportional to the horizon area. We conclude that there are unavoidable contributions from the Misner strings to the charges, still, the mass and angular momentum gets standard values. However, there are no independent charges associated with the Misner strings.
It has been proposed that spacetimes with a U(1) isometry group have contributions to the entropy from Misner strings as well as from the area of $d-2$ dimensional fixed point sets. In this paper we test this proposal by constructing Taub-Nut-AdS and Taub-Bolt-AdS solutions which are examples of a new class of asymptotically locally anti-de Sitter spaces. We find that with the additional contribution from the Misner strings, we exactly reproduce the entropy calculated from the action by the usual thermodynamic relations. This entropy has the right parameter dependence to agree with the entropy…
This article focuses on the new approach to the nature of a nut parameter $n$, usually treated as a dual charge to the mass. Instead of thinking about it as a gravitational analog of the magnetic monopole, we will show that the Taub-NUT spacetime conceals a peculiar rotation coming from the Misner strings depending on the nut value. Besides reconciling a number of confusing results present in the literature, this allows us to establish a consistent description of the black hole thermodynamics for the Lorentzian Taub--NUT spacetime with essential contribution from the Misner strings to the angu…
In a previous paper (hep-th/0509067) using matrix model, we showed that closed string tachyons can resolve spacelike singularity in one particular class of Misner space (with anti-periodic boundary conditions for fermions around the spatial circle). In this note, we show that for Misner space without closed string tachyons, there also exists a mechanism to resolve the singularity in the context of the matrix model, namely cosmological winding string production. We show that here space and time also become noncommutative due to these winding strings. Employing optical theorem, we study the bulk…
Using the revised Komar-Tomimatsu approach, we derive Smarr mass formulas for stationary axisymmetric solutions of the Einstein-Maxwell equations containing line singularities (defects) on the polar axis. In terms of the rod structure associated with Weyl representation of the metric, the horizons and the defects are formally similar up to differences due to their timelike/spacelike character. We derive (previously unknown or incorrect) horizon and global Smarr formulas in presence of a Newman-Unti-Tamburino (NUT) parameter. To avoid the divergence of the Komar angular momentum of semi-infinit…
The thermodynamics of the Taub-NUT solution has been predominantly studied in the Euclidean sector, upon imposing the condition for the absence of Misner strings. Such thermodynamics is quite exceptional: the periodicity of the Euclidean time is restricted and thence the NUT charge cannot be independently varied, the entropy is not equal to a quarter of the area, and the thermodynamic volume can be negative. In this paper we revisit this paradigm and study the thermodynamics of the Lorentzian Taub-NUT solution, maintaining (as recently shown relatively harmless) Misner strings. We argue that i…
In this paper, we investigate the holographic complexity in the charged Taub-NUT-AdS black holes with Misner strings present in the Einstein-Maxwell gravity. We show that differing from the normal black holes, where the late-time complexity growth rate is only determined by the quantities at outer and inner ``Reissner-Nordstrom''-type (RN-type) horizons, here the quantities (the Misner potential and Misner charge) related to the Misner strings also play an important role in CA complexity. Similar to the case of the normal electromagnetic black hole, the late-time rate for the original CA conje…
We present the complete set of analytical solutions of the geodesic equation in Taub-NUT space-times in terms of the Weierstrass elliptic function. We systematically study the underlying polynomials and characterize the motion of test particles by its zeros. Since the presence of the "Misner string" in the Taub-NUT metric has led to different interpretations, we consider these in terms of the geodesics of the space-time. In particular, we address the geodesic incompleteness at the horizons discussed by Misner and Taub, and the analytic extension of Miller, Kruskal and Godfrey, and compare with…
The non-linear sigma model of the dimensionally reduced Einstein (-Maxwell) theory is diagonally embedded into that of the two-dimensional heterotic string theory. Consequently, the embedded string backgrounds satisfy the (electro-magnetic) Ernst equation. In the pure Einstein theory, the Matzner-Misner SL(2,{\bf R}) transformation can be viewed as a change of conformal structure of the compactified flat two-torus, and in particular its integral subgroup SL(2,{\bf Z}) acts as the modular transformation. The Ehlers SL(2,{\bf R}) and SL(2,{\bf Z}) similarly act on another torus whose conformal s…
We demonstrate that $(D+1)$-dimensional, locally asymptotically anti-deSitter spacetimes with nonzero NUT charge generically do not respect the usual relationship between area and entropy. This result does not depend on either the existence of closed timelike curves nor on the removal of Misner string singularities, but instead is a consequence of the first law of thermodynamics.
