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arXiv:2512.21327

Aspects of holographic timelike entanglement entropy in black hole backgrounds

Mir Afrasiar, Jaydeep Kumar Basak, Keun-Young Kim

Published Dec 24, 2025• 0 citations
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Abstract

We study the holographic construction of timelike entanglement entropy (tEE) in black hole backgrounds in Lorentzian geometries. The holographic tEE is realized through extremal surfaces consisting of spacelike and timelike branches that encode its real and imaginary components, respectively. In the BTZ black hole, these surfaces extend into the interior of the black hole and reproduce the field-theoretic results. The analysis is further generalized to higher-dimensional AdS-Schwarzschild black holes, where the characteristics of tEE are obtained with increasing size of the boundary subsystem. Besides, we also show that the boundary subsystem length diverges at a dimension-dependent critical turning point. Notably, this critical point moves closer to the black hole horizon as the dimensionality of the bulk increases. For large subsystem lengths, the finite part of the tEE displays a characteristic volume-plus-area structure, with a real volume term and a complex coefficient of the area term approaching constant values at large dimensions. Besides, we also study the monotonicity of a new quantity, timelike entanglement density, which offers insights into a timelike area theorem in specific limits. Subsequently, we investigate the near-horizon dynamics in various black hole backgrounds, where the spacelike and timelike surfaces exhibit exponential growth of the form $e^{\frac{2π}β Δt}$ with inverse black hole temperature $β$.

