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Carroll hydrodynamics arises in the $c\to 0$ limit of relativistic hydrodynamics. Instances of its relevance include the Bjorken and Gubser flow models of heavy-ion collisions, where the ultrarelativistic nature of the flow makes the physics effectively Carrollian. In this paper, we explore the structure of hydrodynamics in what can be termed as the Carrollian regime, where instead of keeping only the leading terms in the $c\to 0$ limit of relativistic hydrodynamics, we perform a small-$c$ expansion and retain the subleading terms as well. We do so both for perfect fluids as well as viscous fluids incorporating first order derivative corrections. As apposite applications of the formalism, we utilize the subleading terms to compute modifications to the Bjorken and Gubser flow equations which bring in, in particular, dependence on rapidity., Comment: 31 pages, 1 figure

Rotational Freudenthal duality (RFD) relates two extremal Kerr-Newman (KN) black holes (BHs) with different angular momenta and electric-magnetic charges, but with the same Bekenstein-Hawking entropy. Through the Kerr/CFT correspondence (and its KN extension), a four-dimensional, asymptotically flat extremal KN BH is endowed with a dual thermal, two-dimensional conformal field theory (CFT) such that the Cardy entropy of the CFT is the same as the Bekenstein-Hawking entropy of the KN BH itself. Using this connection, we study the effect of the RFD on the thermal CFT dual to the KN extremal BH. We find that the RFD maps two different thermal, two-dimensional CFTs with different temperatures and central charges, but with the same asymptotic density of states, thereby matching the Cardy entropy. In an appendix, we discuss the action of the RFD on doubly-extremal rotating BHs, finding a spurious branch in the non-rotating limit, and determining that for this class of BH solutions the image of the RFD necessarily over-rotates., Comment: 13+11 pages, comments welcome

Freudenthal duality (FD) is a non-linear symmetry of the Bekenstein-Hawking entropy of extremal dyonic black holes (BHs) in Maxwell-Einstein-scalar theories in four space-time dimensions realized as an anti-involutive map in the symplectic space of electric-magnetic BH charges. In this paper, we generalize FD to the class of rotating (stationary) extremal BHs, both in the under- and over-rotating regime, defining a (generalized) rotating FD (generally, non-anti-involutive) map (RFD), which also acts on the BH angular momentum. We prove that the RFD map is unique, and we compute the explicit expression of its non-linear action on the angular momentum itself. Interestingly, in the non-rotating limit, RFD bifurcates into the usual, non-rotating FD branch and into a spurious branch, named "golden" branch, mapping a non-rotating (static) extremal BH to an under-rotating (stationary) extremal BH, in which the ratio between the angular momentum and the non-rotating entropy is the square root of the golden ratio. Finally, we investigate the possibility of inducing transitions between the under- and over-rotating regimes by means of RFD, obtaining a no-go result., Comment: 30 pages, 7 figures. Typos are corrected. A paragraph has been added in Sec. 2

Gubser flow provides an analytic model for describing the spacetime dynamics of the quark-gluon plasma produced in heavy-ion collisions. Along with boost and rotation invariance along the beam axis, the model assumes invariance under a combination of translations and special conformal transformations in the transverse plane, leading to a flow profile which evolves not just along the beam axis, but also radially. We argue that Gubser flow and its associated symmetry assumptions arise naturally as a consequence of Carrollian symmetries for a conformal Carroll fluid, thereby providing a dual geometric picture for the flow. Given the inherent ultrarelativistic nature of the flow, this duality with Carroll hydrodynamics - which arises in the $c \to 0$ limit of relativistic hydrodynamics, is natural. We provide a precise map between Gubser flow and the conformal Carroll fluid, appropriate to capture the duality between the two not just at the ideal level, but also with the inclusion of hydrodynamic derivative corrections., Comment: 11 pages, 1 figure, two-column format

We use holography to compute the exact form of retarded Green's functions for a scalar operator with conformal dimension $\Delta$ in a thermal CFT and in its related counterpart with chemical potential in $R^1 \times H^3$. In our analysis, we recast the wave equation of a scalar field in the normal form of Heun's equation in the dual gravity theories described by the AdS hyperbolic blackhole and its charged version. Heun's equation is identified to the semiclassical limit of the BPZ equation for a five-point correlator with one degenerate field insertion in the Liouville theory on the Riemann sphere. The crossing symmetry of conformal block in the Liouville theory eventually gives rise to a set of connection formulas among the solutions of Heun's equation evaluated at different regular singularities. We use the connection formula to reproduce the leading order behaviors of the scalar field near the horizon as well as near the boundary and achieve the exact form of the retarded thermal Green's function. We show a recipe to obtain the exact retarded Green's function for a thermal CFT dual to AdS blackbrane from a high-temperature limit accompanied by a complex mapping on AdS hyperbolic blackhole. Moreover, we show the retarded Green's function for the boundary CFT of Rindler AdS spacetime admits a free integer parameter., Comment: 17 pages, 7 tables