A master action for bosonic strings and membranes, interpolating between the Nambu--Goto and Polyakov formalisms, is discussed. The role of the gauge symmetries vis-à-vis reparametrization symmetries of the various actions is analyzed by a constrained Hamiltonian approach. This analysis reveals the difference between strings and higher branes, which is essentially tied to a degree of freedom count. The cosmological term for membranes follows naturally in this scheme. The conncetion of our aproach with the Arnowitt--Deser--Misner representation in general relativity is illuminated.
The statistical entropy of a Schwarzschild black string in five dimensions is obtained by counting the black string states which form a representation of the near-horizon conformal symmetry with a central charge. The statistical entropy of the string agrees with its Bekenstein-Hawking entropy as well as that of the Schwarzschild black hole in four dimensions. The choice of the string length which gives the Virasoro algebra also reproduces the precise value of the Bekenstein-Hawking entropy and lies inside the stability bound of the string.
The string-black hole correspondence is considered in the context of the correspondence principle proposed recently by Horowitz and Polchinski. We demonstrate that the entropy of string states and the entropy of a Schwarzschild black hole can be matched including the subleading terms which depend on mass logarithmically. We argue the necessity to include the string interaction (with coupling $g$) in the consideration and propose the $g^2$-dependent modification of the string entropy. The matching of it with the entropy of Schwarzschild black hole is analyzed.
Suggested correspondence between a black hole and a highly excited elementary string is explored. Black hole entropy is calculated by computing the density of states for an open excited string. We identify the square root of oscillator number of the excited string with Rindler energy of black hole to obtain an entropy formula which, not only agrees at the leading order with the Bekenstein-Hawking entropy, but also reproduces the logarithmic correction obtained for black hole entropy in the quantum geometry framework. This provides an additional supporting evidence for correspondence between bl…
We provide formulas for the entropy of free-string states depending on their mass, charges and size, both in bosonic and superstring theory (IIA or IIB). We properly define these quantities in full-fledged string theory. We then investigate the corrections to the entropy due to self-interactions of the string for states with fixed mass, charge and size, both for BPS and non-BPS configurations. Again, the analysis is performed using string theory techniques.
For extremal black holes, the thermodynamic entropy is not proportional to the area. The general form allowed by thermodynamics is worked out for three classes of extremal black hole solutions of string theory and shown to be consistent with the entropy calculated from the density of elementary string states. On the other hand, the entanglement entropy does not in general agree with these results.
According to Susskind, a string falling toward a black hole spreads exponentially over the stretched horizon due to repulsive interactions of the string bits. In this paper such a string is modeled as a self-avoiding walk and the string entropy is found. It is shown that the rate at which information/entropy contained in the string spreads is the maximum rate allowed by quantum theory. The maximum rate at which the black hole entropy can increase when a string falls into a black hole is also discussed.