DOI
10.48550/arxiv.2512.21327

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We study the holographic construction of timelike entanglement entropy (tEE) in black hole backgrounds in Lorentzian geometries. The holographic tEE is realized through extremal surfaces consisting of spacelike and timelike branches that encode its real and imaginary components, respectively. In the BTZ black hole, these surfaces extend into the interior of the black hole and reproduce the field-theoretic results. The analysis is further generalized to higher-dimensional AdS-Schwarzschild black holes, where the characteristics of tEE are obtained with increasing size of the boundary subsystem. Besides, we also show that the boundary subsystem length diverges at a dimension-dependent critical turning point. Notably, this critical point moves closer to the black hole horizon as the dimensionality of the bulk increases. For large subsystem lengths, the finite part of the tEE displays a characteristic volume-plus-area structure, with a real volume term and a complex coefficient of the area term approaching constant values at large dimensions. Besides, we also study the monotonicity of a new quantity, timelike entanglement density, which offers insights into a timelike area theorem in specific limits. Subsequently, we investigate the near-horizon dynamics in various black hole backgrounds, where the spacelike and timelike surfaces exhibit exponential growth of the form e2πβΔte^{\frac{2π}β Δt}eβ2π​Δt with inverse black hole temperature βββ.
We study timelike entanglement entropy and timelike subregion complexity in localized black holes with asymptotic AdS3*S3*T4 geometry, focusing on the black-pole solution. Unlike the BTZ solution, the black pole exhibits a nontrivial dependence on the internal sphere through the functions Ky(r,θ)K_y(r,θ)Ky​(r,θ) and G(r,θ)G(r,θ)G(r,θ). Both observables are constructed from spacelike and timelike Lorentzian branches, but they probe the geometry in different ways: timelike entanglement yields a complex lifted area, while timelike complexity gives a real, finite renormalized volume. We employ a localized timelike prescription in which the branch profile is built at an angular label θ0θ_0θ0​ and subsequently lifted over the physical internal angle θθθ. In the large-rrr regime, the leading angular dependence drops out, recovering the expected short-interval behaviour. In the exact black-pole geometry, the temporal families become non-monotonic, making a fixed-boundary-interval selection essential. As the boundary interval increases, the selected branches move inward and become sensitive to the localized cap-horizon transition region. These results demonstrate that timelike Lorentzian observables probe localized-geometry effects that are absent in BTZ and in the leading large-rrr description.
A bstract We consider holographic entanglement entropy in AdS black hole backgrounds by using the limit of large number of dimensions. By dividing the geometry to two patches (with one patch covering the vicinity of the black hole horizon and another covering the other regions), we are able to obtain fully analytic expressions for the entropy when the entanglement region is a strip. We argue that apart from conformal field theories at finite temperature in high number of dimensions, our method works for nearly critical theories in 3+1 dimensions. In the case of extremal black holes, dual to quantum critical systems, the results take a particularly simple form. We also comment on the case of soliton geometries. Finally, we analyze entanglement entropy for wide strips, and propose a general formula for the first subleading term in the expansion of the entropy in (inverse) system size for generic entanglement regions.
A bstract We study the timelike entanglement entropy (TEE) in two dimensional conformal field theories (CFT) with gravitational anomalies. We employ analytical continuation to compute the timelike entanglement entropy for a pure timelike interval in such CFTs. We find that, unlike the real part, the imaginary part of the TEE displays an asymmetric dependence on the central charges of the left and right moving modes. We propose that the asymmetric dependence on central charges of the imaginary part of the TEE can be used to probe the presence of gravitational anomalies in chiral CFT. Furthermore, we propose a holographic construction to obtain the timelike entanglement entropy from the bulk dual geometries involving topologically massive gravity in AdS 3 . The holographic results obtained match exactly with the dual field theory results.
A bstract Timelike entanglement entropy is a complex measure of information that is holographically realized by an appropriate combination of spacelike and timelike extremal surfaces. This measure is highly sensitive to Lorentz invariance breaking. In this work, we study the timelike entanglement entropy in non-relativistic theories, focusing on theories with hyperscaling violation and Lifshitz-like spatial anisotropy. The properties of the extremal surfaces, as well as the timelike entanglement entropy itself, depend heavily on the symmetry-breaking parameters of the theory. Consequently, we show that timelike entanglement can encode, to a large extent, the stability and naturalness of the theory. Furthermore, we find that timelike entanglement entropy identifies Fermi surfaces either through the logarithmic behavior of its real part or, alternatively, via its constant imaginary part, with this constant value depending on the theory’s Lifshitz exponent. This provides a novel interpretation for the imaginary component of this pseudoentropy. Additionally, we examine temporal entanglement entropy, an extension of timelike entanglement entropy to Euclidean space, and provide a comprehensive discussion of its properties in these theories.
Abstract We define a generalized entanglement measure in the context of the AdS/CFT correspondence. Compared to the ordinary entanglement entropy for a spatial subregion dual to the area of the Ryu-Takayanagi surface, we take into account both entanglement between spatial degrees of freedom as well as between different fields of the boundary theory. Moreover, we resolve the contribution to the entanglement entropy of strings with different winding numbers in the bulk geometry. We then calculate this generalized entanglement measure in a thermal state dual to the BTZ black hole in the setting of the D1/D5 system at and close to the orbifold point. We find that the entanglement entropy defined in this way is dual to the length of a geodesic with non-zero winding number. Such geodesics probe the entire bulk geometry, including the entanglement shadow up to the horizon in the one-sided black hole as well as the wormhole growth in the case of a two-sided black hole for an arbitrarily long time. Therefore, we propose that the entanglement structure of the boundary state is enough to reconstruct asymptotically AdS3 geometries up to extremal surface barriers.
The relationship between Bekenstein-Hawking and entanglement entropy is one \nof the most intriguing problems of black hole and theoretical physics. Although both entropies have the same geometric characterization (they scale as an area), they have a different origin. The Bekenstein-Hawking entropy has it’s roots in the thermal correlations whereas the entanglement entropy describes the quantum correlations. In this thesis we address this problem from a holographic \nperspective, making large use of the AdS/CFT correspondence. \nWe first look at the BTZ black hole in which case the black hole horizon and \nthe conical singularity are related to each other. Using the modular transformations of the dual 2D CFT, we first obtain an expression of the holographicentanglement entropy for the Euclidean BTZ black hole, AdS3 vacua and conical singularity and then analyse the behaviour of the leading terms in the expansions of the holographic entanglement entropy for the BTZ black hole and the \nconical singularity. From these calculations, we have extracted the “signatures” through which entanglement entropy differentiates between the horizon and the conical singularity. When we deal with CFT at a finite temperature then it is well known that, entanglement entropy fails as a measure and hence it is replaced by entanglement negativity which is able to separate the thermal/classical \ncorrelations from the quantum correlations thereby capturing “distillable” entanglement. We address the problem of finding a suitable holographic prescription \nto calculate the entanglement negativity for two adjacent intervals when the CFT is at a finite temperature and in turn dual to a black hole in the bulk. We first propose a conjecture for the holographic entanglement negativity for two adjacent intervals in the \nAdS3/CFT2 setup and perform calculations in the \nvarious cases to support this conjecture. We further push forward the validity of this conjecture by calculating the holographic entanglement negativity for two \nadjacent subsystems when we have RN-AdS black holes in the bulk which in \nturn are dual to CFT with a conserved charge.