Understanding the loss landscape is an important problem in machine learning. One key feature of the loss function, common to many neural network architectures, is the presence of exponentially many low lying local minima. Physical systems with similar energy landscapes may provide useful insights. In this work, we point out that black holes naturally give rise to such landscapes, owing to the existence of black hole entropy. For definiteness, we consider 1/8 BPS black holes in $\mathcal{N} = 8$ string theory. These provide an infinite family of potential landscapes arising in the microscopic descriptions of corresponding black holes. The counting of minima amounts to black hole microstate counting. Moreover, the exact numbers of the minima for these landscapes are a priori known from dualities in string theory. Some of the minima are connected by paths of low loss values, resembling mode connectivity. We estimate the number of runs needed to find all the solutions. Initial explorations suggest that Stochastic Gradient Descent can find a significant fraction of the minima., Comment: 32 pages, 4 figures

Freudenthal duality is, as of now, the unique non-linear map on electric-magnetic (e.m.) charges which is a symmetry of the Bekenstein-Hawking entropy of extremal black holes in Maxwell-Einstein-scalar theories in four space-time dimensions. In this paper, we present a consistent generalization of Freudenthal duality to near-extremal black holes, whose entropy is obtained within a Jackiw-Teitelboim gravity upon dimensional reduction. We name such a generalization near-extremal Freudenthal duality. Upon such a duality, two near-extremal black holes with two different (and both small) temperatures have the same entropy when their e.m. charges are related by a Freudenthal transformation. By exploiting Descartes' rule of signs as well as Sturm's Theorem, we show that our formulation of the near-extremal Freudenthal duality is analytical and unique., Comment: 29 pages, 2 figures

We discuss two different approaches to synthesise holographic non-relativistic fluid from its relativistic counterpart. In the first approach we obtain the non-relativistic fluid by light-cone reduction of a relativistic conformal fluid. In the second approach we consider the bulk dual of the relativistic fluid, uplift the solution to 10 dimensions and perform TsT transformations on the bulk solution to change the asymptotic structure. Reducing the TsT transformed geometry over $S^5$ we find an effective 5 dimensional locally boosted solution. We then use the bulk-boundary dictionary to compute the non-relativistic constitutive relations. We show that the non-relativistic fluids obtained by these two methods are equivalent up to second order in derivative expansion. Our results also provide explicit expressions for different constitutive relations and transports of holographic $U(1)$ charged non-relativistic fluids (both parity odd and even) up to second order in derivative expansion., Comment: 40 pages, 1 figure, 13 tables

We compute the exact retarded Green's functions in thermal $CFT$s with chemical potential and angular momenta using holography respectively. We consider the field equations satisfied by the quasi-normal modes in both charged and rotating black holes in $AdS$ spacetime and mapped them to the Heun equations by appropriate changes of variables. The AGT correspondence allows us to find the connection formulae among the solutions of the Heun equations near different singularities by using the crossing relations of the five-point correlators in the Liouville $CFT$. The connection formulae associated with the boundary conditions imposed on the bulk field equations yield the exact thermal correlators in the boundary $CFT$., Comment: 15+1 pages, minor changes and clarifications, references added, matches version to be published in JHEP

Quantum complexity of CFT states can be computed holographically from the dual gravitational solutions. In this paper, we have studied the late time growth of holographic complexity of a charged black hole in five-dimensional, Anti-de Sitter spacetime in the presence of quartic derivative interaction terms using the Complexity = Action conjecture. These interaction terms in the gravitational action can lead to the violation of Llyod's bound. The dual CFT is known to admit a hydrodynamic description where the KSS bound is also violated due to the presence of higher derivative terms in the bulk action. The origin of terms which violate both the bounds are the same for the gravitational action of consideration. We have also discussed the late time complexity growth rate of the Jackiw-Teitelboim (JT) model with higher derivative corrections., Comment: 29 Pages, 2 Figures

Freudenthal duality (F-duality), an anti-involution of charge vectors keep the entropy and attractor solutions invariant for an extremal supersymmetric black hole. In this paper, we analyze the effect of F-duality on the entropy of a near-extremal $STU$ black hole in $\mathcal{N}=2$ ungauged, four-dimensional supergravity. We consider double-extremal black holes, whose attractor solutions are fixed in terms of the black hole charges throughout the moduli space. It is well known that JT gravity governs the dynamics of the near-horizon regions of higher dimensional, near-extremal black holes. Owing to this fact, we reduce the four-dimensional supergravity theory to two dimensions to construct a Jackiw-Teitelboim (JT) gravity like model and compute the near-extremal entropy. We then analyze the effect of F-duality on this entropy. We show that the F-duality breaks down for the case of near-extremal solutions if one considers the duality operation generated through near-extremal entropy rather than the extremal one., Comment: 20 pages; V2: Typos corrected, added some comments and references