We study the entanglement entropy for open bosonic strings on multiple $Dp$-branes by using the covariant open string field theory. Choosing one of the spatial coordinates which are tangential to the hyperplane on which $Dp$-branes are located, we divide the hyperplane into two halves. By using the string wavefunction in the Fock space representation, we evaluate the entanglement entropy. The entanglement entropy is found to be proportional to the area of $(p-1)$-dimensional boundary of the bipartite hyperplanes and divergent in the ultraviolet (UV) region as well as in the infrared (IR) regio…
We compute the entropy of extremal black strings in three dimensions, using Strominger's approach to relate the Anti-de-Sitter near-horizon geometry and the conformal field theory at the asymptotic infinity of this geometry. The result is identical to the geometric Bekenstein-Hawking entropy. We further discuss an embedding of three-dimensional black strings in $N=1 D=10$ supergravity and demonstrate that the extremal strings preserve 1/4 of supersymmetries.
It is observed that the three-dimensional BTZ black hole is a supersymmetric solution of the low-energy field equations of heterotic string theory compactified on an Einstein space. The solution involves a non-zero dilaton and NS-NS H-field. The entropy of the extreme black hole can then be computed using string theory and the asymptotic properties of anti-de Sitter space, without recourse to a D-brane analysis. This provides an explicit example of a black hole whose entropy can be computed using fundamental string theory, as advocated by Susskind.
The coupling of a string to gravity allows for Schwarzschild black holes whose entropy to area relation is $S=(A/4)(1-4μ)$, where $μ$ is the string tension. This departure from the A/4 universality results from a string instanton generating a black hole with smaller entropy at a temperature exceeding the Hawking value. The temperature is sensitive to the presence of classical matter outside the black hole horizon but the entropy is not. The horizon materializes at the quantum level. It is conjectured that such a macroscopic non local effect may be operative in retrieving information from incip…
We study the entropy of the Gibbons-Maeda-Garfinkle-Horowitz-Strominger (GMGHS) charged black hole, originated from the effective action that emerges in the low-energy of string theory, beyond semiclassical approximations. Applying the properties of exact differentials for three variables to the first law thermodynamics we derive the quantum corrections to the entropy of the black hole. The leading (logarithmic) and non leading corrections to the area law are obtained.
The one-loop contribution to the entropy of a black hole from field modes near the horizon is computed in string theory. It is modular invariant and ultraviolet finite. There is an infrared divergence that signifies an instability near the event horizon of the black hole. It is due to the exponential growth of the density of states and the associated Hagedorn transition characteristic of string theory. It is argued that this divergence is indicative of a tree level contribution, and the Bekenstein-Hawking-Gibbons formula for the entropy should be understood in terms of string states stuck near…
Using adiabatic invariance and the Bohr-Sommerfeld quantization rule we investigate the entropy spectroscopy of a charged black hole of heterotic string theory. It is shown that the entropy spectrum is equally spaced identically to the Schwarzschild, Reissner-Nordström and Kerr black holes. Since the adiabatic invariance method does not use quasinormal mode analysis, there is no need to impose the small charge limit and no confusion on whether the real part or imaginary part is responsible for the entropy spectrum.
We discuss further our proposed modification of the Susskind-Horowitz-Polchinski scenario in which black hole entropy goes over to string entropy as one scales the string length scale up and the string coupling constant down, keeping Newton's constant unchanged. In our approach, based on our 'matter-gravity entanglement hypothesis', 'string entropy' here should be interpreted as the likely entanglement entropy between (approximately) the single long string and the stringy atmosphere which, as we argue, arise in a pure multistring state of given energy in a (rescaled) box. In a previous simple …
Exploiting a recently constructed target space action for the exact string black hole, logarithmic corrections to the leading order entropy are studied. There are contributions from thermal fluctuations and from corrections due to alpha'>0 which for the microcanonical entropy appear with different signs and therefore may cancel each other, depending on the overall factor in front of the action. For the canonical entropy no such cancellation occurs. Remarks are made regarding the applicability of the approach and concerning the microstates. As a byproduct a formula for logarithmic entropy corre…
I review some recent work in which the quantum states of string theory which are associated with certain black holes have been identified and counted. For large black holes, the number of states turns out to be precisely the exponential of the Bekenstein-Hawking entropy. This provides a statistical origin for black hole thermodynamics in the context of a potential quantum theory of gravity.