Two derivative Jackiw Teitelboim gravity theory captures the near horizon dynamics of higher dimensional near extremal black holes, which is governed by a Schwarzian action at the boundary in the near horizon region. The partition function corresponding to this boundary action correctly gives the statistical entropy of the near extremal black hole. In this paper, we study the thermodynamics of spherically symmetric four dimensional near extremal black holes in presence of arbitrary perturbative four derivative corrections. We find that the near horizon dynamics is again captured by a JT like action with a particular namely square of Ricci scalar higher derivative modification. Effectively the theory is described by a boundary Schwarzian action which gets suitably modified due to the presence of the higher derivative interactions. Near extremal entropy, free energy also get corrected accordingly., Comment: 40 pages

We construct dynamical black hole solutions to Einstein Equations in presence of matter in the large $D$ limit. The matter stress tensors that we consider are weak in the sense that they source asymptotic spacetimes with internal curvatures of the order of $\mathcal{O}(D^0)$. Apart from this, we work with a generic stress tensor demanding only that the stress tensor satisfies the conservation equations. The black hole solutions are obtained in terms of the dual non-gravitational picture of membranes propagating in spacetimes equivalent to the asymptotes of the black holes. We obtain the metric solutions to the second sub-leading order in $1/D$. We also obtain the equations governing the dual membranes up to the first sub-leading order in $1/D$., Comment: 36 pages, 2 tables

The Rivlin-Ericksen model is one of the oldest models in fluid dynamics to describe non-Newtonian properties. The model comes with two independent transports at second order. In this paper, we study the relativistic origin of the Rivlin-Ericksen fluid. Starting from a relativistic Weyl invariant uncharged fluid in $3+1$ dimensions, we reduce it over light-cone directions and obtain a generic non-relativistic uncharged fluid in one lower dimension with all possible second order terms in the constitutive relations. We observe that the Rivlin-Ericksen fluid is a subclass of our generalised non-relativistic system. We also compute the holographic values of all the non-relativistic second order transports and find that three of them satisfy a universal constraint relation., Comment: 18 pages

We find the membrane equations which describe the leading order in $1/D$ dynamics of black holes in the $D\rightarrow\infty$ limit for the most general four-derivative theory of gravity in the presence of a cosmological constant. We work up to linear order in the parameter determining the strength of the four-derivative corrections to the gravity action and hence there are no ghost modes in the theory. We find that the effective membrane equations we obtain are the covariant version of the membrane equations in absence of the cosmological constant. We also find the world-volume stress tensor for the membrane whose conservation gives the membrane equations. We apply the membrane equations to predict the light quasi-normal mode spectrum of black holes and black branes in the theory of gravity under consideration., Comment: Typos corrected, acknowledgement added

We study the effect of Freudenthal duality on supersymmetric extremal black hole attractors in N = 2, D = 4 ungauged supergravity. Freudenthal duality acts on the dyonic black hole charges as an anti-involution which keeps the black hole entropy and the critical points of the effective black hole potential invariant. We analyze its effect on the recently discovered distinct, mutually exclusive phases of axionic supersymmetric black holes, related to the existence of non-trivial involutory constant matrices. In particular, we consider a supersymmetric D0-D4-D6 black hole and we explicitly Freudenthal-map it to a supersymmetric D0-D2-D4-D6 black hole. We thus show that the charge representation space of a supersymmetric D0-D2-D4-D6 black hole also contains mutually exclusive domains., Comment: 1+13 pages; v2 : two Refs. added, typo fixed

In this paper we consider the four dimensional N=2 supergravity theory arising from the compactification of type IIA string theory on a Calabi-Yau manifold. We analyse the supersymmetric flow equations for static, spherically symmetric, single-centered black holes. These flow equations are solved by a set of algebraic equations involving the holomorphic sections and harmonic functions. We examine black hole configurations with D0-D4-D6 charge for which the most general solution of these algebraic equations are considered. Though the black hole solution is unique for a given value of the charges, we find new phases of the black hole solutions upon varying them., Comment: References added, typos corrected, 10 pages

In this paper we discuss the uniqueness of supersymmetric attractors in four dimensional N=2 supergravity theories coupled to n vector multiplets. We prove that for a given charge configuration the supersymmetry preserving axion free attractors are unique. We generalise the analysis to axionic attractors and state the conditions for uniqueness explicitly. We consider the example of a two-parameter model and find all solutions to the supersymmetric attractor equations and discuss their uniqueness., Comment: 12 pages, Latex

In this paper we study spherically symmetric single-centered attractors in N=2 supergravity in four dimensions. The attractor points are obtained by extremising the effective black hole potential in the moduli space. Using the 4D-5D correspondence of critical points of the effective black hole potential we argue the existence of multiple attractors in four dimensions and explicitly construct a pair of multiple solutions in a simple two parameter model. We further obtain explicit examples of two distinct non-supersymmetric attractors in type IIA string theory compactified on K3 X T2 carrying D0-D4-D6 charges. We compute the entropy of these attractors and analyse their stability in detail., Comment: Modifications in Section 3. Some incorrect results are removed and the section is rewritten