Popular approaches to quantum gravity describe black hole microstates differently and apply different statistics to count them. Since the relationship between the approaches is not clear, this obscures the role of statistics in calculating the black hole entropy. We address this issue by discussing the entropy of eternal AdS black holes in dimension four and above within the context of a midisuperspace model. We determine the black hole eigenstates and find that they describe the quantization in half integer units of a certain function of the Arnowitt-Deser-Misner (ADM) mass and the cosmologic…
We show that the entropy resulting from the counting of microstates of non extremal black holes using field theory duals of string theories can be interpreted as arising from entanglement. The conditions for making such an interpretation consistent are discussed. First, we interpret the entropy (and thermodynamics) of spacetimes with non degenerate, bifurcating Killing horizons as arising from entanglement. We use a path integral method to define the Hartle-Hawking vacuum state in such spacetimes and discuss explicitly its entangled nature and its relation to the geometry. If string theory on …
We discuss whether black hole entropy counts short or long range microstates in quantum gravity. In brick wall and induced gravity models the entropy arises due to short distance correlations across the event horizon cut off at the Planck length. However, the energy of these short range degrees of freedom is too high compared to the black hole energy. We argue that the long string phenomenon, which naturally appears in matrix quantum mechanics, resolves this issue by lowering the excitation energy per degree of freedom. This mechanism also reduces the total number of microscopic degrees of fre…
The quantum corrections to the counting of statistical entropy for the 5+1-dimensional extremal black string in type-IIB supergravity with two observers are studied using anomalous Wess-Zumino actions for the corresponding intersecting D-brane description. The electric-magnetic duality symmetry of the anomalous theory implies a new symmetry between D-string and D-fivebrane sources and renders opposite sign for the RR charge of one of the intersecting D-branes relative to that of the black string. The electric-magnetic symmetric Hilbert space decomposes into subspaces associated with interior a…
We formulate the Rindler space description of rotating black holes in string theories. We argue that the comoving frame is the natural frame for studying thermodynamics of rotating black holes and statistical analysis of rotating black holes gets simplified in this frame. We also calculate statistical entropies of general class of rotating black holes in heterotic strings on tori by applying D-brane description and the correspondence principle. We find at least qualitative agreement between the Bekenstein-Hawking entropies and the statistical entropies of these black hole solutions.
We study the conjectured connection between AdS bubbles (AdS solitons) and closed string tachyon condensations. We confirm that the entanglement entropy, which measures the degree of freedom, decreases under the tachyon condensation. The entropies in supergravity and free Yang-Mills agree with each other remarkably. Next we consider the tachyon condensation on the AdS twisted circle and argue that its endpoint is given by the twisted AdS bubble, defined by the double Wick rotation of rotating black 3-brane solutions. We calculated the Casimir energy and entropy and checked the agreements betwe…
During the last few years, exact solutions that describe black holes that are bound to a two-brane in a four dimensional anti-de Sitter bulk have been constructed. In situations wherein there is a negative cosmological constant on the brane, for large masses, these solutions are exactly the rotating BTZ black holes on the brane and, in fact, describe rotating BTZ black strings in the bulk. We evaluate the canonical entropy of a free and massless scalar field (at the Hawking temperature) around the rotating BTZ black string using the brick wall model. We explicitly show that the Bekenstein-Hawk…
In this paper, we will compute the holographic complexity (dual to a volume in AdS), holographic fidelity susceptibility and the holographic entanglement entropy (dual to an area in AdS) in a two-dimensional version of $AdS$ which is dual to open strings. We will explicitly demonstrate that these quantities are well defined, and then argue that a relation for fidelity susceptibility and time should hold in general due to the $AdS_2$ version of the classical Kepler's principle. We will demonstrate that it holds for $AdS_2$ solution as well as conformal copies metrics in bulk theory of a prescri…
